Abstract group data - 432.624

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• gps_groups •

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

  
  {'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '36.8', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 6, 6, 6], 'aut_gens': [[1, 12, 72], [7, 12, 72], [1, 60, 96], [5, 12, 372], [1, 228, 156], [205, 12, 72], [73, 12, 72]], 'aut_group': '1728.47874', 'aut_hash': 47874, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1728, 'aut_permdeg': 30, 'aut_perms': [194834960537778476166252735780480, 12417660275220902782080, 7757658583731942439804305296785, 6749240097963066996167538392921, 8025249471876834573260250572975, 194261822833690826437648621667898], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 4, 6, 1], [3, 8, 6, 1], [4, 3, 2, 1], [4, 9, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 3, 2, 2], [6, 4, 6, 1], [6, 6, 1, 2], [6, 6, 2, 2], [6, 8, 6, 1], [12, 3, 4, 1], [12, 9, 4, 1], [12, 12, 12, 1]], 'aut_supersolvable': False, 'aut_tex': 'A_4:D_6^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '12.4', 'autcent_hash': 4, 'autcent_nilpotent': False, 'autcent_order': 12, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '144.183', 'autcentquo_hash': 183, 'autcentquo_nilpotent': False, 'autcentquo_order': 144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 1, 2], [3, 2, 3], [3, 4, 6], [3, 8, 6], [4, 3, 2], [4, 9, 2], [6, 1, 2], [6, 2, 3], [6, 3, 4], [6, 4, 6], [6, 6, 6], [6, 8, 6], [12, 3, 4], [12, 9, 4], [12, 12, 12]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '72.44', 'commutator_count': 1, 'commutator_label': '12.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 624, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.1', 1], ['12.3', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 4, 2, 3], [3, 8, 2, 3], [4, 3, 2, 1], [4, 9, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 3, 2, 2], [6, 4, 2, 3], [6, 6, 1, 2], [6, 6, 2, 2], [6, 8, 2, 3], [12, 3, 4, 1], [12, 9, 4, 1], [12, 12, 4, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 12, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '216.166', 'hash': 624, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [6, 6, 6], 'inner_gens': [[1, 276, 348], [241, 12, 72], [229, 12, 72]], 'inner_hash': 44, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': True, 'inner_tex': 'S_3\\times A_4', 'inner_used': [1, 2], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 36], [2, 18], [3, 12], [6, 6]], 'label': '432.624', 'linC_count': 144, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 18, 'linQ_dim': 7, 'linQ_dim_count': 6, 'linR_count': 18, 'linR_degree': 7, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6^2:C12', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 25, 'number_characteristic_subgroups': 25, 'number_conjugacy_classes': 72, 'number_divisions': 35, 'number_normal_subgroups': 40, 'number_subgroup_autclasses': 96, 'number_subgroup_classes': 136, 'number_subgroups': 484, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 7], [3, 80], [4, 24], [6, 128], [12, 192]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[7, 12, 72], [5, 12, 108], [341, 12, 372]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [7, 120, 856], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [4, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 11], [3, 2], [4, 12], [6, 5], [12, 3]], 'representations': {'PC': {'code': 47059216305362613643315984858721558173077, 'gens': [1, 4, 6], 'pres': [7, 2, 2, 3, 2, 3, 2, 3, 14, 36, 7731, 3706, 1613, 80, 1684, 14621, 2280, 3421, 124, 9414]}, 'GLZN': {'d': 2, 'p': 28, 'gens': [548825, 214622, 21977, 285389, 33321, 158599, 340271]}, 'Perm': {'d': 14, 'gens': [6745939320, 4, 403200, 13412044800, 7, 16, 840]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 12], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2:C_{12}', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 110221426
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 624, 'group_order': 432, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 110221437
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 624, 'group_order': 432, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 6, 'size': 1}
  • id: 110221448
    {'aut_label': '2B', 'centralizer': '3.a1.a1', 'counter': 3, 'group_counter': 624, 'group_order': 432, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 252, 'size': 3}
  • id: 110221459
    {'aut_label': '2C', 'centralizer': '3.a1.a1', 'counter': 4, 'group_counter': 624, 'group_order': 432, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 258, 'size': 3}
  • id: 110221470
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 624, 'group_order': 432, 'label': '3A1', 'order': 3, 'powers': [6, 1], 'representative': 168, 'size': 1}
  • id: 110221481
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 624, 'group_order': 432, 'label': '3A-1', 'order': 3, 'powers': [5, 1], 'representative': 336, 'size': 1}
  • id: 110221492
    {'aut_label': '3B', 'centralizer': '2.a1.a1', 'counter': 7, 'group_counter': 624, 'group_order': 432, 'label': '3B', 'order': 3, 'powers': [7, 1], 'representative': 48, 'size': 2}
  • id: 110221496
    {'aut_label': '3C1', 'centralizer': '2.a1.a1', 'counter': 8, 'group_counter': 624, 'group_order': 432, 'label': '3C1', 'order': 3, 'powers': [9, 1], 'representative': 288, 'size': 2}
  • id: 110221497
    {'aut_label': '3C1', 'centralizer': '2.a1.a1', 'counter': 9, 'group_counter': 624, 'group_order': 432, 'label': '3C-1', 'order': 3, 'powers': [8, 1], 'representative': 144, 'size': 2}
  • id: 110221427
    {'aut_label': '3D1', 'centralizer': '4.b1.a1', 'counter': 10, 'group_counter': 624, 'group_order': 432, 'label': '3D1', 'order': 3, 'powers': [11, 1], 'representative': 4, 'size': 4}
  • id: 110221428
    {'aut_label': '3D1', 'centralizer': '4.b1.a1', 'counter': 11, 'group_counter': 624, 'group_order': 432, 'label': '3D-1', 'order': 3, 'powers': [10, 1], 'representative': 8, 'size': 4}
  • id: 110221429
    {'aut_label': '3D1', 'centralizer': '4.b1.a1', 'counter': 12, 'group_counter': 624, 'group_order': 432, 'label': '3E1', 'order': 3, 'powers': [13, 1], 'representative': 172, 'size': 4}
  • id: 110221430
    {'aut_label': '3D1', 'centralizer': '4.b1.a1', 'counter': 13, 'group_counter': 624, 'group_order': 432, 'label': '3E-1', 'order': 3, 'powers': [12, 1], 'representative': 344, 'size': 4}
  • id: 110221431
    {'aut_label': '3D1', 'centralizer': '4.b1.a1', 'counter': 14, 'group_counter': 624, 'group_order': 432, 'label': '3F1', 'order': 3, 'powers': [15, 1], 'representative': 124, 'size': 4}
  • id: 110221432
    {'aut_label': '3D1', 'centralizer': '4.b1.a1', 'counter': 15, 'group_counter': 624, 'group_order': 432, 'label': '3F-1', 'order': 3, 'powers': [14, 1], 'representative': 428, 'size': 4}
  • id: 110221433
    {'aut_label': '3G1', 'centralizer': '8.a1.a1', 'counter': 16, 'group_counter': 624, 'group_order': 432, 'label': '3G1', 'order': 3, 'powers': [17, 1], 'representative': 292, 'size': 8}
  • id: 110221434
    {'aut_label': '3G1', 'centralizer': '8.a1.a1', 'counter': 17, 'group_counter': 624, 'group_order': 432, 'label': '3G-1', 'order': 3, 'powers': [16, 1], 'representative': 152, 'size': 8}
  • id: 110221435
    {'aut_label': '3G1', 'centralizer': '8.a1.a1', 'counter': 18, 'group_counter': 624, 'group_order': 432, 'label': '3H1', 'order': 3, 'powers': [19, 1], 'representative': 184, 'size': 8}
  • id: 110221436
    {'aut_label': '3G1', 'centralizer': '8.a1.a1', 'counter': 19, 'group_counter': 624, 'group_order': 432, 'label': '3H-1', 'order': 3, 'powers': [18, 1], 'representative': 80, 'size': 8}
  • id: 110221438
    {'aut_label': '3G1', 'centralizer': '8.a1.a1', 'counter': 20, 'group_counter': 624, 'group_order': 432, 'label': '3I1', 'order': 3, 'powers': [21, 1], 'representative': 52, 'size': 8}
  • id: 110221439
    {'aut_label': '3G1', 'centralizer': '8.a1.a1', 'counter': 21, 'group_counter': 624, 'group_order': 432, 'label': '3I-1', 'order': 3, 'powers': [20, 1], 'representative': 32, 'size': 8}
  • id: 110221440
    {'aut_label': '4A1', 'centralizer': '3.c1.a1', 'counter': 22, 'group_counter': 624, 'group_order': 432, 'label': '4A1', 'order': 4, 'powers': [2, 23], 'representative': 57, 'size': 3}
  • id: 110221441
    {'aut_label': '4A1', 'centralizer': '3.c1.a1', 'counter': 23, 'group_counter': 624, 'group_order': 432, 'label': '4A-1', 'order': 4, 'powers': [2, 22], 'representative': 51, 'size': 3}
  • id: 110221442
    {'aut_label': '4B1', 'centralizer': '9.b1.a1', 'counter': 24, 'group_counter': 624, 'group_order': 432, 'label': '4B1', 'order': 4, 'powers': [2, 25], 'representative': 249, 'size': 9}
  • id: 110221443
    {'aut_label': '4B1', 'centralizer': '9.b1.a1', 'counter': 25, 'group_counter': 624, 'group_order': 432, 'label': '4B-1', 'order': 4, 'powers': [2, 24], 'representative': 243, 'size': 9}
  • id: 110221444
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 26, 'group_counter': 624, 'group_order': 432, 'label': '6A1', 'order': 6, 'powers': [5, 2], 'representative': 342, 'size': 1}
  • id: 110221445
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 27, 'group_counter': 624, 'group_order': 432, 'label': '6A-1', 'order': 6, 'powers': [6, 2], 'representative': 174, 'size': 1}
  • id: 110221446
    {'aut_label': '6B', 'centralizer': '2.a1.a1', 'counter': 28, 'group_counter': 624, 'group_order': 432, 'label': '6B', 'order': 6, 'powers': [7, 2], 'representative': 30, 'size': 2}
  • id: 110221447
    {'aut_label': '6C1', 'centralizer': '2.a1.a1', 'counter': 29, 'group_counter': 624, 'group_order': 432, 'label': '6C1', 'order': 6, 'powers': [8, 2], 'representative': 150, 'size': 2}
  • id: 110221449
    {'aut_label': '6C1', 'centralizer': '2.a1.a1', 'counter': 30, 'group_counter': 624, 'group_order': 432, 'label': '6C-1', 'order': 6, 'powers': [9, 2], 'representative': 294, 'size': 2}
  • id: 110221450
    {'aut_label': '6D1', 'centralizer': '3.a1.a1', 'counter': 31, 'group_counter': 624, 'group_order': 432, 'label': '6D1', 'order': 6, 'powers': [5, 3], 'representative': 84, 'size': 3}
  • id: 110221451
    {'aut_label': '6D1', 'centralizer': '3.a1.a1', 'counter': 32, 'group_counter': 624, 'group_order': 432, 'label': '6D-1', 'order': 6, 'powers': [6, 3], 'representative': 384, 'size': 3}
  • id: 110221452
    {'aut_label': '6E1', 'centralizer': '3.a1.a1', 'counter': 33, 'group_counter': 624, 'group_order': 432, 'label': '6E1', 'order': 6, 'powers': [5, 4], 'representative': 90, 'size': 3}
  • id: 110221453
    {'aut_label': '6E1', 'centralizer': '3.a1.a1', 'counter': 34, 'group_counter': 624, 'group_order': 432, 'label': '6E-1', 'order': 6, 'powers': [6, 4], 'representative': 390, 'size': 3}
  • id: 110221454
    {'aut_label': '6F1', 'centralizer': '4.b1.a1', 'counter': 35, 'group_counter': 624, 'group_order': 432, 'label': '6F1', 'order': 6, 'powers': [10, 2], 'representative': 2, 'size': 4}
  • id: 110221455
    {'aut_label': '6F1', 'centralizer': '4.b1.a1', 'counter': 36, 'group_counter': 624, 'group_order': 432, 'label': '6F-1', 'order': 6, 'powers': [11, 2], 'representative': 10, 'size': 4}
  • id: 110221456
    {'aut_label': '6F1', 'centralizer': '4.b1.a1', 'counter': 37, 'group_counter': 624, 'group_order': 432, 'label': '6G1', 'order': 6, 'powers': [12, 2], 'representative': 338, 'size': 4}
  • id: 110221457
    {'aut_label': '6F1', 'centralizer': '4.b1.a1', 'counter': 38, 'group_counter': 624, 'group_order': 432, 'label': '6G-1', 'order': 6, 'powers': [13, 2], 'representative': 178, 'size': 4}
  • id: 110221458
    {'aut_label': '6F1', 'centralizer': '4.b1.a1', 'counter': 39, 'group_counter': 624, 'group_order': 432, 'label': '6H1', 'order': 6, 'powers': [14, 2], 'representative': 422, 'size': 4}
  • id: 110221460
    {'aut_label': '6F1', 'centralizer': '4.b1.a1', 'counter': 40, 'group_counter': 624, 'group_order': 432, 'label': '6H-1', 'order': 6, 'powers': [15, 2], 'representative': 130, 'size': 4}
  • id: 110221461
    {'aut_label': '6I', 'centralizer': '6.a1.a1', 'counter': 41, 'group_counter': 624, 'group_order': 432, 'label': '6I', 'order': 6, 'powers': [7, 3], 'representative': 12, 'size': 6}
  • id: 110221462
    {'aut_label': '6J', 'centralizer': '6.a1.a1', 'counter': 42, 'group_counter': 624, 'group_order': 432, 'label': '6J', 'order': 6, 'powers': [7, 4], 'representative': 18, 'size': 6}
  • id: 110221463
    {'aut_label': '6K1', 'centralizer': '6.a1.a1', 'counter': 43, 'group_counter': 624, 'group_order': 432, 'label': '6K1', 'order': 6, 'powers': [9, 3], 'representative': 72, 'size': 6}
  • id: 110221464
    {'aut_label': '6K1', 'centralizer': '6.a1.a1', 'counter': 44, 'group_counter': 624, 'group_order': 432, 'label': '6K-1', 'order': 6, 'powers': [8, 3], 'representative': 156, 'size': 6}
  • id: 110221465
    {'aut_label': '6L1', 'centralizer': '6.a1.a1', 'counter': 45, 'group_counter': 624, 'group_order': 432, 'label': '6L1', 'order': 6, 'powers': [9, 4], 'representative': 78, 'size': 6}
  • id: 110221466
    {'aut_label': '6L1', 'centralizer': '6.a1.a1', 'counter': 46, 'group_counter': 624, 'group_order': 432, 'label': '6L-1', 'order': 6, 'powers': [8, 4], 'representative': 162, 'size': 6}
  • id: 110221467
    {'aut_label': '6M1', 'centralizer': '8.a1.a1', 'counter': 47, 'group_counter': 624, 'group_order': 432, 'label': '6M1', 'order': 6, 'powers': [16, 2], 'representative': 146, 'size': 8}
  • id: 110221468
    {'aut_label': '6M1', 'centralizer': '8.a1.a1', 'counter': 48, 'group_counter': 624, 'group_order': 432, 'label': '6M-1', 'order': 6, 'powers': [17, 2], 'representative': 82, 'size': 8}
  • id: 110221469
    {'aut_label': '6M1', 'centralizer': '8.a1.a1', 'counter': 49, 'group_counter': 624, 'group_order': 432, 'label': '6N1', 'order': 6, 'powers': [18, 2], 'representative': 74, 'size': 8}
  • id: 110221471
    {'aut_label': '6M1', 'centralizer': '8.a1.a1', 'counter': 50, 'group_counter': 624, 'group_order': 432, 'label': '6N-1', 'order': 6, 'powers': [19, 2], 'representative': 154, 'size': 8}
  • id: 110221472
    {'aut_label': '6M1', 'centralizer': '8.a1.a1', 'counter': 51, 'group_counter': 624, 'group_order': 432, 'label': '6O1', 'order': 6, 'powers': [20, 2], 'representative': 26, 'size': 8}
  • id: 110221473
    {'aut_label': '6M1', 'centralizer': '8.a1.a1', 'counter': 52, 'group_counter': 624, 'group_order': 432, 'label': '6O-1', 'order': 6, 'powers': [21, 2], 'representative': 34, 'size': 8}
  • id: 110221474
    {'aut_label': '12A1', 'centralizer': '3.c1.a1', 'counter': 53, 'group_counter': 624, 'group_order': 432, 'label': '12A1', 'order': 12, 'powers': [26, 22], 'representative': 147, 'size': 3}
  • id: 110221475
    {'aut_label': '12A1', 'centralizer': '3.c1.a1', 'counter': 54, 'group_counter': 624, 'group_order': 432, 'label': '12A-1', 'order': 12, 'powers': [27, 23], 'representative': 297, 'size': 3}
  • id: 110221476
    {'aut_label': '12A1', 'centralizer': '3.c1.a1', 'counter': 55, 'group_counter': 624, 'group_order': 432, 'label': '12A5', 'order': 12, 'powers': [27, 22], 'representative': 291, 'size': 3}
  • id: 110221477
    {'aut_label': '12A1', 'centralizer': '3.c1.a1', 'counter': 56, 'group_counter': 624, 'group_order': 432, 'label': '12A-5', 'order': 12, 'powers': [26, 23], 'representative': 153, 'size': 3}
  • id: 110221478
    {'aut_label': '12B1', 'centralizer': '9.b1.a1', 'counter': 57, 'group_counter': 624, 'group_order': 432, 'label': '12B1', 'order': 12, 'powers': [27, 24], 'representative': 75, 'size': 9}
  • id: 110221479
    {'aut_label': '12B1', 'centralizer': '9.b1.a1', 'counter': 58, 'group_counter': 624, 'group_order': 432, 'label': '12B-1', 'order': 12, 'powers': [26, 25], 'representative': 165, 'size': 9}
  • id: 110221480
    {'aut_label': '12B1', 'centralizer': '9.b1.a1', 'counter': 59, 'group_counter': 624, 'group_order': 432, 'label': '12B5', 'order': 12, 'powers': [26, 24], 'representative': 159, 'size': 9}
  • id: 110221482
    {'aut_label': '12B1', 'centralizer': '9.b1.a1', 'counter': 60, 'group_counter': 624, 'group_order': 432, 'label': '12B-5', 'order': 12, 'powers': [27, 25], 'representative': 81, 'size': 9}
  • id: 110221483
    {'aut_label': '12C1', 'centralizer': '12.g1.a1', 'counter': 61, 'group_counter': 624, 'group_order': 432, 'label': '12C1', 'order': 12, 'powers': [35, 23], 'representative': 1, 'size': 12}
  • id: 110221484
    {'aut_label': '12C1', 'centralizer': '12.g1.a1', 'counter': 62, 'group_counter': 624, 'group_order': 432, 'label': '12C-1', 'order': 12, 'powers': [36, 22], 'representative': 11, 'size': 12}
  • id: 110221485
    {'aut_label': '12C1', 'centralizer': '12.g1.a1', 'counter': 63, 'group_counter': 624, 'group_order': 432, 'label': '12C5', 'order': 12, 'powers': [36, 23], 'representative': 5, 'size': 12}
  • id: 110221486
    {'aut_label': '12C1', 'centralizer': '12.g1.a1', 'counter': 64, 'group_counter': 624, 'group_order': 432, 'label': '12C-5', 'order': 12, 'powers': [35, 22], 'representative': 7, 'size': 12}
  • id: 110221487
    {'aut_label': '12C1', 'centralizer': '12.g1.a1', 'counter': 65, 'group_counter': 624, 'group_order': 432, 'label': '12D1', 'order': 12, 'powers': [37, 23], 'representative': 145, 'size': 12}
  • id: 110221488
    {'aut_label': '12C1', 'centralizer': '12.g1.a1', 'counter': 66, 'group_counter': 624, 'group_order': 432, 'label': '12D-1', 'order': 12, 'powers': [38, 22], 'representative': 83, 'size': 12}
  • id: 110221489
    {'aut_label': '12C1', 'centralizer': '12.g1.a1', 'counter': 67, 'group_counter': 624, 'group_order': 432, 'label': '12D5', 'order': 12, 'powers': [38, 23], 'representative': 77, 'size': 12}
  • id: 110221490
    {'aut_label': '12C1', 'centralizer': '12.g1.a1', 'counter': 68, 'group_counter': 624, 'group_order': 432, 'label': '12D-5', 'order': 12, 'powers': [37, 22], 'representative': 151, 'size': 12}
  • id: 110221491
    {'aut_label': '12C1', 'centralizer': '12.g1.a1', 'counter': 69, 'group_counter': 624, 'group_order': 432, 'label': '12E1', 'order': 12, 'powers': [39, 23], 'representative': 73, 'size': 12}
  • id: 110221493
    {'aut_label': '12C1', 'centralizer': '12.g1.a1', 'counter': 70, 'group_counter': 624, 'group_order': 432, 'label': '12E-1', 'order': 12, 'powers': [40, 22], 'representative': 155, 'size': 12}
  • id: 110221494
    {'aut_label': '12C1', 'centralizer': '12.g1.a1', 'counter': 71, 'group_counter': 624, 'group_order': 432, 'label': '12E5', 'order': 12, 'powers': [40, 23], 'representative': 149, 'size': 12}
  • id: 110221495
    {'aut_label': '12C1', 'centralizer': '12.g1.a1', 'counter': 72, 'group_counter': 624, 'group_order': 432, 'label': '12E-5', 'order': 12, 'powers': [39, 22], 'representative': 79, 'size': 12}
• gps_qchar •

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

  
  
  • id: 4556689
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4556700
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4556711
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, 2, -1, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1], 'schur_index': 1}
  • id: 4556718
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1d', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 4556719
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, 2], 'schur_index': 1}
  • id: 4556720
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1f', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4556721
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1g', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556722
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, 2, -1, -2, -2, -2, -2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, -2, -2, 1, 1, 1], 'schur_index': 1}
  • id: 4556723
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1i', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -2, -2, -2, -2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, 1, 1, -2, 1, 1, 1, -2, 1, 1], 'schur_index': 1}
  • id: 4556690
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -2, -2, -2, -2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, -2, 1, 1, 1, -2, -2], 'schur_index': 1}
  • id: 4556691
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1k', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4556696
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556697
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.2b', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, -2, -2, 1, 1, 1, -2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 4556707
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.3a', 'multiplicity': 1, 'nt': [4, 4], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -1, -1, 3, 3, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556708
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.3b', 'multiplicity': 1, 'nt': [6, 6], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 1, 1, 3, 3, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556692
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1l', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -2, -2, 4, -2, -2, -2, -2, 4, -2, -2, 4, -2, -2, -2, 4, 4, -2, 0, 0, 0, 0, 2, 2, -4, 2, 2, 2, -2, 2, -2, 2, -4, -4, 2, 2, 2, -2, -4, 2, -2, 2, 4, 2, 2, 2, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556693
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1m', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -2, -2, 4, -2, -2, -2, 4, -2, 4, -2, -2, 4, -2, -2, -2, -2, 4, 0, 0, 0, 0, 2, 2, -4, 2, 2, 2, -2, 2, -2, -4, 2, 2, 2, -4, 2, -2, -4, 2, -2, 2, 4, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556694
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1n', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -2, -2, 4, -2, -2, 4, -2, -2, -2, 4, -2, -2, 4, 4, -2, -2, -2, 0, 0, 0, 0, 2, 2, -4, 2, 2, 2, -2, 2, -2, 2, 2, 2, -4, 2, -4, -2, -4, 2, -2, 2, 4, 2, 2, -4, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556695
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.1o', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 4, -4, 4, 2, 2, 2, 2, 2, 2, 4, -4, -4, 4, -4, 4, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556698
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.2c', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -2, -2, -2, 1, 1, -2, -2, 4, -2, -2, 4, 1, 1, 1, -2, -2, 1, 0, 0, 0, 0, -2, -2, -2, 1, 1, -2, -2, -2, -2, -2, 4, 4, -2, -2, -2, 1, -2, 1, 1, 1, -2, 1, 1, 1, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556699
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.2d', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -2, -2, -2, 1, 1, -2, 4, -2, 4, -2, -2, -2, 1, 1, 1, 1, -2, 0, 0, 0, 0, -2, -2, -2, 1, 1, -2, -2, -2, -2, 4, -2, -2, -2, 4, -2, 1, -2, 1, 1, 1, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556701
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.2e', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -2, -2, -2, 1, 1, 4, -2, -2, -2, 4, -2, 1, -2, -2, 1, 1, 1, 0, 0, 0, 0, -2, -2, -2, 1, 1, -2, -2, -2, -2, -2, -2, -2, 4, -2, 4, 1, -2, 1, 1, 1, -2, 1, 1, -2, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556702
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.2f', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 4, 4, -2, -2, -2, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556703
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.2g', 'multiplicity': 2, 'nt': [12, 19], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -2, -2, -2, 1, 1, -2, -2, 4, -2, -2, 4, 1, 1, 1, -2, -2, 1, 0, 0, 0, 0, 2, 2, 2, -1, -1, 2, -2, 2, -2, 2, -4, -4, 2, 2, 2, 1, 2, -1, 1, -1, -2, -1, -1, -1, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556704
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.2h', 'multiplicity': 2, 'nt': [12, 19], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -2, -2, -2, 1, 1, -2, 4, -2, 4, -2, -2, -2, 1, 1, 1, 1, -2, 0, 0, 0, 0, 2, 2, 2, -1, -1, 2, -2, 2, -2, -4, 2, 2, 2, -4, 2, 1, 2, -1, 1, -1, -2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556705
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.2i', 'multiplicity': 2, 'nt': [12, 19], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -2, -2, -2, 1, 1, 4, -2, -2, -2, 4, -2, 1, -2, -2, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, -1, -1, 2, -2, 2, -2, 2, 2, 2, -4, 2, -4, 1, 2, -1, 1, -1, -2, -1, -1, 2, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556706
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.2j', 'multiplicity': 2, 'nt': [12, 19], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, -4, -4, 2, 2, 2, -4, 4, -4, 4, 2, 2, 2, 2, 2, 2, -2, 2, 2, -2, 2, -2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556709
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.3c', 'multiplicity': 2, 'nt': [12, 20], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -2, -2, -3, -3, 6, -3, -3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, -2, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556710
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.3d', 'multiplicity': 2, 'nt': [12, 29], 'qdim': 6, 'qvalues': [6, -6, -2, 2, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, -6, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556712
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.3e', 'multiplicity': 2, 'nt': [18, 25], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 2, 2, -3, -3, 6, -3, -3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, -2, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556714
    {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.6a', 'multiplicity': 1, 'nt': [12, 43], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -3, -3, -3, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556715
    {'cdim': 6, 'counter': 33, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.6b', 'multiplicity': 1, 'nt': [36, 106], 'qdim': 6, 'qvalues': [6, -6, -2, 2, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 3, 3, 3, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 4556713
    {'cdim': 3, 'counter': 31, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.3f', 'multiplicity': 4, 'nt': [36, 102], 'qdim': 12, 'qvalues': [12, -12, -4, 4, -6, -6, 12, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -12, 6, 6, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 2, 4, -2, 2, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556716
    {'cdim': 6, 'counter': 34, 'faithful': False, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.6c', 'multiplicity': 2, 'nt': [24, 563], 'qdim': 12, 'qvalues': [12, 12, -4, -4, -6, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, 3, 3, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4556717
    {'cdim': 6, 'counter': 35, 'faithful': True, 'group': '432.624', 'group_order': 432, 'image': None, 'label': '432.624.6d', 'multiplicity': 2, 'nt': [36, 562], 'qdim': 12, 'qvalues': [12, -12, -4, 4, -6, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, -3, -3, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, -1, -2, 1, -1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 7128885
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 432, 'label': '432.624.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7128896
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 216, 'label': '432.624.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7128907
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.b1', 'kernel_order': 144, 'label': '432.624.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 7128918
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.b1', 'kernel_order': 144, 'label': '432.624.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 7128929
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.c1', 'kernel_order': 144, 'label': '432.624.1d1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 7128940
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.c1', 'kernel_order': 144, 'label': '432.624.1d2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 7128951
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.a1', 'kernel_order': 144, 'label': '432.624.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]]]}
  • id: 7128955
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.a1', 'kernel_order': 144, 'label': '432.624.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]]]}
  • id: 7128956
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 144, 'label': '432.624.1f1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 7128886
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 144, 'label': '432.624.1f2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 7128887
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 108, 'label': '432.624.1g1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 7128888
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 108, 'label': '432.624.1g2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 7128889
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.b1', 'kernel_order': 72, 'label': '432.624.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 7128890
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.b1', 'kernel_order': 72, 'label': '432.624.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 7128891
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.c1', 'kernel_order': 72, 'label': '432.624.1i1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 7128892
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.c1', 'kernel_order': 72, 'label': '432.624.1i2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 7128893
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 72, 'label': '432.624.1j1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]]]}
  • id: 7128894
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 72, 'label': '432.624.1j2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]]]}
  • id: 7128895
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 19, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 72, 'label': '432.624.1k1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 7128897
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 20, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 72, 'label': '432.624.1k2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 7128898
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 21, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.b1', 'kernel_order': 36, 'label': '432.624.1l1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 4]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[1, 4]], [[-1, 4]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 4]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 5]], [[1, 5]], [[1, 1]]]}
  • id: 7128899
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 22, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.b1', 'kernel_order': 36, 'label': '432.624.1l2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[1, 2]], [[1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[1, 5]], [[1, 5]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[-1, 5]]]}
  • id: 7128900
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 23, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.b1', 'kernel_order': 36, 'label': '432.624.1l3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 4]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[1, 4]], [[-1, 4]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 4]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 5]], [[-1, 5]], [[-1, 1]]]}
  • id: 7128901
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 24, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.b1', 'kernel_order': 36, 'label': '432.624.1l4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[1, 2]], [[1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 5]], [[-1, 5]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 5]]]}
  • id: 7128902
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 25, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.c1', 'kernel_order': 36, 'label': '432.624.1m1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[1, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 5]], [[1, 1]], [[1, 3]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[1, 3]], [[1, 1]], [[1, 5]]]}
  • id: 7128903
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 26, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.c1', 'kernel_order': 36, 'label': '432.624.1m2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[1, 3]], [[1, 5]], [[1, 3]], [[1, 1]], [[-1, 5]], [[-1, 3]], [[1, 1]], [[1, 5]], [[-1, 1]], [[-1, 3]], [[-1, 5]], [[-1, 1]]]}
  • id: 7128904
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 27, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.c1', 'kernel_order': 36, 'label': '432.624.1m3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[1, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 3]], [[1, 5]], [[-1, 1]], [[-1, 3]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 3]], [[-1, 1]], [[-1, 5]]]}
  • id: 7128905
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 28, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.c1', 'kernel_order': 36, 'label': '432.624.1m4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[-1, 3]], [[-1, 5]], [[-1, 3]], [[-1, 1]], [[1, 5]], [[1, 3]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 3]], [[1, 5]], [[1, 1]]]}
  • id: 7128906
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 29, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.a1', 'kernel_order': 36, 'label': '432.624.1n1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[1, 4]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 0]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[1, 5]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[-1, 3]]]}
  • id: 7128908
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 30, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.a1', 'kernel_order': 36, 'label': '432.624.1n2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[1, 2]], [[1, 0]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[-1, 1]], [[-1, 3]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 5]], [[1, 5]], [[1, 3]], [[1, 3]]]}
  • id: 7128909
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 31, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.a1', 'kernel_order': 36, 'label': '432.624.1n3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[1, 4]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 0]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[-1, 5]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 1]], [[1, 3]], [[1, 3]]]}
  • id: 7128910
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 32, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.a1', 'kernel_order': 36, 'label': '432.624.1n4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[1, 2]], [[1, 0]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[1, 1]], [[1, 3]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[-1, 3]], [[-1, 3]]]}
  • id: 7128911
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 33, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.a1', 'kernel_order': 36, 'label': '432.624.1o1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[-1, 1]], [[1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]]]}
  • id: 7128912
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 34, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.a1', 'kernel_order': 36, 'label': '432.624.1o2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 4]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[1, 5]], [[-1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]]]}
  • id: 7128913
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 35, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.a1', 'kernel_order': 36, 'label': '432.624.1o3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[1, 1]], [[-1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]]]}
  • id: 7128914
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 36, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.a1', 'kernel_order': 36, 'label': '432.624.1o4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 4]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[-1, 5]], [[1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]]]}
  • id: 7128915
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 37, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 72, 'label': '432.624.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128916
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 38, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.c1.a1', 'kernel_order': 36, 'label': '432.624.2b', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128917
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 39, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.b1', 'kernel_order': 24, 'label': '432.624.2c1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128919
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 40, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.b1', 'kernel_order': 24, 'label': '432.624.2c2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128920
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 41, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.c1', 'kernel_order': 24, 'label': '432.624.2d1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128921
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 42, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.c1', 'kernel_order': 24, 'label': '432.624.2d2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128922
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 43, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 24, 'label': '432.624.2e1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128923
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 44, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 24, 'label': '432.624.2e2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128924
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 45, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 24, 'label': '432.624.2f1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128925
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 46, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 24, 'label': '432.624.2f2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128926
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 47, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '36.6', 'image_order': 36, 'indicator': 0, 'kernel': '36.d1.b1', 'kernel_order': 12, 'label': '432.624.2g1', 'nt': [12, 19], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, 1]], [[2, -1]], [[-2, -1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128927
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 48, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '36.6', 'image_order': 36, 'indicator': 0, 'kernel': '36.d1.b1', 'kernel_order': 12, 'label': '432.624.2g2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, -1]], [[2, 1]], [[-2, 1]], [[2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128928
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 49, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '36.6', 'image_order': 36, 'indicator': 0, 'kernel': '36.d1.c1', 'kernel_order': 12, 'label': '432.624.2h1', 'nt': [12, 19], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, 1]], [[2, -1]], [[-2, -1]], [[2, 1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128930
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 50, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '36.6', 'image_order': 36, 'indicator': 0, 'kernel': '36.d1.c1', 'kernel_order': 12, 'label': '432.624.2h2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, -1]], [[2, 1]], [[-2, 1]], [[2, -1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128931
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 51, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '36.6', 'image_order': 36, 'indicator': 0, 'kernel': '36.d1.a1', 'kernel_order': 12, 'label': '432.624.2i1', 'nt': [12, 19], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, 1]], [[2, -1]], [[-2, -1]], [[2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128932
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 52, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '36.6', 'image_order': 36, 'indicator': 0, 'kernel': '36.d1.a1', 'kernel_order': 12, 'label': '432.624.2i2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, -1]], [[2, 1]], [[-2, 1]], [[2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-1, -1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128933
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 53, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '36.6', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.a1', 'kernel_order': 12, 'label': '432.624.2j1', 'nt': [12, 19], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128934
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 54, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '36.6', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.a1', 'kernel_order': 12, 'label': '432.624.2j2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128935
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 55, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '12.3', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 36, 'label': '432.624.3a', 'nt': [4, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128936
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 56, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '24.13', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 18, 'label': '432.624.3b', 'nt': [6, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128937
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 57, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 12, 'label': '432.624.3c1', 'nt': [12, 20], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128938
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 58, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 12, 'label': '432.624.3c2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128939
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 59, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '48.31', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 9, 'label': '432.624.3d1', 'nt': [12, 29], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[1, 1]], [[-1, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[3, 1]], [[-3, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128941
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 60, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '48.31', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 9, 'label': '432.624.3d2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[-1, 1]], [[1, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[-3, 1]], [[3, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128942
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 61, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 6, 'label': '432.624.3e1', 'nt': [18, 25], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128943
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 62, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '72.47', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 6, 'label': '432.624.3e2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128944
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 63, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '144.155', 'image_order': 144, 'indicator': 0, 'kernel': '144.b1.a1', 'kernel_order': 3, 'label': '432.624.3f1', 'nt': [36, 102], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-3, 2]], [[3, 4]], [[3, 0]], [[3, 4]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 3]], [[3, 3]], [[1, 3]], [[-1, 3]], [[-3, 4]], [[3, 2]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[1, 4]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4]], [[1, 0]], [[-1, 2]], [[1, 2]], [[1, 4]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 5]], [[3, 1]], [[-3, 1]], [[3, 5]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128945
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 64, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '144.155', 'image_order': 144, 'indicator': 0, 'kernel': '144.b1.a1', 'kernel_order': 3, 'label': '432.624.3f2', 'nt': [36, 4], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 4]], [[-3, 2]], [[3, 0]], [[-3, 2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 3]], [[-3, 3]], [[-1, 3]], [[1, 3]], [[3, 2]], [[-3, 4]], [[-3, 0]], [[-3, 4]], [[3, 2]], [[-1, 2]], [[-1, 4]], [[1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, 0]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 5]], [[3, 5]], [[-3, 1]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128946
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 65, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '144.155', 'image_order': 144, 'indicator': 0, 'kernel': '144.b1.a1', 'kernel_order': 3, 'label': '432.624.3f3', 'nt': [36, 102], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-3, 2]], [[3, 4]], [[3, 0]], [[3, 4]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 3]], [[-3, 3]], [[-1, 3]], [[1, 3]], [[-3, 4]], [[3, 2]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[1, 4]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4]], [[1, 0]], [[-1, 2]], [[1, 2]], [[1, 4]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 5]], [[-3, 1]], [[3, 1]], [[-3, 5]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128947
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 66, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '144.155', 'image_order': 144, 'indicator': 0, 'kernel': '144.b1.a1', 'kernel_order': 3, 'label': '432.624.3f4', 'nt': [36, 4], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 4]], [[-3, 2]], [[3, 0]], [[-3, 2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 3]], [[3, 3]], [[1, 3]], [[-1, 3]], [[3, 2]], [[-3, 4]], [[-3, 0]], [[-3, 4]], [[3, 2]], [[-1, 2]], [[-1, 4]], [[1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, 0]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 5]], [[-3, 5]], [[3, 1]], [[1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128948
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 6, 'counter': 67, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '72.44', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 6, 'label': '432.624.6a', 'nt': [12, 43], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128949
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 6, 'counter': 68, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '144.129', 'image_order': 144, 'indicator': -1, 'kernel': '144.a1.a1', 'kernel_order': 3, 'label': '432.624.6b', 'nt': [36, 106], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128950
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 6, 'counter': 69, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '216.166', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 2, 'label': '432.624.6c1', 'nt': [24, 563], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128952
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 6, 'counter': 70, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '216.166', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 2, 'label': '432.624.6c2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128953
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 6, 'counter': 71, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '432.624', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 1, 'label': '432.624.6d1', 'nt': [36, 562], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[-6, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[2, 1]], [[-2, -1]], [[2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7128954
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 6, 'counter': 72, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '432.624', 'group_counter': 624, 'group_order': 432, 'image': None, 'image_isoclass': '432.624', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 1, 'label': '432.624.6d2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, -1]], [[-6, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[2, -1]], [[-2, 1]], [[2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 66575018
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 432, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '432.624.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.624', 'subgroup_hash': 624, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 66575066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 216, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.173', 'subgroup_hash': 173, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 66575077
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 144, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.166', 'subgroup_hash': 166, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66575088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.624.3.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.129', 'subgroup_hash': 129, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575099
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.624.3.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.129', 'subgroup_hash': 129, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.624.3.b1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.129', 'subgroup_hash': 129, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575121
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.3.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.155', 'subgroup_hash': 155, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575132
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 108, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575143
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.4.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575019
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 72, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575030
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 72, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575041
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 72, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575052
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 72, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.6.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575060
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 72, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.6.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575061
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575062
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575063
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575064
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575065
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.6.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575067
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 24, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.6.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575068
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575069
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 48, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66575070
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.9.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575072
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.9.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.9.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575074
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 72, 'characteristic': True, 'core_order': 36, 'counter': 27, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.624.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575075
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 36, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575076
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 36, 'counter': 29, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.624.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575080
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.12.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575081
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575083
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575084
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575085
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.12.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.12.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575087
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575089
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575091
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.12.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575092
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.12.k1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575093
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '432.624.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 3}
  • id: 66575094
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 24, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575095
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 24, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575096
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575097
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.18.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575098
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.18.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575100
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575101
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575102
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66575103
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66575104
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575105
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.18.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575107
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.18.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575108
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 18, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575109
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575111
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575112
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575113
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575114
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.24.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575115
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575116
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575117
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.24.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575118
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575119
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575120
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '432.624.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 2}
  • id: 66575122
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 72, 'characteristic': True, 'core_order': 12, 'counter': 70, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.624.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66575123
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 12, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.6', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575124
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 12, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.8', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575125
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 73, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.624.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.6', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575126
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 74, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.624.36.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.6', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575127
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 75, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.624.36.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.6', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575128
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575129
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575130
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575131
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 79, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575133
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 80, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575134
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66575135
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575136
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.36.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575137
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 84, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.36.k1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.k1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66575138
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575139
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575140
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575141
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575142
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575144
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.36.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575145
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.36.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66575146
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 9, 'counter': 92, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.31', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575147
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575148
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575149
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575150
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.48.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575151
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.48.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575152
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575153
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.48.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575020
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.48.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575021
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 8, 'counter': 101, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66575022
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66575023
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66575024
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 6, 'counter': 104, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.624.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.44', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 44, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times A_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575025
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 6, 'counter': 105, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.624.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.47', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575026
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 106, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575027
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 107, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575028
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 108, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.72.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575029
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 109, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.72.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575031
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 110, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575032
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 111, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.72.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575033
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 112, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.72.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575034
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 113, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575035
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 114, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575036
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575037
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 116, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575038
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 117, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575039
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 118, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66575040
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 4, 'counter': 119, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.624.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.32', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 32, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575042
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575043
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 121, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66575044
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 122, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66575045
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.624.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66575046
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 3, 'counter': 124, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '432.624.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.129', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 129, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4\\times C_3:C_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66575047
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 3, 'counter': 125, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.624.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.155', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 155, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_{12}\\times A_4', 'simple': True, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66575048
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 126, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66575049
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 127, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66575050
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 128, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.144.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66575051
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 129, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.144.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66575053
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 130, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66575054
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 131, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.144.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66575055
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 132, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.144.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66575056
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 2, 'counter': 133, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.624.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.166', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 166, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2:C_6', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66575057
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 134, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66575058
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.624.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66575059
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.624', 'ambient_counter': 624, 'ambient_order': 432, 'ambient_tex': 'C_6^2:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 1, 'counter': 136, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '432.624.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '432.624', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 624, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2:C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 66575018
    {'ambient': '432.624', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.a1', 'complements': ['432.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '3.b1.a1', '3.b1.b1', '3.b1.c1', '3.c1.a1', '4.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6510, 6123, 7582, 7119, 5840, 6071, 6662, 6413], 'generators': [3, 216, 36, 4, 24, 144, 6], 'label': '432.624.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '3.a1.a1', '3.b1.a1', '3.b1.c1', '3.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 66575019
    {'ambient': '432.624', 'aut_centralizer_order': 72, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '12.i1.a1', '18.a1.a1', '18.b1.a1', '18.h1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5342, 6244, 6718, 7065, 4699, 6373, 5468, 7217], 'generators': [6, 24, 252, 216, 144], 'label': '432.624.6.a1.a1', 'mobius_quo': 1, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '18.a1.a1', '18.b1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '72.44', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 66575020
    {'ambient': '432.624', 'aut_centralizer_order': 18, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.c1', '16.a1.a1', '24.e1.c1'], 'contains': ['144.c1.a1', '144.d1.c1', '144.e1.b1', '144.e1.c1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [622, -1, 910, -1, 1212, -1, 1830, -1], 'generators': [52, 144], 'label': '432.624.48.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.e1.c1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575021
    {'ambient': '432.624', 'aut_centralizer_order': 288, 'aut_label': '54.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '3.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '18.c1.b1', '18.c1.c1', '18.h1.a1', '18.i1.a1', '18.i1.b1', '18.i1.c1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.b1.a1', '108.e1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4330, 3566, 5582, 4779, 4430, 5652, 4192, 4921], 'generators': [6, 252, 216], 'label': '432.624.54.a1.a1', 'mobius_quo': 1, 'mobius_sub': 9, 'normal_closure': '54.a1.a1', 'normal_contained_in': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '18.c1.c1', '18.c1.b1'], 'normal_contains': ['108.a1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '216.166', 'quotient_action_image': '3.1', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66575022
    {'ambient': '432.624', 'aut_centralizer_order': 96, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.f1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.c1.a1', '108.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8842, -1, 9071, -1, 8672, -1, 8962, -1], 'generators': [3, 252], 'label': '432.624.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.b1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575023
    {'ambient': '432.624', 'aut_centralizer_order': 48, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '9.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.g1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7976, -1, 8798, -1, 9321, -1, 9233, -1], 'generators': [219, 252], 'label': '432.624.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.c1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575024
    {'ambient': '432.624', 'aut_centralizer_order': 864, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '36.e1.a1', '36.h1.a1', '36.i1.a1'], 'contains': ['144.a1.a1', '216.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9219, 5742, 9354, 6466, 6538, 6207, 6968, 6648], 'generators': [6, 168], 'label': '432.624.72.a1.a1', 'mobius_quo': 1, 'mobius_sub': 12, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['18.a1.a1', '24.a1.a1'], 'normal_contains': ['144.a1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '72.44', 'quotient_action_image': '1.1', 'quotient_action_kernel': '72.44', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575025
    {'ambient': '432.624', 'aut_centralizer_order': 864, 'aut_label': '72.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.d1.a1', '24.d1.b1', '24.d1.c1', '36.a1.a1', '36.f1.a1', '36.j1.a1'], 'contains': ['144.b1.a1', '216.a1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7892, 7568, 8102, 7630, 6984, 6908, 6538, 7937], 'generators': [6, 24], 'label': '432.624.72.b1.a1', 'mobius_quo': 1, 'mobius_sub': 12, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['18.b1.a1', '24.a1.a1', '36.a1.a1'], 'normal_contains': ['144.b1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '216.166', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.11', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575026
    {'ambient': '432.624', 'aut_centralizer_order': 432, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.e1.a1', '24.e1.b1', '24.e1.c1', '36.g1.a1'], 'contains': ['144.c1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6029, -1, 4062, -1, 5912, -1, 3619, -1], 'generators': [6, 144], 'label': '432.624.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575027
    {'ambient': '432.624', 'aut_centralizer_order': 72, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '24.b1.a1', '24.d1.a1', '24.e1.a1', '36.k1.a1'], 'contains': ['144.d1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3522, -1, 6395, -1, 3468, -1, 4670, -1], 'generators': [6, 4], 'label': '432.624.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.d1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575028
    {'ambient': '432.624', 'aut_centralizer_order': 72, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.b1', '24.b1.a1', '24.d1.b1', '24.e1.b1', '36.k1.b1'], 'contains': ['144.d1.b1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3522, -1, 4354, -1, 3468, -1, 5026, -1], 'generators': [6, 172], 'label': '432.624.72.d1.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.d1.b1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575029
    {'ambient': '432.624', 'aut_centralizer_order': 72, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.c1', '24.b1.a1', '24.d1.c1', '24.e1.c1', '36.k1.c1'], 'contains': ['144.d1.c1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3522, -1, 5918, -1, 3468, -1, 4409, -1], 'generators': [6, 340], 'label': '432.624.72.d1.c1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.d1.c1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575030
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.183', 'aut_weyl_index': 12, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.c1.a1'], 'contains': ['12.c1.a1', '18.a1.a1', '18.c1.a1', '18.c1.b1', '18.c1.c1', '24.b1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3926, 1951, 5652, 1308, 3674, 3637, 4938, 2260], 'generators': [6, 216, 4, 168, 252], 'label': '432.624.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.c1.a1', '18.a1.a1', '18.c1.a1', '18.c1.c1', '18.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575031
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.a1', '24.c1.a1', '24.d1.c1', '24.e1.a1', '24.e1.b1'], 'contains': ['144.e1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1630, -1, 2461, -1, 2695, -1, 2290, -1], 'generators': [6, 292], 'label': '432.624.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575032
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.b1', '24.c1.a1', '24.d1.b1', '24.e1.a1', '24.e1.c1'], 'contains': ['144.e1.b1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1630, -1, 1566, -1, 2695, -1, 3074, -1], 'generators': [6, 148], 'label': '432.624.72.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.e1.b1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575033
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.c1', '24.c1.a1', '24.d1.a1', '24.e1.b1', '24.e1.c1'], 'contains': ['144.e1.c1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1630, -1, 1805, -1, 2695, -1, 2146, -1], 'generators': [6, 28], 'label': '432.624.72.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.e1.c1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575034
    {'ambient': '432.624', 'aut_centralizer_order': 288, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.b1.a1', '36.e1.a1', '36.l1.a1'], 'contains': ['144.a1.a1', '216.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5631, -1, 7220, -1, 5049, -1, 6395, -1], 'generators': [252, 168], 'label': '432.624.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.f1.a1', 'projective_image': '144.129', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575035
    {'ambient': '432.624', 'aut_centralizer_order': 288, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.c1.a1', '36.f1.a1', '36.m1.a1'], 'contains': ['144.b1.a1', '216.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5429, -1, 6872, -1, 5258, -1, 5782, -1], 'generators': [252, 24], 'label': '432.624.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.g1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575036
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.g1.a1', '36.n1.a1', '36.o1.a1'], 'contains': ['144.c1.a1', '216.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4887, -1, 4874, -1, 4603, -1, 5639, -1], 'generators': [252, 144], 'label': '432.624.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.h1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575037
    {'ambient': '432.624', 'aut_centralizer_order': 288, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '36.e1.a1', '36.l1.a1'], 'contains': ['144.a1.a1', '216.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6837, -1, 7870, -1, 6121, -1, 7275, -1], 'generators': [258, 168], 'label': '432.624.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.i1.a1', 'projective_image': '144.129', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575038
    {'ambient': '432.624', 'aut_centralizer_order': 288, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '36.f1.a1', '36.m1.a1'], 'contains': ['144.b1.a1', '216.c1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7039, -1, 7624, -1, 6329, -1, 6825, -1], 'generators': [258, 24], 'label': '432.624.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.j1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575039
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '36.g1.a1', '36.n1.a1'], 'contains': ['144.c1.a1', '216.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5827, -1, 4987, -1, 5704, -1, 6089, -1], 'generators': [258, 144], 'label': '432.624.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.k1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575040
    {'ambient': '432.624', 'aut_centralizer_order': 288, 'aut_label': '108.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '3.a1.a1', 'complements': ['4.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.c1.a1', '36.d1.a1', '36.d1.b1', '36.d1.c1', '36.o1.a1', '36.p1.a1', '36.p1.b1', '36.p1.c1', '54.a1.a1'], 'contains': ['216.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2295, 2433, 3654, 2626, 1924, 3919, 2682, 4921], 'generators': [252, 216], 'label': '432.624.108.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': ['36.b1.a1', '36.c1.a1', '36.d1.a1', '36.d1.c1', '36.d1.b1', '54.a1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '432.624', 'quotient_action_image': '3.1', 'quotient_action_kernel': '36.6', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66575041
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '18.b1.a1', '18.c1.a1', '18.i1.c1', '24.d1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3131, 4619, 6017, 5175, 3265, 4951, 4202, 3143], 'generators': [6, 216, 4, 24, 36], 'label': '432.624.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.a1.a1', '3.b1.a1'], 'normal_contains': ['12.d1.a1', '18.b1.a1', '18.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 66575042
    {'ambient': '432.624', 'aut_centralizer_order': 576, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.f1.a1', '36.g1.a1', '54.a1.a1', '54.b1.a1', '54.c1.a1'], 'contains': ['216.a1.a1', '216.b1.a1', '216.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7341, -1, 8136, -1, 6761, -1, 7121, -1], 'generators': [6, 252], 'label': '432.624.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575043
    {'ambient': '432.624', 'aut_centralizer_order': 288, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '3.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.h1.a1', '36.k1.a1', '36.k1.b1', '36.k1.c1', '54.b1.a1'], 'contains': ['216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8842, -1, 7956, -1, 8081, -1, 6682, -1], 'generators': [3], 'label': '432.624.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.c1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575044
    {'ambient': '432.624', 'aut_centralizer_order': 96, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '36.j1.a1', '54.b1.a1', '54.c1.a1'], 'contains': ['216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8611, -1, 9071, -1, 8997, -1, 9233, -1], 'generators': [255], 'label': '432.624.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.d1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575045
    {'ambient': '432.624', 'aut_centralizer_order': 288, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.m1.a1', '36.n1.a1', '54.a1.a1'], 'contains': ['216.b1.a1', '216.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5248, -1, 5886, -1, 5481, -1, 5935, -1], 'generators': [222, 252], 'label': '432.624.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '108.e1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575046
    {'ambient': '432.624', 'aut_centralizer_order': 864, 'aut_label': '144.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '1.a1.a1', 'complements': ['3.b1.a1', '3.b1.b1', '3.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '72.a1.a1', '72.f1.a1', '72.i1.a1'], 'contains': ['432.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6096, 4519, 7262, 5834, 4936, 4718, 6242, 6720], 'generators': [168], 'label': '432.624.144.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['36.b1.a1', '48.a1.a1', '72.a1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '144.129', 'quotient_action_image': '1.1', 'quotient_action_kernel': '144.129', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575047
    {'ambient': '432.624', 'aut_centralizer_order': 864, 'aut_label': '144.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '2.a1.a1', 'complements': ['3.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.d1.a1', '48.d1.b1', '48.d1.c1', '72.b1.a1', '72.g1.a1', '72.j1.a1'], 'contains': ['432.a1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6287, 6755, 6959, 6850, 5353, 5419, 4192, 7328], 'generators': [24], 'label': '432.624.144.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '144.b1.a1', 'normal_contained_in': ['36.c1.a1', '48.a1.a1', '72.b1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '432.624', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.47', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575048
    {'ambient': '432.624', 'aut_centralizer_order': 432, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.e1.a1', '48.e1.b1', '48.e1.c1', '72.c1.a1', '72.h1.a1', '72.k1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5844, -1, 3944, -1, 4728, -1, 3559, -1], 'generators': [144], 'label': '432.624.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '144.c1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575049
    {'ambient': '432.624', 'aut_centralizer_order': 72, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '48.b1.a1', '48.d1.a1', '48.e1.a1', '72.d1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1304, -1, 4473, -1, 1560, -1, 3089, -1], 'generators': [4], 'label': '432.624.144.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '144.d1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575050
    {'ambient': '432.624', 'aut_centralizer_order': 72, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.b1', '48.b1.a1', '48.d1.b1', '48.e1.b1', '72.d1.b1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1304, -1, 3043, -1, 1560, -1, 3358, -1], 'generators': [172], 'label': '432.624.144.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '144.d1.b1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575051
    {'ambient': '432.624', 'aut_centralizer_order': 72, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.c1', '48.b1.a1', '48.d1.c1', '48.e1.c1', '72.d1.c1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1304, -1, 3475, -1, 1560, -1, 2817, -1], 'generators': [340], 'label': '432.624.144.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '144.d1.c1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575052
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.b1'], 'contains': ['12.d1.b1', '18.b1.a1', '18.c1.b1', '18.i1.b1', '24.d1.b1'], 'core': '6.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3131, 4619, 3783, 4268, 3265, 4951, 4670, 5935], 'generators': [6, 216, 148, 24, 36], 'label': '432.624.6.c1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.b1', 'normal_contained_in': ['2.a1.a1', '3.b1.b1'], 'normal_contains': ['12.d1.b1', '18.b1.a1', '18.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.b1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 66575053
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.a1', '48.c1.a1', '48.d1.c1', '48.e1.a1', '48.e1.b1', '72.e1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [723, -1, 2282, -1, 1337, -1, 1983, -1], 'generators': [292], 'label': '432.624.144.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.e1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575054
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.b1', '48.c1.a1', '48.d1.b1', '48.e1.a1', '48.e1.c1', '72.e1.b1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [723, -1, 880, -1, 1337, -1, 2126, -1], 'generators': [148], 'label': '432.624.144.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.e1.b1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575055
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.c1', '48.c1.a1', '48.d1.a1', '48.e1.b1', '48.e1.c1', '72.e1.c1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [723, -1, 1178, -1, 1337, -1, 1830, -1], 'generators': [28], 'label': '432.624.144.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.e1.c1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575056
    {'ambient': '432.624', 'aut_centralizer_order': 1728, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '72.d1.a1', '72.d1.b1', '72.d1.c1', '72.e1.a1', '72.e1.b1', '72.e1.c1', '108.b1.a1', '108.c1.a1', '108.d1.a1'], 'contains': ['432.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7341, 5642, 4746, 6359, 6538, 6159, 4670, 6249], 'generators': [6], 'label': '432.624.216.a1.a1', 'mobius_quo': -1, 'mobius_sub': -36, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['54.a1.a1', '72.a1.a1', '72.b1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '216.166', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.166', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575057
    {'ambient': '432.624', 'aut_centralizer_order': 576, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '72.g1.a1', '72.h1.a1', '108.a1.a1', '108.b1.a1', '108.e1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5424, -1, 4926, -1, 5145, -1, 5782, -1], 'generators': [252], 'label': '432.624.216.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575058
    {'ambient': '432.624', 'aut_centralizer_order': 576, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '72.j1.a1', '72.k1.a1', '108.b1.a1', '108.e1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6470, -1, 7389, -1, 5912, -1, 6604, -1], 'generators': [258], 'label': '432.624.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575059
    {'ambient': '432.624', 'aut_centralizer_order': None, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '144.d1.a1', '144.d1.b1', '144.d1.c1', '144.e1.a1', '144.e1.b1', '144.e1.c1', '216.a1.a1', '216.b1.a1', '216.c1.a1'], 'contains': [], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5896, 5372, 4122, 6177, 5041, 5068, 3430, 6485], 'generators': [], 'label': '432.624.432.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['108.a1.a1', '144.a1.a1', '144.b1.a1', '216.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575060
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.c1'], 'contains': ['12.d1.c1', '18.b1.a1', '18.c1.c1', '18.i1.a1', '24.d1.c1'], 'core': '6.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3131, 4619, 5361, 6083, 3265, 4951, 3856, 5052], 'generators': [6, 216, 292, 24, 36], 'label': '432.624.6.c1.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.c1', 'normal_contained_in': ['2.a1.a1', '3.b1.c1'], 'normal_contains': ['12.d1.c1', '18.b1.a1', '18.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.c1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.c1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 66575061
    {'ambient': '432.624', 'aut_centralizer_order': 24, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.a1.a1', '12.e1.a1', '12.f1.a1', '18.d1.a1', '18.f1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8776, -1, 9350, -1, 7395, -1, 8403, -1], 'generators': [3, 24, 252, 144, 6], 'label': '432.624.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66575062
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 36, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.e1.a1', '12.f1.a1', '18.e1.a1', '18.g1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7849, -1, 8922, -1, 8823, -1, 8871, -1], 'generators': [219, 24, 252, 144, 6], 'label': '432.624.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66575063
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.183', 'aut_weyl_index': 12, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.j1.a1', '18.a1.a1', '18.i1.a1', '18.i1.b1', '18.i1.c1', '24.c1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1907, -1, 967, -1, 2370, -1, 1213, -1], 'generators': [6, 216, 28, 168, 252], 'label': '432.624.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575064
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.k1.a1', '18.c1.a1', '18.h1.a1', '18.i1.a1', '18.i1.b1', '24.e1.a1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2462, -1, 3238, -1, 2761, -1, 2853, -1], 'generators': [6, 216, 4, 144, 252], 'label': '432.624.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575065
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.k1.b1', '18.c1.b1', '18.h1.a1', '18.i1.a1', '18.i1.c1', '24.e1.b1'], 'core': '18.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2462, -1, 1538, -1, 2761, -1, 1482, -1], 'generators': [6, 216, 28, 144, 252], 'label': '432.624.6.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.g1.b1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575066
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 6, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1', '6.c1.b1', '6.c1.c1', '6.f1.a1', '6.g1.a1', '6.g1.b1', '6.g1.c1', '8.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3248, 4619, 4273, 4806, 3141, 4240, 3943, 4097], 'generators': [6, 216, 36, 4, 144, 24], 'label': '432.624.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1', '6.c1.c1', '6.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 66575067
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.k1.c1', '18.c1.c1', '18.h1.a1', '18.i1.b1', '18.i1.c1', '24.e1.c1'], 'core': '18.c1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [2462, -1, 277, -1, 2761, -1, 2584, -1], 'generators': [6, 216, 52, 144, 252], 'label': '432.624.6.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.g1.c1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575068
    {'ambient': '432.624', 'aut_centralizer_order': 18, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.b1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '24.d1.b1', '24.d1.c1', '24.e1.a1', '24.e1.b1', '24.e1.c1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3362, -1, 4532, -1, 2944, -1, 4407, -1], 'generators': [6, 4, 144, 24], 'label': '432.624.8.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.a1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575069
    {'ambient': '432.624', 'aut_centralizer_order': 24, 'aut_label': '9.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 24, 'centralizer': '18.a1.a1', 'complements': ['48.e1.a1', '48.e1.b1', '48.e1.c1', '48.b1.a1', '48.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1', '3.b1.b1', '3.b1.c1'], 'contains': ['18.b1.a1', '18.f1.a1', '18.g1.a1', '27.a1.a1'], 'core': '9.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7246, 8280, 8216, 8490, 7911, 8057, 7545, 8349], 'generators': [3, 24, 252, 216, 6], 'label': '432.624.9.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.a1.a1', 'normal_contained_in': ['3.a1.a1', '3.b1.a1', '3.b1.c1', '3.b1.b1'], 'normal_contains': ['18.b1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '216.166', 'quotient_action_image': '9.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 66575070
    {'ambient': '432.624', 'aut_centralizer_order': 24, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '9.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.c1.a1'], 'contains': ['18.a1.a1', '18.d1.a1', '18.e1.a1', '27.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8245, -1, 8628, -1, 6885, -1, 7915, -1], 'generators': [3, 6, 252, 216, 168], 'label': '432.624.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.b1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66575071
    {'ambient': '432.624', 'aut_centralizer_order': 4, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '3.c1.a1'], 'contains': ['18.c1.a1', '27.a1.a1', '36.k1.a1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6308, -1, 7782, -1, 6402, -1, 6427, -1], 'generators': [3, 216, 4, 6, 252], 'label': '432.624.9.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.c1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575072
    {'ambient': '432.624', 'aut_centralizer_order': 4, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.b1', '3.c1.a1'], 'contains': ['18.c1.b1', '27.a1.a1', '36.k1.b1'], 'core': '18.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6308, -1, 7207, -1, 6402, -1, 7147, -1], 'generators': [3, 216, 172, 6, 252], 'label': '432.624.9.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.c1.b1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575073
    {'ambient': '432.624', 'aut_centralizer_order': 4, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.c1', '3.c1.a1'], 'contains': ['18.c1.c1', '27.a1.a1', '36.k1.c1'], 'core': '18.c1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6308, -1, 6511, -1, 6402, -1, 5921, -1], 'generators': [3, 216, 340, 6, 252], 'label': '432.624.9.c1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.c1.c1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575074
    {'ambient': '432.624', 'aut_centralizer_order': 72, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '6.b1.a1', 'complements': ['36.d1.a1', '36.p1.c1', '36.p1.b1', '36.d1.b1', '36.p1.a1', '36.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '36.a1.a1', '36.h1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8842, 9413, 9155, 9176, 6935, 9274, 8206, 9513], 'generators': [3, 144, 6, 24], 'label': '432.624.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 4, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['24.a1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '72.44', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66575075
    {'ambient': '432.624', 'aut_centralizer_order': 72, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '6.a1.a1', 'complements': ['36.k1.a1', '36.k1.b1', '36.k1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['24.f1.a1', '36.b1.a1', '36.c1.a1', '36.o1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3060, 5040, 5241, 5404, 1846, 2945, 4646, 7420], 'generators': [252, 216, 144, 24], 'label': '432.624.12.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['36.b1.a1', '36.c1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '144.129', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 66575076
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.183', 'aut_weyl_index': 12, 'centralizer': '12.a1.a1', 'complements': ['36.a1.a1', '36.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1'], 'contains': ['36.b1.a1', '36.d1.a1', '36.d1.b1', '36.d1.c1', '48.b1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2468, 587, 4039, 393, 1455, 570, 2920, 1266], 'generators': [4, 168, 252, 216], 'label': '432.624.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.a1'], 'normal_contains': ['36.b1.a1', '36.d1.a1', '36.d1.c1', '36.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '144.129', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.1', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575077
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 12, 'centralizer': '18.a1.a1', 'complements': ['144.d1.a1', '144.e1.c1', '144.e1.b1', '144.d1.b1', '144.e1.a1', '144.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.d1.a1', '6.e1.a1', '9.a1.a1', '9.b1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7524, 8209, 8536, 9607, 7140, 8057, 7734, 8833], 'generators': [3, 24, 6, 252, 216, 144], 'label': '432.624.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '9.a1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '72.44', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 66575078
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '12.d1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '24.a1.a1', 'complements': ['36.h1.a1', '36.i1.a1', '36.k1.b1', '36.k1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.c1.a1'], 'contains': ['36.c1.a1', '36.d1.a1', '36.p1.c1', '48.d1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1198, 3536, 4837, 2989, 951, 1884, 2230, 2148], 'generators': [4, 24, 36, 216], 'label': '432.624.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.a1.a1', '6.c1.a1'], 'normal_contains': ['36.c1.a1', '36.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '432.624', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 66575079
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '12.d1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '24.a1.a1', 'complements': ['36.h1.a1', '36.i1.a1', '36.k1.c1', '36.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.c1.b1'], 'contains': ['36.c1.a1', '36.d1.b1', '36.p1.b1', '48.d1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1198, 3536, 2645, 1563, 951, 1884, 3189, 5680], 'generators': [148, 24, 36, 216], 'label': '432.624.12.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': ['4.a1.a1', '6.c1.b1'], 'normal_contains': ['36.c1.a1', '36.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '432.624', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 66575080
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '12.d1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '24.a1.a1', 'complements': ['36.h1.a1', '36.i1.a1', '36.k1.a1', '36.k1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.c1.c1'], 'contains': ['36.c1.a1', '36.d1.c1', '36.p1.a1', '48.d1.c1'], 'core': '12.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1198, 3536, 3041, 4416, 951, 1884, 1961, 3914], 'generators': [292, 24, 36, 216], 'label': '432.624.12.d1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.d1.c1', 'normal_contained_in': ['4.a1.a1', '6.c1.c1'], 'normal_contains': ['36.c1.a1', '36.d1.c1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.c1', 'projective_image': '432.624', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.d1.c1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 66575081
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.f1.a1', '24.g1.a1', '36.e1.a1', '36.f1.a1', '36.g1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7286, -1, 8612, -1, 6576, -1, 7645, -1], 'generators': [6, 252, 144, 24], 'label': '432.624.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575082
    {'ambient': '432.624', 'aut_centralizer_order': 24, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '36.i1.a1', '36.j1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9660, -1, 9654, -1, 9301, -1, 9852, -1], 'generators': [255, 144, 6, 24], 'label': '432.624.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66575083
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1', '4.b1.a1'], 'contains': ['24.b1.a1', '36.h1.a1', '36.k1.a1', '36.k1.b1', '36.k1.c1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6665, -1, 7800, -1, 5628, -1, 6831, -1], 'generators': [3, 4, 168, 6], 'label': '432.624.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '12.g1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575084
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '4.b1.a1'], 'contains': ['24.d1.a1', '36.a1.a1', '36.k1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4596, -1, 8238, -1, 6106, -1, 6427, -1], 'generators': [3, 4, 6, 24], 'label': '432.624.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '12.h1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66575085
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.b1', '4.b1.a1'], 'contains': ['24.d1.b1', '36.a1.a1', '36.k1.b1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4596, -1, 7422, -1, 6106, -1, 7322, -1], 'generators': [3, 148, 6, 24], 'label': '432.624.12.h1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '12.h1.b1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66575086
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.c1', '4.b1.a1'], 'contains': ['24.d1.c1', '36.a1.a1', '36.k1.c1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4596, -1, 6535, -1, 6106, -1, 6095, -1], 'generators': [3, 292, 6, 24], 'label': '432.624.12.h1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '12.h1.c1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66575087
    {'ambient': '432.624', 'aut_centralizer_order': 72, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.f1.a1', '24.g1.a1', '36.l1.a1', '36.m1.a1', '36.n1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5453, -1, 6789, -1, 5272, -1, 7076, -1], 'generators': [222, 252, 144, 24], 'label': '432.624.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '144.129', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575088
    {'ambient': '432.624', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 6, 'centralizer': '72.a1.a1', 'complements': ['144.c1.a1', '144.a1.a1', '144.e1.b1', '144.d1.b1', '144.e1.a1', '144.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.c1.a1', '9.a1.a1', '9.c1.a1', '12.h1.a1'], 'core': '3.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6210, 6123, 8200, 7119, 6150, 6071, 6335, 5327], 'generators': [3, 24, 216, 4, 6, 36], 'label': '432.624.3.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.c1.a1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.a1', 'projective_image': '216.166', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 66575089
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.183', 'aut_weyl_index': 12, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.f1.a1'], 'contains': ['36.b1.a1', '36.p1.a1', '36.p1.b1', '36.p1.c1', '48.c1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [481, -1, 924, -1, 169, -1, 116, -1], 'generators': [28, 168, 252, 216], 'label': '432.624.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.j1.a1', 'projective_image': '144.129', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575090
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.g1.a1'], 'contains': ['36.d1.a1', '36.o1.a1', '36.p1.a1', '36.p1.b1', '48.e1.a1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [840, -1, 2223, -1, 560, -1, 1692, -1], 'generators': [4, 144, 252, 216], 'label': '432.624.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.k1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575091
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.g1.b1'], 'contains': ['36.d1.b1', '36.o1.a1', '36.p1.a1', '36.p1.c1', '48.e1.b1'], 'core': '36.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [840, -1, 1555, -1, 560, -1, 463, -1], 'generators': [28, 144, 252, 216], 'label': '432.624.12.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.k1.b1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575092
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.g1.c1'], 'contains': ['36.d1.c1', '36.o1.a1', '36.p1.b1', '36.p1.c1', '48.e1.c1'], 'core': '36.d1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [840, -1, 390, -1, 560, -1, 1078, -1], 'generators': [52, 144, 252, 216], 'label': '432.624.12.k1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.k1.c1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575093
    {'ambient': '432.624', 'aut_centralizer_order': 18, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.a1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '48.d1.a1', '48.d1.b1', '48.d1.c1', '48.e1.a1', '48.e1.b1', '48.e1.c1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1790, -1, 2904, -1, 711, -1, 1251, -1], 'generators': [4, 144, 24], 'label': '432.624.16.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.a1.a1', 'projective_image': '144.129', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575094
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '3.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.f1.a1', '9.b1.a1'], 'contains': ['36.b1.a1', '36.e1.a1', '36.l1.a1', '54.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6034, 3295, 7268, 6097, 4470, 5428, 5696, 6635], 'generators': [6, 252, 216, 168], 'label': '432.624.18.a1.a1', 'mobius_quo': -1, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '6.b1.a1'], 'normal_contains': ['36.b1.a1', '54.a1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '72.44', 'quotient_action_image': '3.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66575095
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '18.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.a1', '6.c1.b1', '6.c1.c1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.f1.a1', '36.m1.a1', '54.a1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4908, 6404, 6364, 7152, 4925, 6957, 5306, 8205], 'generators': [6, 252, 216, 24], 'label': '432.624.18.b1.a1', 'mobius_quo': -1, 'mobius_sub': -3, 'normal_closure': '18.b1.a1', 'normal_contained_in': ['6.a1.a1', '6.c1.a1', '6.c1.c1', '6.c1.b1', '9.a1.a1'], 'normal_contains': ['36.c1.a1', '54.a1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '216.166', 'quotient_action_image': '6.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 66575096
    {'ambient': '432.624', 'aut_centralizer_order': 24, 'aut_label': '18.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.a1', '6.g1.a1', '9.c1.a1'], 'contains': ['36.d1.a1', '54.a1.a1', '72.d1.a1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3594, 1439, 6135, 2659, 3480, 4007, 4116, 383], 'generators': [6, 4, 252, 216], 'label': '432.624.18.c1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.c1.a1', 'normal_contained_in': ['6.b1.a1', '6.c1.a1'], 'normal_contains': ['36.d1.a1', '54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575097
    {'ambient': '432.624', 'aut_centralizer_order': 24, 'aut_label': '18.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.b1', '6.g1.b1', '9.c1.b1'], 'contains': ['36.d1.b1', '54.a1.a1', '72.d1.b1'], 'core': '18.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3594, 1439, 4158, 978, 3480, 4007, 4938, 4798], 'generators': [6, 172, 252, 216], 'label': '432.624.18.c1.b1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.c1.b1', 'normal_contained_in': ['6.b1.a1', '6.c1.b1'], 'normal_contains': ['36.d1.b1', '54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.c1.b1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575098
    {'ambient': '432.624', 'aut_centralizer_order': 24, 'aut_label': '18.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.c1', '6.g1.c1', '9.c1.c1'], 'contains': ['36.d1.c1', '54.a1.a1', '72.d1.c1'], 'core': '18.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3594, 1439, 5499, 4085, 3480, 4007, 3458, 3031], 'generators': [6, 340, 252, 216], 'label': '432.624.18.c1.c1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.c1.c1', 'normal_contained_in': ['6.b1.a1', '6.c1.c1'], 'normal_contains': ['36.d1.c1', '54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.c1.c1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575099
    {'ambient': '432.624', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 6, 'centralizer': '72.a1.a1', 'complements': ['144.c1.a1', '144.a1.a1', '144.e1.a1', '144.d1.c1', '144.d1.a1', '144.e1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.c1.b1', '9.a1.a1', '9.c1.b1', '12.h1.b1'], 'core': '3.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6210, 6123, 7324, 6002, 6150, 6071, 7147, 7499], 'generators': [3, 24, 216, 148, 6, 36], 'label': '432.624.3.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.c1.b1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.b1', 'projective_image': '216.166', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.b1.b1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 66575100
    {'ambient': '432.624', 'aut_centralizer_order': 48, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '9.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.b1.a1'], 'contains': ['36.e1.a1', '36.h1.a1', '36.i1.a1', '54.b1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9929, -1, 9909, -1, 7413, -1, 9199, -1], 'generators': [3, 252, 168, 6], 'label': '432.624.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.d1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575101
    {'ambient': '432.624', 'aut_centralizer_order': 24, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '9.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.b1.a1'], 'contains': ['36.e1.a1', '36.i1.a1', '54.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9496, -1, 9653, -1, 8823, -1, 9523, -1], 'generators': [219, 252, 168, 6], 'label': '432.624.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.e1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575102
    {'ambient': '432.624', 'aut_centralizer_order': 48, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.f1.a1', '36.j1.a1', '54.b1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8250, -1, 8916, -1, 8345, -1, 8538, -1], 'generators': [3, 252, 6, 24], 'label': '432.624.18.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.f1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66575103
    {'ambient': '432.624', 'aut_centralizer_order': 24, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.a1.a1'], 'contains': ['36.f1.a1', '36.j1.a1', '54.c1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7709, -1, 8596, -1, 9784, -1, 8871, -1], 'generators': [219, 252, 6, 24], 'label': '432.624.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.g1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66575104
    {'ambient': '432.624', 'aut_centralizer_order': 72, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.g1.a1', '6.g1.b1', '6.g1.c1'], 'contains': ['36.g1.a1', '36.n1.a1', '36.o1.a1', '54.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4287, -1, 3688, -1, 4015, -1, 3748, -1], 'generators': [6, 252, 216, 144], 'label': '432.624.18.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.h1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66575105
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.c1', '6.f1.a1', '6.g1.a1', '6.g1.b1'], 'contains': ['36.p1.a1', '54.a1.a1', '72.e1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [954, -1, 1549, -1, 2408, -1, 1346, -1], 'generators': [6, 292, 252, 216], 'label': '432.624.18.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.i1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575106
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '6.f1.a1', '6.g1.a1', '6.g1.c1'], 'contains': ['36.p1.b1', '54.a1.a1', '72.e1.b1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [954, -1, 515, -1, 2408, -1, 2499, -1], 'generators': [6, 148, 252, 216], 'label': '432.624.18.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.i1.b1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575107
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.f1.a1', '6.g1.b1', '6.g1.c1'], 'contains': ['36.p1.c1', '54.a1.a1', '72.e1.c1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [954, -1, 91, -1, 2408, -1, 731, -1], 'generators': [6, 28, 252, 216], 'label': '432.624.18.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.i1.c1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575108
    {'ambient': '432.624', 'aut_centralizer_order': 432, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.e1.a1', '12.f1.a1'], 'contains': ['48.a1.a1', '72.a1.a1', '72.b1.a1', '72.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8688, 7518, 9109, 7899, 6969, 7600, 7792, 7937], 'generators': [6, 144, 24], 'label': '432.624.24.a1.a1', 'mobius_quo': -1, 'mobius_sub': -4, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '72.44', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575109
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '8.a1.a1', '12.g1.a1'], 'contains': ['48.b1.a1', '72.a1.a1', '72.d1.a1', '72.d1.b1', '72.d1.c1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4056, -1, 5878, -1, 3720, -1, 5296, -1], 'generators': [6, 4, 168], 'label': '432.624.24.b1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.b1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575110
    {'ambient': '432.624', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 6, 'centralizer': '72.a1.a1', 'complements': ['144.c1.a1', '144.a1.a1', '144.d1.a1', '144.e1.c1', '144.e1.b1', '144.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.c1.c1', '9.a1.a1', '9.c1.c1', '12.h1.c1'], 'core': '3.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6210, 6123, 6444, 8235, 6150, 6071, 6005, 6413], 'generators': [3, 24, 216, 292, 6, 36], 'label': '432.624.3.b1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.c1.c1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.c1', 'projective_image': '216.166', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.b1.c1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 66575111
    {'ambient': '432.624', 'aut_centralizer_order': 18, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '8.a1.a1'], 'contains': ['48.c1.a1', '72.a1.a1', '72.e1.a1', '72.e1.b1', '72.e1.c1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1588, -1, 1685, -1, 2318, -1, 1468, -1], 'generators': [6, 28, 168], 'label': '432.624.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575112
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '8.a1.a1', '12.h1.a1'], 'contains': ['48.d1.a1', '72.b1.a1', '72.d1.a1', '72.e1.c1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3392, -1, 6092, -1, 3216, -1, 4755, -1], 'generators': [6, 4, 24], 'label': '432.624.24.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.d1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575113
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '8.a1.a1', '12.h1.b1'], 'contains': ['48.d1.b1', '72.b1.a1', '72.d1.b1', '72.e1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3392, -1, 4234, -1, 3216, -1, 5026, -1], 'generators': [6, 148, 24], 'label': '432.624.24.d1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.d1.b1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575114
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.c1', '8.a1.a1', '12.h1.c1'], 'contains': ['48.d1.c1', '72.b1.a1', '72.d1.c1', '72.e1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3392, -1, 5545, -1, 3216, -1, 4409, -1], 'generators': [6, 292, 24], 'label': '432.624.24.d1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.d1.c1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575115
    {'ambient': '432.624', 'aut_centralizer_order': 18, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '8.a1.a1'], 'contains': ['48.e1.a1', '72.c1.a1', '72.d1.a1', '72.e1.a1', '72.e1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2051, -1, 3552, -1, 2822, -1, 3064, -1], 'generators': [6, 4, 144], 'label': '432.624.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575116
    {'ambient': '432.624', 'aut_centralizer_order': 18, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.b1', '8.a1.a1'], 'contains': ['48.e1.b1', '72.c1.a1', '72.d1.b1', '72.e1.a1', '72.e1.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2051, -1, 2580, -1, 2822, -1, 1738, -1], 'generators': [6, 28, 144], 'label': '432.624.24.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.e1.b1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575117
    {'ambient': '432.624', 'aut_centralizer_order': 18, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.c1', '8.a1.a1'], 'contains': ['48.e1.c1', '72.c1.a1', '72.d1.c1', '72.e1.b1', '72.e1.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2051, -1, 1464, -1, 2822, -1, 2793, -1], 'generators': [6, 52, 144], 'label': '432.624.24.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.e1.c1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575118
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.e1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '72.f1.a1', '72.g1.a1', '72.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5427, -1, 7072, -1, 4114, -1, 6534, -1], 'generators': [252, 144, 24], 'label': '432.624.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '144.129', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575119
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '72.i1.a1', '72.j1.a1', '72.k1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6611, -1, 7583, -1, 6576, -1, 7521, -1], 'generators': [258, 144, 24], 'label': '432.624.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.g1.a1', 'projective_image': '144.129', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575120
    {'ambient': '432.624', 'aut_centralizer_order': 48, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '9.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1', '9.c1.a1', '9.c1.b1', '9.c1.c1'], 'contains': ['54.a1.a1', '54.b1.a1', '54.c1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7246, -1, 7984, -1, 7876, -1, 7884, -1], 'generators': [3, 252, 216], 'label': '432.624.27.a1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '27.a1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66575121
    {'ambient': '432.624', 'aut_centralizer_order': 2, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 6, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '9.b1.a1', '9.c1.a1', '9.c1.b1', '9.c1.c1', '12.g1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6911, -1, 7582, -1, 5550, -1, 6662, -1], 'generators': [3, 216, 252, 4, 168, 6], 'label': '432.624.3.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '3.c1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575122
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '36.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '6.b1.a1', 'complements': ['12.k1.a1', '12.k1.b1', '12.k1.c1', '12.c1.a1', '12.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.h1.a1', '12.h1.b1', '12.h1.c1', '18.f1.a1'], 'contains': ['72.b1.a1', '108.c1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8444, 8471, 8500, 8490, 8342, 8710, 8019, 9513], 'generators': [3, 6, 24], 'label': '432.624.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['9.a1.a1', '12.a1.a1'], 'normal_contains': ['72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '216.166', 'quotient_action_image': '3.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66575123
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '36.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '3.a1.a1', 'complements': ['12.h1.a1', '12.h1.b1', '12.h1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.j1.a1', '18.a1.a1'], 'contains': ['72.f1.a1', '108.a1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2568, 2473, 4936, 5363, 1531, 2897, 3975, 5634], 'generators': [252, 216, 168], 'label': '432.624.36.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.b1.a1', '12.c1.a1', '18.a1.a1'], 'normal_contains': ['108.a1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '144.129', 'quotient_action_image': '3.1', 'quotient_action_kernel': '12.1', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66575124
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '36.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '6.a1.a1', 'complements': ['12.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.d1.a1', '12.d1.b1', '12.d1.c1', '18.b1.a1'], 'contains': ['72.g1.a1', '108.a1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3493, 5040, 5150, 4193, 1924, 4221, 3629, 6524], 'generators': [252, 216, 24], 'label': '432.624.36.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': ['12.b1.a1', '12.d1.a1', '12.d1.c1', '12.d1.b1', '18.b1.a1'], 'normal_contains': ['108.a1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '432.624', 'quotient_action_image': '6.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 66575125
    {'ambient': '432.624', 'aut_centralizer_order': 24, 'aut_label': '36.d1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '12.a1.a1', 'complements': ['12.a1.a1', '12.f1.a1', '12.h1.b1', '12.h1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.d1.a1', '12.k1.a1', '18.c1.a1'], 'contains': ['108.a1.a1', '144.d1.a1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1081, 948, 4535, 1906, 488, 1884, 2510, 1710], 'generators': [4, 252, 216], 'label': '432.624.36.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.d1.a1', 'normal_contained_in': ['12.c1.a1', '12.d1.a1', '18.c1.a1'], 'normal_contains': ['108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '432.624', 'quotient_action_image': '1.1', 'quotient_action_kernel': '36.6', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575126
    {'ambient': '432.624', 'aut_centralizer_order': 24, 'aut_label': '36.d1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '12.a1.a1', 'complements': ['12.a1.a1', '12.f1.a1', '12.h1.c1', '12.h1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.d1.b1', '12.k1.b1', '18.c1.b1'], 'contains': ['108.a1.a1', '144.d1.b1'], 'core': '36.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1081, 948, 3089, 844, 488, 1884, 3346, 4418], 'generators': [172, 252, 216], 'label': '432.624.36.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.d1.b1', 'normal_contained_in': ['12.c1.a1', '12.d1.b1', '18.c1.b1'], 'normal_contains': ['108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.d1.b1', 'projective_image': '432.624', 'quotient_action_image': '1.1', 'quotient_action_kernel': '36.6', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '36.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575127
    {'ambient': '432.624', 'aut_centralizer_order': 24, 'aut_label': '36.d1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '12.a1.a1', 'complements': ['12.a1.a1', '12.f1.a1', '12.h1.a1', '12.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.d1.c1', '12.k1.c1', '18.c1.c1'], 'contains': ['108.a1.a1', '144.d1.c1'], 'core': '36.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1081, 948, 3747, 2706, 488, 1884, 2021, 3476], 'generators': [340, 252, 216], 'label': '432.624.36.d1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.d1.c1', 'normal_contained_in': ['12.c1.a1', '12.d1.c1', '18.c1.c1'], 'normal_contains': ['108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.d1.c1', 'projective_image': '432.624', 'quotient_action_image': '1.1', 'quotient_action_kernel': '36.6', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '36.d1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575128
    {'ambient': '432.624', 'aut_centralizer_order': 288, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.a1.a1', '18.d1.a1', '18.e1.a1'], 'contains': ['72.a1.a1', '72.f1.a1', '72.i1.a1', '108.b1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8746, -1, 9271, -1, 7363, -1, 8692, -1], 'generators': [6, 252, 168], 'label': '432.624.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575129
    {'ambient': '432.624', 'aut_centralizer_order': 288, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.b1.a1', '18.f1.a1', '18.g1.a1'], 'contains': ['72.b1.a1', '72.g1.a1', '72.j1.a1', '108.b1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7471, -1, 8322, -1, 7757, -1, 8246, -1], 'generators': [6, 252, 24], 'label': '432.624.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575130
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.h1.a1'], 'contains': ['72.c1.a1', '72.h1.a1', '72.k1.a1', '108.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6048, -1, 5722, -1, 5927, -1, 6089, -1], 'generators': [6, 252, 144], 'label': '432.624.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575131
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '3.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.g1.a1', '18.d1.a1'], 'contains': ['72.a1.a1', '108.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9525, -1, 9571, -1, 8081, -1, 8469, -1], 'generators': [3, 168, 6], 'label': '432.624.36.h1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.h1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575132
    {'ambient': '432.624', 'aut_centralizer_order': 6, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 6, 'centralizer': '24.a1.a1', 'complements': ['108.c1.a1', '108.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1', '12.d1.c1', '12.j1.a1', '12.k1.a1', '12.k1.b1', '12.k1.c1', '16.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1530, 3626, 2880, 3063, 1203, 2108, 1961, 4097], 'generators': [4, 216, 144, 24, 36], 'label': '432.624.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.b1.a1', '12.c1.a1', '12.d1.a1', '12.d1.c1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '144.129', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 66575133
    {'ambient': '432.624', 'aut_centralizer_order': 48, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '9.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.d1.a1', '18.e1.a1'], 'contains': ['72.a1.a1', '108.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9860, -1, 9909, -1, 8997, -1, 9639, -1], 'generators': [255, 168, 6], 'label': '432.624.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.i1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575134
    {'ambient': '432.624', 'aut_centralizer_order': 48, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.f1.a1', '18.g1.a1'], 'contains': ['72.b1.a1', '108.d1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8199, -1, 8854, -1, 9651, -1, 9460, -1], 'generators': [255, 6, 24], 'label': '432.624.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.j1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66575135
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1', '12.g1.a1', '12.h1.a1'], 'contains': ['72.d1.a1', '108.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6547, -1, 8145, -1, 6251, -1, 6311, -1], 'generators': [3, 4, 6], 'label': '432.624.36.k1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '36.k1.a1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575136
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.b1', '12.g1.a1', '12.h1.b1'], 'contains': ['72.d1.b1', '108.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6547, -1, 7476, -1, 6251, -1, 7299, -1], 'generators': [3, 172, 6], 'label': '432.624.36.k1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '36.k1.b1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575137
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.c1', '12.g1.a1', '12.h1.c1'], 'contains': ['72.d1.c1', '108.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6547, -1, 6673, -1, 6251, -1, 5595, -1], 'generators': [3, 340, 6], 'label': '432.624.36.k1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '36.k1.c1', 'projective_image': '216.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575138
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.a1.a1'], 'contains': ['72.f1.a1', '72.i1.a1', '108.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5686, -1, 7301, -1, 5139, -1, 7076, -1], 'generators': [222, 252, 168], 'label': '432.624.36.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.l1.a1', 'projective_image': '144.129', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575139
    {'ambient': '432.624', 'aut_centralizer_order': 144, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.b1.a1'], 'contains': ['72.g1.a1', '72.j1.a1', '108.e1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5123, -1, 6908, -1, 5533, -1, 6805, -1], 'generators': [222, 252, 24], 'label': '432.624.36.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.m1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575140
    {'ambient': '432.624', 'aut_centralizer_order': 72, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.h1.a1'], 'contains': ['72.h1.a1', '72.k1.a1', '108.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': '36T562', 'count': 6, 'diagramx': [4662, -1, 4252, -1, 4745, -1, 5818, -1], 'generators': [222, 252, 144], 'label': '432.624.36.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.n1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575141
    {'ambient': '432.624', 'aut_centralizer_order': 72, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.k1.a1', '12.k1.b1', '12.k1.c1', '18.h1.a1'], 'contains': ['72.h1.a1', '108.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3031, -1, 2384, -1, 1137, -1, 2228, -1], 'generators': [252, 216, 144], 'label': '432.624.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.o1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66575142
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.c1', '12.j1.a1', '12.k1.a1', '12.k1.b1', '18.i1.a1'], 'contains': ['108.a1.a1', '144.e1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [71, -1, 996, -1, 169, -1, 803, -1], 'generators': [292, 252, 216], 'label': '432.624.36.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.p1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575143
    {'ambient': '432.624', 'aut_centralizer_order': 3, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.192', 'aut_weyl_index': 12, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '12.g1.a1', '12.h1.a1', '12.h1.b1', '12.h1.c1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6510, -1, 7760, -1, 5823, -1, 6749, -1], 'generators': [3, 24, 4, 144, 6], 'label': '432.624.4.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '4.b1.a1', 'projective_image': '72.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66575144
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.j1.a1', '12.k1.a1', '12.k1.c1', '18.i1.b1'], 'contains': ['108.a1.a1', '144.e1.b1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [71, -1, 492, -1, 169, -1, 1098, -1], 'generators': [148, 252, 216], 'label': '432.624.36.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.p1.b1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575145
    {'ambient': '432.624', 'aut_centralizer_order': 12, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.j1.a1', '12.k1.b1', '12.k1.c1', '18.i1.c1'], 'contains': ['108.a1.a1', '144.e1.c1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [71, -1, 319, -1, 169, -1, 584, -1], 'generators': [28, 252, 216], 'label': '432.624.36.p1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.p1.c1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66575146
    {'ambient': '432.624', 'aut_centralizer_order': 432, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '2.a1.a1', 'complements': ['9.c1.a1', '9.c1.b1', '9.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.f1.a1', '24.g1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '144.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6351, 6374, 7205, 6863, 4826, 5088, 6242, 7400], 'generators': [144, 24], 'label': '432.624.48.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.b1.a1', '24.a1.a1'], 'normal_contains': ['144.a1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '144.129', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.13', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575147
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '16.a1.a1', '24.b1.a1'], 'contains': ['144.a1.a1', '144.d1.a1', '144.d1.b1', '144.d1.c1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2093, -1, 3519, -1, 1687, -1, 3227, -1], 'generators': [4, 168], 'label': '432.624.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.b1.a1', 'projective_image': '144.129', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575148
    {'ambient': '432.624', 'aut_centralizer_order': 18, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '16.a1.a1', '24.c1.a1'], 'contains': ['144.a1.a1', '144.e1.a1', '144.e1.b1', '144.e1.c1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1201, -1, 1148, -1, 975, -1, 1503, -1], 'generators': [28, 168], 'label': '432.624.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '144.129', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575149
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '16.a1.a1', '24.d1.a1'], 'contains': ['144.b1.a1', '144.d1.a1', '144.e1.c1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [982, -1, 4523, -1, 1449, -1, 2845, -1], 'generators': [4, 24], 'label': '432.624.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.d1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575150
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '16.a1.a1', '24.d1.b1'], 'contains': ['144.b1.a1', '144.d1.b1', '144.e1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [982, -1, 2615, -1, 1449, -1, 3466, -1], 'generators': [148, 24], 'label': '432.624.48.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.d1.b1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575151
    {'ambient': '432.624', 'aut_centralizer_order': 36, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.c1', '16.a1.a1', '24.d1.c1'], 'contains': ['144.b1.a1', '144.d1.c1', '144.e1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [982, -1, 3391, -1, 1449, -1, 2443, -1], 'generators': [292, 24], 'label': '432.624.48.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.d1.c1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66575152
    {'ambient': '432.624', 'aut_centralizer_order': 18, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '16.a1.a1', '24.e1.a1'], 'contains': ['144.c1.a1', '144.d1.a1', '144.e1.a1', '144.e1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [622, -1, 2743, -1, 1212, -1, 1993, -1], 'generators': [4, 144], 'label': '432.624.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.e1.a1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66575153
    {'ambient': '432.624', 'aut_centralizer_order': 18, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.b1', '16.a1.a1', '24.e1.b1'], 'contains': ['144.c1.a1', '144.d1.b1', '144.e1.a1', '144.e1.c1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [622, -1, 2103, -1, 1212, -1, 1667, -1], 'generators': [28, 144], 'label': '432.624.48.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.e1.b1', 'projective_image': '432.624', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}