Abstract group data - 432.354

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 36, 'aut_gen_orders': [6, 2, 4, 2, 36], 'aut_gens': [[1, 6, 216], [217, 138, 216], [1, 222, 216], [163, 426, 324], [325, 6, 216], [175, 6, 216]], 'aut_group': '3456.rl', 'aut_hash': 8949063060183674827, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3456, 'aut_permdeg': 72, 'aut_perms': [3108098226062547656163773775752907145219557479098548509344089005248157587827217517977349415193951110239, 1105185179356109173975863683792108631108011745940816645500432546423972724845089167698528457812, 53746304526495215425825969999500177241755482581765812151617259402091162043357400334845310860305222898987, 9206069298840326857780766702460158376171718704459906769290051174524422690073136960237357935518456968946, 5408001406647989706311608753492607519858416056321830530041252226795350665161935057202809853460223510969], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 18, 4, 1], [3, 2, 1, 1], [3, 3, 1, 2], [4, 2, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 3, 1, 2], [6, 3, 2, 2], [6, 18, 4, 2], [9, 6, 1, 3], [12, 2, 4, 1], [12, 6, 2, 2], [18, 6, 1, 3], [18, 6, 2, 3], [36, 6, 4, 3]], 'aut_supersolvable': True, 'aut_tex': 'C_6^2.(D_4\\times D_6)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 18, 'autcentquo_group': '108.26', 'autcentquo_hash': 26, 'autcentquo_nilpotent': False, 'autcentquo_order': 108, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_{18}:C_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 18, 4], [3, 2, 1], [3, 3, 2], [4, 2, 2], [6, 2, 3], [6, 3, 6], [6, 18, 8], [9, 6, 3], [12, 2, 4], [12, 6, 4], [18, 6, 9], [36, 6, 12]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '108.26', 'commutator_count': 1, 'commutator_label': '18.2', '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': 354, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['216.54', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 18, 1, 4], [3, 2, 1, 1], [3, 3, 2, 1], [4, 2, 1, 2], [6, 2, 1, 3], [6, 3, 2, 3], [6, 18, 2, 4], [9, 6, 1, 1], [9, 6, 2, 1], [12, 2, 2, 2], [12, 6, 2, 2], [18, 6, 1, 3], [18, 6, 2, 3], [36, 6, 2, 2], [36, 6, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6552, 'exponent': 36, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': '72.48', 'hash': 354, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [6, 18, 1], 'inner_gens': [[1, 66, 216], [157, 6, 216], [1, 6, 216]], 'inner_hash': 26, 'inner_nilpotent': False, 'inner_order': 108, 'inner_split': False, 'inner_tex': 'C_{18}:C_6', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 30], [6, 8]], 'label': '432.354', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D36:C6', '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': 31, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 62, 'number_divisions': 38, 'number_normal_subgroups': 62, 'number_subgroup_autclasses': 78, 'number_subgroup_classes': 170, 'number_subgroups': 782, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 75], [3, 8], [4, 4], [6, 168], [9, 18], [12, 32], [18, 54], [36, 72]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [54, 54, 2, 0], 'outer_gens': [[55, 6, 324], [55, 6, 216], [325, 174, 216], [55, 222, 216]], 'outer_group': '32.27', 'outer_hash': 27, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [414, 288, 40319, 23056], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\wr C_2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 14], [4, 8], [6, 4], [8, 2], [12, 2]], 'representations': {'PC': {'code': 7814399692962205374615554739907841702, 'gens': [1, 3, 7], 'pres': [7, -2, -3, -2, -2, -3, -3, -2, 14, 1388, 828, 58, 3699, 2194, 80, 1684, 1691, 137, 6053]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [1166413, 1104817, 47305, 46801, 46981, 47089, 886483]}, 'Perm': {'d': 15, 'gens': [14377673526, 127, 295, 19255587120, 126, 113527451520, 195128564400]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{36}:C_6', 'transitive_degree': 72, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 105199255
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 354, 'group_order': 432, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 105199266
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 354, 'group_order': 432, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 216, 'size': 1}
  • id: 105199277
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 354, 'group_order': 432, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 324, 'size': 1}
  • id: 105199288
    {'aut_label': '2C', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 354, 'group_order': 432, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 108, 'size': 1}
  • id: 105199299
    {'aut_label': '2D', 'centralizer': '18.b1', 'counter': 5, 'group_counter': 354, 'group_order': 432, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 3, 'size': 18}
  • id: 105199310
    {'aut_label': '2D', 'centralizer': '18.b1', 'counter': 6, 'group_counter': 354, 'group_order': 432, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 219, 'size': 18}
  • id: 105199314
    {'aut_label': '2D', 'centralizer': '18.b1', 'counter': 7, 'group_counter': 354, 'group_order': 432, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 153, 'size': 18}
  • id: 105199315
    {'aut_label': '2D', 'centralizer': '18.b1', 'counter': 8, 'group_counter': 354, 'group_order': 432, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 369, 'size': 18}
  • id: 105199316
    {'aut_label': '3A', 'centralizer': '2.b1', 'counter': 9, 'group_counter': 354, 'group_order': 432, 'label': '3A', 'order': 3, 'powers': [9, 1], 'representative': 144, 'size': 2}
  • id: 105199256
    {'aut_label': '3B1', 'centralizer': '3.b1', 'counter': 10, 'group_counter': 354, 'group_order': 432, 'label': '3B1', 'order': 3, 'powers': [11, 1], 'representative': 4, 'size': 3}
  • id: 105199257
    {'aut_label': '3B-1', 'centralizer': '3.b1', 'counter': 11, 'group_counter': 354, 'group_order': 432, 'label': '3B-1', 'order': 3, 'powers': [10, 1], 'representative': 2, 'size': 3}
  • id: 105199258
    {'aut_label': '4A', 'centralizer': '2.b1', 'counter': 12, 'group_counter': 354, 'group_order': 432, 'label': '4A', 'order': 4, 'powers': [4, 12], 'representative': 54, 'size': 2}
  • id: 105199259
    {'aut_label': '4A', 'centralizer': '2.b1', 'counter': 13, 'group_counter': 354, 'group_order': 432, 'label': '4B', 'order': 4, 'powers': [4, 13], 'representative': 270, 'size': 2}
  • id: 105199260
    {'aut_label': '6A', 'centralizer': '2.b1', 'counter': 14, 'group_counter': 354, 'group_order': 432, 'label': '6A', 'order': 6, 'powers': [9, 2], 'representative': 288, 'size': 2}
  • id: 105199261
    {'aut_label': '6A', 'centralizer': '2.b1', 'counter': 15, 'group_counter': 354, 'group_order': 432, 'label': '6B', 'order': 6, 'powers': [9, 3], 'representative': 252, 'size': 2}
  • id: 105199262
    {'aut_label': '6C', 'centralizer': '2.b1', 'counter': 16, 'group_counter': 354, 'group_order': 432, 'label': '6C', 'order': 6, 'powers': [9, 4], 'representative': 36, 'size': 2}
  • id: 105199263
    {'aut_label': '6D1', 'centralizer': '3.b1', 'counter': 17, 'group_counter': 354, 'group_order': 432, 'label': '6D1', 'order': 6, 'powers': [10, 2], 'representative': 218, 'size': 3}
  • id: 105199264
    {'aut_label': '6D-1', 'centralizer': '3.b1', 'counter': 18, 'group_counter': 354, 'group_order': 432, 'label': '6D-1', 'order': 6, 'powers': [11, 2], 'representative': 220, 'size': 3}
  • id: 105199265
    {'aut_label': '6D1', 'centralizer': '3.b1', 'counter': 19, 'group_counter': 354, 'group_order': 432, 'label': '6E1', 'order': 6, 'powers': [10, 3], 'representative': 254, 'size': 3}
  • id: 105199267
    {'aut_label': '6D-1', 'centralizer': '3.b1', 'counter': 20, 'group_counter': 354, 'group_order': 432, 'label': '6E-1', 'order': 6, 'powers': [11, 3], 'representative': 256, 'size': 3}
  • id: 105199268
    {'aut_label': '6F1', 'centralizer': '3.b1', 'counter': 21, 'group_counter': 354, 'group_order': 432, 'label': '6F1', 'order': 6, 'powers': [11, 4], 'representative': 40, 'size': 3}
  • id: 105199269
    {'aut_label': '6F-1', 'centralizer': '3.b1', 'counter': 22, 'group_counter': 354, 'group_order': 432, 'label': '6F-1', 'order': 6, 'powers': [10, 4], 'representative': 182, 'size': 3}
  • id: 105199270
    {'aut_label': '6G1', 'centralizer': '18.b1', 'counter': 23, 'group_counter': 354, 'group_order': 432, 'label': '6G1', 'order': 6, 'powers': [11, 5], 'representative': 1, 'size': 18}
  • id: 105199271
    {'aut_label': '6G-1', 'centralizer': '18.b1', 'counter': 24, 'group_counter': 354, 'group_order': 432, 'label': '6G-1', 'order': 6, 'powers': [10, 5], 'representative': 5, 'size': 18}
  • id: 105199272
    {'aut_label': '6G1', 'centralizer': '18.b1', 'counter': 25, 'group_counter': 354, 'group_order': 432, 'label': '6H1', 'order': 6, 'powers': [11, 6], 'representative': 217, 'size': 18}
  • id: 105199273
    {'aut_label': '6G-1', 'centralizer': '18.b1', 'counter': 26, 'group_counter': 354, 'group_order': 432, 'label': '6H-1', 'order': 6, 'powers': [10, 6], 'representative': 221, 'size': 18}
  • id: 105199274
    {'aut_label': '6G1', 'centralizer': '18.b1', 'counter': 27, 'group_counter': 354, 'group_order': 432, 'label': '6I1', 'order': 6, 'powers': [11, 7], 'representative': 7, 'size': 18}
  • id: 105199275
    {'aut_label': '6G-1', 'centralizer': '18.b1', 'counter': 28, 'group_counter': 354, 'group_order': 432, 'label': '6I-1', 'order': 6, 'powers': [10, 7], 'representative': 11, 'size': 18}
  • id: 105199276
    {'aut_label': '6G1', 'centralizer': '18.b1', 'counter': 29, 'group_counter': 354, 'group_order': 432, 'label': '6J1', 'order': 6, 'powers': [11, 8], 'representative': 223, 'size': 18}
  • id: 105199278
    {'aut_label': '6G-1', 'centralizer': '18.b1', 'counter': 30, 'group_counter': 354, 'group_order': 432, 'label': '6J-1', 'order': 6, 'powers': [10, 8], 'representative': 227, 'size': 18}
  • id: 105199279
    {'aut_label': '9A', 'centralizer': '6.c1', 'counter': 31, 'group_counter': 354, 'group_order': 432, 'label': '9A', 'order': 9, 'powers': [31, 9], 'representative': 48, 'size': 6}
  • id: 105199280
    {'aut_label': '9B1', 'centralizer': '6.f1', 'counter': 32, 'group_counter': 354, 'group_order': 432, 'label': '9B1', 'order': 9, 'powers': [33, 9], 'representative': 124, 'size': 6}
  • id: 105199281
    {'aut_label': '9B-1', 'centralizer': '6.f1', 'counter': 33, 'group_counter': 354, 'group_order': 432, 'label': '9B-1', 'order': 9, 'powers': [32, 9], 'representative': 170, 'size': 6}
  • id: 105199282
    {'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 34, 'group_counter': 354, 'group_order': 432, 'label': '12A1', 'order': 12, 'powers': [16, 12], 'representative': 18, 'size': 2}
  • id: 105199283
    {'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 35, 'group_counter': 354, 'group_order': 432, 'label': '12A5', 'order': 12, 'powers': [16, 12], 'representative': 90, 'size': 2}
  • id: 105199284
    {'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 36, 'group_counter': 354, 'group_order': 432, 'label': '12B1', 'order': 12, 'powers': [16, 13], 'representative': 234, 'size': 2}
  • id: 105199285
    {'aut_label': '12A1', 'centralizer': '2.b1', 'counter': 37, 'group_counter': 354, 'group_order': 432, 'label': '12B5', 'order': 12, 'powers': [16, 13], 'representative': 306, 'size': 2}
  • id: 105199286
    {'aut_label': '12C1', 'centralizer': '6.b1', 'counter': 38, 'group_counter': 354, 'group_order': 432, 'label': '12C1', 'order': 12, 'powers': [21, 12], 'representative': 20, 'size': 6}
  • id: 105199287
    {'aut_label': '12C-1', 'centralizer': '6.b1', 'counter': 39, 'group_counter': 354, 'group_order': 432, 'label': '12C-1', 'order': 12, 'powers': [22, 12], 'representative': 22, 'size': 6}
  • id: 105199289
    {'aut_label': '12C1', 'centralizer': '6.b1', 'counter': 40, 'group_counter': 354, 'group_order': 432, 'label': '12D1', 'order': 12, 'powers': [21, 13], 'representative': 236, 'size': 6}
  • id: 105199290
    {'aut_label': '12C-1', 'centralizer': '6.b1', 'counter': 41, 'group_counter': 354, 'group_order': 432, 'label': '12D-1', 'order': 12, 'powers': [22, 13], 'representative': 238, 'size': 6}
  • id: 105199291
    {'aut_label': '18A', 'centralizer': '6.c1', 'counter': 42, 'group_counter': 354, 'group_order': 432, 'label': '18A', 'order': 18, 'powers': [31, 14], 'representative': 240, 'size': 6}
  • id: 105199292
    {'aut_label': '18A', 'centralizer': '6.c1', 'counter': 43, 'group_counter': 354, 'group_order': 432, 'label': '18B', 'order': 18, 'powers': [31, 15], 'representative': 228, 'size': 6}
  • id: 105199293
    {'aut_label': '18C', 'centralizer': '6.c1', 'counter': 44, 'group_counter': 354, 'group_order': 432, 'label': '18C', 'order': 18, 'powers': [31, 16], 'representative': 12, 'size': 6}
  • id: 105199294
    {'aut_label': '18D1', 'centralizer': '6.f1', 'counter': 45, 'group_counter': 354, 'group_order': 432, 'label': '18D1', 'order': 18, 'powers': [32, 14], 'representative': 242, 'size': 6}
  • id: 105199295
    {'aut_label': '18D-1', 'centralizer': '6.f1', 'counter': 46, 'group_counter': 354, 'group_order': 432, 'label': '18D-1', 'order': 18, 'powers': [33, 14], 'representative': 244, 'size': 6}
  • id: 105199296
    {'aut_label': '18D1', 'centralizer': '6.f1', 'counter': 47, 'group_counter': 354, 'group_order': 432, 'label': '18E1', 'order': 18, 'powers': [32, 15], 'representative': 230, 'size': 6}
  • id: 105199297
    {'aut_label': '18D-1', 'centralizer': '6.f1', 'counter': 48, 'group_counter': 354, 'group_order': 432, 'label': '18E-1', 'order': 18, 'powers': [33, 15], 'representative': 232, 'size': 6}
  • id: 105199298
    {'aut_label': '18F1', 'centralizer': '6.f1', 'counter': 49, 'group_counter': 354, 'group_order': 432, 'label': '18F1', 'order': 18, 'powers': [33, 16], 'representative': 88, 'size': 6}
  • id: 105199300
    {'aut_label': '18F-1', 'centralizer': '6.f1', 'counter': 50, 'group_counter': 354, 'group_order': 432, 'label': '18F-1', 'order': 18, 'powers': [32, 16], 'representative': 206, 'size': 6}
  • id: 105199301
    {'aut_label': '36A1', 'centralizer': '6.c1', 'counter': 51, 'group_counter': 354, 'group_order': 432, 'label': '36A1', 'order': 36, 'powers': [44, 34], 'representative': 6, 'size': 6}
  • id: 105199302
    {'aut_label': '36A1', 'centralizer': '6.c1', 'counter': 52, 'group_counter': 354, 'group_order': 432, 'label': '36A5', 'order': 36, 'powers': [44, 35], 'representative': 30, 'size': 6}
  • id: 105199303
    {'aut_label': '36A1', 'centralizer': '6.c1', 'counter': 53, 'group_counter': 354, 'group_order': 432, 'label': '36B1', 'order': 36, 'powers': [44, 36], 'representative': 222, 'size': 6}
  • id: 105199304
    {'aut_label': '36A1', 'centralizer': '6.c1', 'counter': 54, 'group_counter': 354, 'group_order': 432, 'label': '36B5', 'order': 36, 'powers': [44, 37], 'representative': 246, 'size': 6}
  • id: 105199305
    {'aut_label': '36C1', 'centralizer': '6.f1', 'counter': 55, 'group_counter': 354, 'group_order': 432, 'label': '36C1', 'order': 36, 'powers': [49, 34], 'representative': 8, 'size': 6}
  • id: 105199306
    {'aut_label': '36C-1', 'centralizer': '6.f1', 'counter': 56, 'group_counter': 354, 'group_order': 432, 'label': '36C-1', 'order': 36, 'powers': [50, 34], 'representative': 10, 'size': 6}
  • id: 105199307
    {'aut_label': '36C-1', 'centralizer': '6.f1', 'counter': 57, 'group_counter': 354, 'group_order': 432, 'label': '36C5', 'order': 36, 'powers': [50, 35], 'representative': 34, 'size': 6}
  • id: 105199308
    {'aut_label': '36C1', 'centralizer': '6.f1', 'counter': 58, 'group_counter': 354, 'group_order': 432, 'label': '36C-5', 'order': 36, 'powers': [49, 35], 'representative': 32, 'size': 6}
  • id: 105199309
    {'aut_label': '36C1', 'centralizer': '6.f1', 'counter': 59, 'group_counter': 354, 'group_order': 432, 'label': '36D1', 'order': 36, 'powers': [49, 36], 'representative': 224, 'size': 6}
  • id: 105199311
    {'aut_label': '36C-1', 'centralizer': '6.f1', 'counter': 60, 'group_counter': 354, 'group_order': 432, 'label': '36D-1', 'order': 36, 'powers': [50, 36], 'representative': 226, 'size': 6}
  • id: 105199312
    {'aut_label': '36C-1', 'centralizer': '6.f1', 'counter': 61, 'group_counter': 354, 'group_order': 432, 'label': '36D5', 'order': 36, 'powers': [50, 37], 'representative': 250, 'size': 6}
  • id: 105199313
    {'aut_label': '36C1', 'centralizer': '6.f1', 'counter': 62, 'group_counter': 354, 'group_order': 432, 'label': '36D-5', 'order': 36, 'powers': [49, 37], 'representative': 248, 'size': 6}
• 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: 3356188
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1a', '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], 'schur_index': 1}
  • id: 3356199
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1b', '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], 'schur_index': 1}
  • id: 3356210
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 3356220
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 3356221
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 3356222
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3356223
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3356224
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3356225
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1i', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 3356189
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, -2, 2, 2, -1, -1, 2, -2, -2, -2, 2, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -2, -2, -1, -1, 1, 1, -2, 1, 1, 1, -1, -2, 2, 1, -1, 1, -1, -2, -1, 2, 1, 2, -1, 1, -2, -1, 1], 'schur_index': 1}
  • id: 3356190
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1k', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, 2, -2, 2, -1, -1, -2, 2, -2, -2, 2, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 2, -1, -1, -2, -2, 2, 2, 1, 1, -1, -1, -2, 1, 1, 1, -1, -2, 2, 1, -1, -1, 1, 2, 1, -2, -1, -2, 1, -1, 2, 1, -1], 'schur_index': 1}
  • id: 3356191
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1l', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, -2, 2, 2, -1, -1, -2, 2, -2, -2, 2, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 2, -1, -1, -2, -2, 2, 2, 1, 1, -1, -1, -2, 1, 1, 1, -1, -2, 2, 1, -1, -1, 1, 2, 1, -2, -1, -2, 1, -1, 2, 1, -1], 'schur_index': 1}
  • id: 3356192
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1m', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, 2, -2, 2, -1, -1, 2, -2, -2, -2, 2, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 2, -1, -1, 2, 2, -2, -2, -1, -1, 1, 1, -2, 1, 1, 1, -1, -2, 2, 1, -1, 1, -1, -2, -1, 2, 1, 2, -1, 1, -2, -1, 1], 'schur_index': 1}
  • id: 3356193
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1n', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 2, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 2, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 3356194
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1o', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 2, -1, -1, -2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 2, -1, -1, -2, -2, -2, -2, 1, 1, 1, 1, 2, -1, -1, -1, -1, 2, 2, -1, -1, 1, 1, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1], 'schur_index': 1}
  • id: 3356195
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.1p', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, 2, -1, -1, -2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 2, -1, -1, -2, -2, -2, -2, 1, 1, 1, 1, 2, -1, -1, -1, -1, 2, 2, -1, -1, 1, 1, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1], 'schur_index': 1}
  • id: 3356196
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -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: 3356197
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, 0, 0, 2, 2, 2, 0, 0, -2, 2, -2, -2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, -2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356198
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, -2, -2, 2, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356200
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 2, -2, 2, -2, -2, 2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -2, -2, 2, 2, -2, -2, 2, 2, 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: 3356201
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 2, -2, -2, 2, 2, -2, -2, 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: 3356202
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -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: 3356203
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2g', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 4, -2, -2, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 4, 4, 4, 4, -2, -2, -2, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1], 'schur_index': 1}
  • id: 3356204
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2h', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 4, 4, 4, 0, 0, -4, 4, -4, -4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356205
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2i', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 4, 4, 4, 0, 0, 4, -4, -4, 4, -4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356206
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2j', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 4, -2, -2, 0, 0, -4, 4, -4, 2, -2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 2, 2, 2, -4, -4, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356207
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2k', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 4, -2, -2, 0, 0, 4, -4, -4, -2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, -2, -2, 2, 4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356208
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2l', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 4, -2, -2, -4, 4, -4, -4, 4, 2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -4, -4, 4, 4, 2, 2, -2, -2, 2, -1, -1, -1, 1, 2, -2, -1, 1, 1, -1, -2, -1, 2, 1, 2, -1, 1, -2, -1, 1], 'schur_index': 1}
  • id: 3356209
    {'cdim': 2, 'counter': 29, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2m', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 4, -2, -2, 4, -4, -4, -4, 4, 2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 4, 4, -4, -4, -2, -2, 2, 2, 2, -1, -1, -1, 1, 2, -2, -1, 1, -1, 1, 2, 1, -2, -1, -2, 1, -1, 2, 1, -1], 'schur_index': 1}
  • id: 3356211
    {'cdim': 2, 'counter': 30, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2n', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 4, -2, -2, -4, -4, 4, 4, 4, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -4, -4, -4, -4, 2, 2, 2, 2, -2, 1, 1, 1, 1, -2, -2, 1, 1, -1, -1, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 3356214
    {'cdim': 6, 'counter': 33, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.6a', 'multiplicity': 1, 'nt': [9, 10], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 0, -3, 0, 0, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356215
    {'cdim': 6, 'counter': 34, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.6b', 'multiplicity': 1, 'nt': [18, 45], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, 0, 0, -3, 0, 0, -6, 6, 3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356216
    {'cdim': 6, 'counter': 35, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.6c', 'multiplicity': 1, 'nt': [18, 45], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, 0, 0, -3, 0, 0, 6, -6, 3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356217
    {'cdim': 6, 'counter': 36, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.6d', 'multiplicity': 1, 'nt': [18, 45], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 0, -3, 0, 0, -6, -6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356212
    {'cdim': 2, 'counter': 31, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2o', 'multiplicity': 4, 'nt': [24, 67], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 8, -4, -4, 0, 0, -8, 8, -8, 4, -4, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, -2, -2, -2, 4, 4, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356213
    {'cdim': 2, 'counter': 32, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.2p', 'multiplicity': 4, 'nt': [24, 67], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, 8, -4, -4, 0, 0, 8, -8, -8, -4, 4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 2, 2, -2, -4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356218
    {'cdim': 6, 'counter': 37, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.6e', 'multiplicity': 2, 'nt': [36, 215], 'qdim': 12, 'qvalues': [12, -12, 12, -12, 0, 0, 0, 0, -6, 0, 0, 0, 0, 6, -6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356219
    {'cdim': 6, 'counter': 38, 'faithful': False, 'group': '432.354', 'group_order': 432, 'image': None, 'label': '432.354.6f', 'multiplicity': 2, 'nt': [36, 215], 'qdim': 12, 'qvalues': [12, 12, -12, -12, 0, 0, 0, 0, -6, 0, 0, 0, 0, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 4605353
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 432, 'label': '432.354.1a', '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]]]}
  • id: 4605364
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 216, 'label': '432.354.1b', '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]]]}
  • id: 4605375
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 216, 'label': '432.354.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 4605386
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 216, 'label': '432.354.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 4605397
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 216, 'label': '432.354.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 4605408
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 216, 'label': '432.354.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 4605412
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 216, 'label': '432.354.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 4605413
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 216, 'label': '432.354.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 4605414
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 144, 'label': '432.354.1i1', '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, 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, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]]]}
  • id: 4605354
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 144, 'label': '432.354.1i2', '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, 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, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]]]}
  • id: 4605355
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 72, 'label': '432.354.1j1', '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, 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, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-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, 0]], [[-1, -1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]]]}
  • id: 4605356
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 72, 'label': '432.354.1j2', '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, 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, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-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, 0]], [[-1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[1, -1]], [[-1, -1]]]}
  • id: 4605357
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 72, 'label': '432.354.1k1', '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, 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, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-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, 0]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]]]}
  • id: 4605358
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 72, 'label': '432.354.1k2', '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, 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, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-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, 0]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[1, -1]], [[1, 0]], [[-1, -1]], [[1, -1]]]}
  • id: 4605359
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 72, 'label': '432.354.1l1', '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, 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, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-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, 0]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]]]}
  • id: 4605360
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 72, 'label': '432.354.1l2', '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, 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, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-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, 0]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[1, -1]], [[1, 0]], [[-1, -1]], [[1, -1]]]}
  • id: 4605361
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 72, 'label': '432.354.1m1', '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, 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, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-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, 0]], [[-1, -1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]]]}
  • id: 4605362
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 72, 'label': '432.354.1m2', '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, 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, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-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, 0]], [[-1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[1, -1]], [[-1, -1]]]}
  • id: 4605363
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 19, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1', 'kernel_order': 72, 'label': '432.354.1n1', '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, 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, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]]]}
  • id: 4605365
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 20, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1', 'kernel_order': 72, 'label': '432.354.1n2', '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, 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, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]]]}
  • id: 4605366
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 21, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 72, 'label': '432.354.1o1', '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, 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, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[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, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]]]}
  • id: 4605367
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 22, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 72, 'label': '432.354.1o2', '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, 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, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[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, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]]]}
  • id: 4605368
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 23, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 72, 'label': '432.354.1p1', '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, 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, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[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, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]]]}
  • id: 4605369
    {'center': '1.a1', 'center_index': 1, 'center_order': 432, 'counter': 24, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 72, 'label': '432.354.1p2', '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, 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, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[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, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]]]}
  • id: 4605370
    {'center': '6.b1', 'center_index': 6, 'center_order': 72, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1', 'kernel_order': 72, 'label': '432.354.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 4605371
    {'center': '4.a1', 'center_index': 4, 'center_order': 108, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 54, 'label': '432.354.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[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: 4605372
    {'center': '4.a1', 'center_index': 4, 'center_order': 108, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 54, 'label': '432.354.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[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: 4605373
    {'center': '6.b1', 'center_index': 6, 'center_order': 72, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1', 'kernel_order': 36, 'label': '432.354.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-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: 4605374
    {'center': '6.b1', 'center_index': 6, 'center_order': 72, 'counter': 29, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1', 'kernel_order': 36, 'label': '432.354.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[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: 4605376
    {'center': '6.b1', 'center_index': 6, 'center_order': 72, 'counter': 30, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 36, 'label': '432.354.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 4605377
    {'center': '6.b1', 'center_index': 6, 'center_order': 72, 'counter': 31, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1', 'kernel_order': 24, 'label': '432.354.2g1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-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, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]]]}
  • id: 4605378
    {'center': '6.b1', 'center_index': 6, 'center_order': 72, 'counter': 32, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1', 'kernel_order': 24, 'label': '432.354.2g2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-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, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]]]}
  • id: 4605379
    {'center': '12.a1', 'center_index': 12, 'center_order': 36, 'counter': 33, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 18, 'label': '432.354.2h1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[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: 4605380
    {'center': '12.a1', 'center_index': 12, 'center_order': 36, 'counter': 34, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 18, 'label': '432.354.2h2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-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: 4605381
    {'center': '12.a1', 'center_index': 12, 'center_order': 36, 'counter': 35, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 18, 'label': '432.354.2i1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-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: 4605382
    {'center': '12.a1', 'center_index': 12, 'center_order': 36, 'counter': 36, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 18, 'label': '432.354.2i2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[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: 4605383
    {'center': '4.a1', 'center_index': 4, 'center_order': 108, 'counter': 37, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1', 'kernel_order': 18, 'label': '432.354.2j1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605384
    {'center': '4.a1', 'center_index': 4, 'center_order': 108, 'counter': 38, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1', 'kernel_order': 18, 'label': '432.354.2j2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, -1]], [[2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605385
    {'center': '4.a1', 'center_index': 4, 'center_order': 108, 'counter': 39, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1', 'kernel_order': 18, 'label': '432.354.2k1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605387
    {'center': '4.a1', 'center_index': 4, 'center_order': 108, 'counter': 40, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1', 'kernel_order': 18, 'label': '432.354.2k2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, -1]], [[-2, -1]], [[2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605388
    {'center': '6.b1', 'center_index': 6, 'center_order': 72, 'counter': 41, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1', 'kernel_order': 12, 'label': '432.354.2l1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 1]], [[-2, -1]], [[2, 1]], [[2, -1]], [[1, 0]], [[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, 0]], [[-1, -1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]]]}
  • id: 4605389
    {'center': '6.b1', 'center_index': 6, 'center_order': 72, 'counter': 42, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1', 'kernel_order': 12, 'label': '432.354.2l2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, -1]], [[-2, 1]], [[2, -1]], [[2, 1]], [[1, 0]], [[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, 0]], [[-1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[1, -1]], [[-1, -1]]]}
  • id: 4605390
    {'center': '6.b1', 'center_index': 6, 'center_order': 72, 'counter': 43, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1', 'kernel_order': 12, 'label': '432.354.2m1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 1]], [[2, -1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[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, 0]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]]]}
  • id: 4605391
    {'center': '6.b1', 'center_index': 6, 'center_order': 72, 'counter': 44, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1', 'kernel_order': 12, 'label': '432.354.2m2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, -1]], [[2, 1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[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, 0]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[1, -1]], [[1, 0]], [[-1, -1]], [[1, -1]]]}
  • id: 4605392
    {'center': '6.b1', 'center_index': 6, 'center_order': 72, 'counter': 45, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1', 'kernel_order': 12, 'label': '432.354.2n1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-1, 0]], [[-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, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]]]}
  • id: 4605393
    {'center': '6.b1', 'center_index': 6, 'center_order': 72, 'counter': 46, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1', 'kernel_order': 12, 'label': '432.354.2n2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-1, 0]], [[-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, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]]]}
  • id: 4605394
    {'center': '12.a1', 'center_index': 12, 'center_order': 36, 'counter': 47, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 6, 'label': '432.354.2o1', 'nt': [24, 67], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 2]], [[2, 4]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 4]], [[2, 4]], [[2, 2]], [[-2, 4]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, 4]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, 3]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[-1, 1], [2, 3]], [[-1, 1], [-1, -1]], [[1, 1], [-2, 3]], [[1, 1], [-2, 3]]]}
  • id: 4605395
    {'center': '12.a1', 'center_index': 12, 'center_order': 36, 'counter': 48, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 6, 'label': '432.354.2o2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 4]], [[-2, 2]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 2]], [[-2, 2]], [[-2, 4]], [[2, 2]], [[-2, 4]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 0]], [[1, 0]], [[-1, 4]], [[-1, 2]], [[-1, 1], [2, 3]], [[1, 1], [-2, 3]], [[1, 1], [1, -1]], [[-1, 1], [2, 3]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, 3]], [[1, 1], [1, 3]]]}
  • id: 4605396
    {'center': '12.a1', 'center_index': 12, 'center_order': 36, 'counter': 49, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 6, 'label': '432.354.2o3', 'nt': [24, 67], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 2]], [[2, 4]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 4]], [[2, 4]], [[2, 2]], [[-2, 4]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, 4]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[1, 1], [-2, 3]], [[1, 1], [1, -1]], [[-1, 1], [2, 3]], [[-1, 1], [2, 3]]]}
  • id: 4605398
    {'center': '12.a1', 'center_index': 12, 'center_order': 36, 'counter': 50, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 6, 'label': '432.354.2o4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 4]], [[-2, 2]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 2]], [[-2, 2]], [[-2, 4]], [[2, 2]], [[-2, 4]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 0]], [[1, 0]], [[-1, 4]], [[-1, 2]], [[1, 1], [-2, 3]], [[-1, 1], [2, 3]], [[-1, 1], [-1, -1]], [[1, 1], [-2, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 4605399
    {'center': '12.a1', 'center_index': 12, 'center_order': 36, 'counter': 51, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 6, 'label': '432.354.2p1', 'nt': [24, 67], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 2]], [[2, 4]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 4]], [[-2, 4]], [[-2, 2]], [[-2, 4]], [[2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, 3]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[-1, 1], [2, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[1, 1], [-2, 3]]]}
  • id: 4605400
    {'center': '12.a1', 'center_index': 12, 'center_order': 36, 'counter': 52, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 6, 'label': '432.354.2p2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 4]], [[-2, 2]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 2]], [[2, 2]], [[2, 4]], [[2, 2]], [[-2, 4]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 1], [2, 3]], [[-1, 1], [2, 3]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[-1, 1], [-1, -1]], [[1, 1], [-2, 3]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 4605401
    {'center': '12.a1', 'center_index': 12, 'center_order': 36, 'counter': 53, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 6, 'label': '432.354.2p3', 'nt': [24, 67], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 2]], [[2, 4]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 4]], [[-2, 4]], [[-2, 2]], [[-2, 4]], [[2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[1, 1], [-2, 3]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[-1, 1], [2, 3]]]}
  • id: 4605402
    {'center': '12.a1', 'center_index': 12, 'center_order': 36, 'counter': 54, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 6, 'label': '432.354.2p4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 4]], [[-2, 2]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 2]], [[2, 2]], [[2, 4]], [[2, 2]], [[-2, 4]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 1], [-2, 3]], [[1, 1], [-2, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[1, 1], [1, -1]], [[-1, 1], [2, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 4605403
    {'center': '54.a1', 'center_index': 54, 'center_order': 8, 'counter': 55, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '54.6', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1', 'kernel_order': 8, 'label': '432.354.6a', 'nt': [9, 10], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[0, 0]], [[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: 4605404
    {'center': '54.a1', 'center_index': 54, 'center_order': 8, 'counter': 56, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.b1', 'kernel_order': 4, 'label': '432.354.6b', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[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: 4605405
    {'center': '54.a1', 'center_index': 54, 'center_order': 8, 'counter': 57, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.b1', 'kernel_order': 4, 'label': '432.354.6c', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[0, 0]], [[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: 4605406
    {'center': '54.a1', 'center_index': 54, 'center_order': 8, 'counter': 58, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 4, 'label': '432.354.6d', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[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: 4605407
    {'center': '108.a1', 'center_index': 108, 'center_order': 4, 'counter': 59, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '216.54', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 2, 'label': '432.354.6e1', 'nt': [36, 215], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[3, 1], [3, -1]], [[3, 1], [3, -1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605409
    {'center': '108.a1', 'center_index': 108, 'center_order': 4, 'counter': 60, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '216.54', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 2, 'label': '432.354.6e2', 'nt': [36, 215], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[-3, 1], [-3, -1]], [[-3, 1], [-3, -1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605410
    {'center': '108.a1', 'center_index': 108, 'center_order': 4, 'counter': 61, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '216.54', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 2, 'label': '432.354.6f1', 'nt': [36, 215], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[3, 1], [3, -1]], [[-3, 1], [-3, -1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605411
    {'center': '108.a1', 'center_index': 108, 'center_order': 4, 'counter': 62, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '432.354', 'group_counter': 354, 'group_order': 432, 'image': None, 'image_isoclass': '216.54', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 2, 'label': '432.354.6f2', 'nt': [36, 215], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[-3, 1], [-3, -1]], [[3, 1], [3, -1]], [[-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]], [[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: 58381804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 432, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '432.354.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, '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': '432.354', 'subgroup_hash': 354, 'subgroup_order': 432, 'subgroup_tex': 'D_{36}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.111', 'subgroup_hash': 111, 'subgroup_order': 216, 'subgroup_tex': 'D_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 216, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, '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': ['F', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.75', 'subgroup_hash': 75, 'subgroup_order': 216, 'subgroup_tex': 'C_{18}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.354.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.54', 'subgroup_hash': 54, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 144, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.3.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1', 'outer_equivalence': True, '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': '144.39', 'subgroup_hash': 39, 'subgroup_order': 144, 'subgroup_tex': 'C_2\\times D_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 58381859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.3.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1', 'outer_equivalence': True, 'perfect': False, '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': '144.160', 'subgroup_hash': 160, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 108, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.31', 'subgroup_hash': 31, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 108, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.14', 'subgroup_hash': 14, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, '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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381806
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.17', 'subgroup_hash': 17, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381807
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 72, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, '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': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381808
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 72, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.c1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 58381809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.6', 'subgroup_hash': 6, 'subgroup_order': 72, 'subgroup_tex': 'D_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 58381810
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, '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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381811
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, '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': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 58381812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, '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': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 54, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, '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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381819
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 36, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 58381820
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 36, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381822
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381823
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 27, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.354.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 58381824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, '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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381827
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, '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': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381829
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.354.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, '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': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 58381830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 27, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '432.354.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 3}
  • id: 58381831
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 24, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1', 'outer_equivalence': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381832
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, '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: 58381833
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381834
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, '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: 58381835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381838
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381839
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 41, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.354.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381840
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 18, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381841
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 18, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.354.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.15', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381842
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 44, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.354.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381843
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 45, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.354.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381844
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381845
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.24.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, '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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 58381846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '432.354.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 2}
  • id: 58381847
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 12, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381849
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 12, 'counter': 50, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.354.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381850
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, '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: 58381851
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381852
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, '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: 58381853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, '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: 58381854
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381855
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.354.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, '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: 58381856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 9, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.36', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 58381857
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 9, 'counter': 58, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.354.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.45', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 58381858
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.354.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, '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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 58381860
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 8, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9:C_6', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, '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: 58381861
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 58381862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381863
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 63, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.354.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{12}', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381864
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 6, 'counter': 64, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.354.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.48', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], '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: 58381865
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.354.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, '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: 58381866
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.354.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, '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: 58381867
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.354.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, '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: 58381868
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381869
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 4, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.354.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}:C_6', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 58381871
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 4, 'counter': 70, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.354.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381872
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, '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: 58381873
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.354.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, 'perfect': False, '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: 58381874
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 3, 'counter': 73, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.354.144.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '144.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.160', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 160, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_{12}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381875
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.354.144.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.b1', 'outer_equivalence': True, 'perfect': False, '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: 58381876
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 75, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '432.354.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.54', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 54, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{36}:C_6', 'simple': True, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 58381877
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 2, 'counter': 76, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.354.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.111', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 111, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{18}:C_6', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 58381878
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.354.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1', 'outer_equivalence': True, 'perfect': False, '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: 58381879
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.354', 'ambient_counter': 354, 'ambient_order': 432, 'ambient_tex': 'D_{36}:C_6', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 1, 'counter': 78, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '432.354.432.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '432.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '432.354', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 354, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{36}:C_6', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 58381818
    {'ambient': '432.354', 'aut_centralizer_order': 3, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.12882', 'aut_weyl_index': 9, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '3.b1'], 'contains': ['18.a1', '18.c1', '18.f1', '27.a1'], 'core': '18.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9106, -1, 6377, -1], 'generators': [3, 72, 162, 216, 108], 'label': '432.354.9.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '9.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 58381804
    {'ambient': '432.354', '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': '108.a1', 'complements': ['432.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '3.a1', '3.b1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6874, 7107, 4240, 5561], 'generators': [3, 96, 108, 54, 72, 216, 2], 'label': '432.354.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '3.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 58381805
    {'ambient': '432.354', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '108.26', 'aut_weyl_index': 32, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.c1', '12.f1', '12.g1'], 'core': '8.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1606, -1, 731, -1], 'generators': [141, 72, 216, 2, 96], 'label': '432.354.4.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.d1', 'projective_image': '216.54', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381806
    {'ambient': '432.354', 'aut_centralizer_order': 4, 'aut_label': '6.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '432.362', 'aut_weyl_index': 8, 'centralizer': '108.a1', 'complements': ['72.e1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.b1', '12.c1', '12.g1', '18.c1'], 'core': '6.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4935, 6685, 1356, 7797], 'generators': [213, 72, 108, 216, 96], 'label': '432.354.6.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1', '3.a1'], 'normal_contains': ['12.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '108.26', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 58381807
    {'ambient': '432.354', 'aut_centralizer_order': 72, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.38', 'aut_weyl_index': 72, 'centralizer': '6.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.b1'], 'contains': ['12.a1', '12.d1', '18.a1', '18.d1'], 'core': '6.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7892, 4637, 7006, 673], 'generators': [162, 108, 216, 2, 72], 'label': '432.354.6.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['12.a1', '12.d1', '18.a1'], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': '108.26', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381808
    {'ambient': '432.354', 'aut_centralizer_order': 72, 'aut_label': '6.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.45', 'aut_weyl_index': 72, 'centralizer': '6.c1', 'complements': ['72.e1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.b1', '12.e1', '18.a1'], 'core': '6.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6726, 8403, 3335, 2185], 'generators': [54, 72, 216, 168, 108], 'label': '432.354.6.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1', 'normal_contained_in': ['2.b1', '3.a1'], 'normal_contains': ['12.b1', '12.e1', '18.a1'], 'normalizer': '1.a1', 'old_label': '6.c1', 'projective_image': '108.26', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381809
    {'ambient': '432.354', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '432.362', 'aut_weyl_index': 8, 'centralizer': '108.a1', 'complements': ['72.c1', '72.e1'], 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.c1', '12.e1', '18.f1'], 'core': '6.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [7388, 9491, 3818, 4903], 'generators': [3, 72, 54, 108, 96], 'label': '432.354.6.d1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1', 'normal_contained_in': ['2.c1', '3.a1'], 'normal_contains': ['12.c1', '12.e1'], 'normalizer': '1.a1', 'old_label': '6.d1', 'projective_image': '216.111', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 58381810
    {'ambient': '432.354', 'aut_centralizer_order': 12, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 72, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.b1'], 'contains': ['12.a1', '12.f1', '12.i1', '18.b1', '18.c1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5824, -1, 5660, -1], 'generators': [141, 72, 108, 216, 2], 'label': '432.354.6.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.e1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 58381811
    {'ambient': '432.354', 'aut_centralizer_order': 72, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.10', 'aut_weyl_index': 144, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['12.h1', '12.j1', '18.a1'], 'core': '18.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4138, -1, 4302, -1], 'generators': [162, 72, 216, 170, 108], 'label': '432.354.6.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '6.f1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381812
    {'ambient': '432.354', 'aut_centralizer_order': 6, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.38', 'aut_weyl_index': 72, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '3.b1'], 'contains': ['12.d1', '12.i1', '18.e1', '18.f1'], 'core': '12.d1', 'coset_action_label': None, 'count': 12, 'diagramx': [8701, -1, 7635, -1], 'generators': [3, 72, 162, 2, 108], 'label': '432.354.6.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.g1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 58381813
    {'ambient': '432.354', 'aut_centralizer_order': 96, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '18.3', 'aut_weyl_index': 192, 'centralizer': '18.a1', 'complements': ['54.c1'], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.d1'], 'contains': ['16.a1', '24.a1', '24.b1', '24.e1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [817, 1114, 627, 9188], 'generators': [216, 2, 168, 72], 'label': '432.354.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.a1', '24.a1', '24.b1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '216.54', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 58381814
    {'ambient': '432.354', 'aut_centralizer_order': 192, 'aut_label': '8.b1', 'aut_quo_index': 21, 'aut_stab_index': 1, 'aut_weyl_group': '18.3', 'aut_weyl_index': 192, 'centralizer': '18.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['16.a1', '24.c1', '24.d1', '24.f1'], 'core': '8.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2620, 2953, 3216, 6813], 'generators': [108, 2, 168, 72], 'label': '432.354.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1'], 'normal_contains': ['16.a1', '24.c1', '24.d1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 58381815
    {'ambient': '432.354', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '432.362', 'aut_weyl_index': 8, 'centralizer': '108.a1', 'complements': ['216.c1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.d1', '6.a1', '6.e1'], 'core': '2.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4575, 4465, 2361, 7722], 'generators': [141, 72, 96, 108, 216, 2], 'label': '432.354.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 58381816
    {'ambient': '432.354', 'aut_centralizer_order': 8, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '54.6', 'aut_weyl_index': 64, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.d1'], 'contains': ['16.a1', '24.g1', '24.h1'], 'core': '16.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1347, -1, 1126, -1], 'generators': [141, 2, 96, 72], 'label': '432.354.8.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.c1', 'projective_image': '432.354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381817
    {'ambient': '432.354', 'aut_centralizer_order': 6, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.138', 'aut_weyl_index': 54, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['18.b1', '18.d1', '18.e1', '27.a1'], 'core': '54.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9892, -1, 8621, -1], 'generators': [3, 108, 54, 216, 2], 'label': '432.354.9.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 58381819
    {'ambient': '432.354', 'aut_centralizer_order': 288, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '6.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.b1', '6.e1'], 'contains': ['24.a1', '24.c1', '36.a1', '36.e1'], 'core': '12.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5096, 2435, 5487, 4142], 'generators': [108, 216, 2, 72], 'label': '432.354.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.b1'], 'normal_contains': ['24.a1', '24.c1', '36.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '108.26', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381820
    {'ambient': '432.354', 'aut_centralizer_order': 288, 'aut_label': '12.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 288, 'centralizer': '6.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.a1', '6.c1'], 'contains': ['24.b1', '24.d1', '36.a1'], 'core': '12.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4603, 5562, 1617, 5283], 'generators': [108, 216, 168, 72], 'label': '432.354.12.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1', 'normal_contained_in': ['4.a1', '6.a1', '6.c1'], 'normal_contains': ['24.b1', '24.d1', '36.a1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '108.26', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381821
    {'ambient': '432.354', 'aut_centralizer_order': 8, 'aut_label': '12.c1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 32, 'centralizer': '108.a1', 'complements': ['36.c1'], 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '6.a1', '6.d1'], 'contains': ['24.d1', '24.h1', '36.g1'], 'core': '12.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [3590, 6986, 2100, 8001], 'generators': [213, 108, 96, 72], 'label': '432.354.12.c1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1', 'normal_contained_in': ['4.b1', '6.a1', '6.d1'], 'normal_contains': ['24.d1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '216.111', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 58381822
    {'ambient': '432.354', 'aut_centralizer_order': 144, 'aut_label': '12.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '6.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.b1', '6.g1'], 'contains': ['24.c1', '36.b1', '36.h1'], 'core': '12.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [7712, 4154, 7443, 2185], 'generators': [162, 2, 72, 108], 'label': '432.354.12.d1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1', 'normal_contained_in': ['4.c1', '6.b1'], 'normal_contains': ['24.c1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.d1', 'projective_image': '216.111', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381823
    {'ambient': '432.354', 'aut_centralizer_order': 144, 'aut_label': '12.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 288, 'centralizer': '6.c1', 'complements': ['36.c1'], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.c1', '6.d1'], 'contains': ['24.d1', '36.b1'], 'core': '12.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [6646, 7858, 3704, 3353], 'generators': [54, 168, 108, 72], 'label': '432.354.12.e1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.e1', 'normal_contained_in': ['4.c1', '6.c1', '6.d1'], 'normal_contains': ['24.d1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.e1', 'projective_image': '216.111', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381824
    {'ambient': '432.354', 'aut_centralizer_order': 12, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '6.e1'], 'contains': ['24.a1', '24.g1', '36.c1', '36.d1'], 'core': '24.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2953, -1, 4471, -1], 'generators': [141, 216, 2, 72], 'label': '432.354.12.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '12.f1', 'projective_image': '216.54', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381825
    {'ambient': '432.354', 'aut_centralizer_order': 4, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '108.26', 'aut_weyl_index': 32, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '6.a1'], 'contains': ['24.b1', '24.h1', '36.d1'], 'core': '24.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1362, -1, 136, -1], 'generators': [213, 216, 96, 72], 'label': '432.354.12.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.g1', 'projective_image': '216.54', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381826
    {'ambient': '432.354', 'aut_centralizer_order': 24, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.162', 'aut_weyl_index': 24, 'centralizer': '18.a1', 'complements': ['216.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '6.b1', '6.c1', '6.f1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6077, 6322, 4240, 3020], 'generators': [54, 72, 108, 216, 2, 168], 'label': '432.354.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '6.b1', '6.c1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 58381827
    {'ambient': '432.354', 'aut_centralizer_order': 288, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 576, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.f1'], 'contains': ['24.e1', '24.f1', '36.a1'], 'core': '36.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2327, -1, 2583, -1], 'generators': [108, 216, 170, 72], 'label': '432.354.12.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '12.h1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381828
    {'ambient': '432.354', 'aut_centralizer_order': 24, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '6.e1', '6.g1'], 'contains': ['24.c1', '24.g1', '36.f1', '36.g1'], 'core': '24.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [5533, -1, 5905, -1], 'generators': [141, 108, 2, 72], 'label': '432.354.12.i1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.i1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 58381829
    {'ambient': '432.354', 'aut_centralizer_order': 144, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.2', 'aut_weyl_index': 576, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.f1'], 'contains': ['24.f1', '36.b1'], 'core': '36.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4098, -1, 4041, -1], 'generators': [162, 170, 108, 72], 'label': '432.354.12.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '12.j1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381830
    {'ambient': '432.354', 'aut_centralizer_order': 192, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '18.3', 'aut_weyl_index': 192, 'centralizer': '18.a1', 'complements': ['27.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1'], 'contains': ['48.a1', '48.b1', '48.c1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [437, 1027, 2238, 8316], 'generators': [2, 168], 'label': '432.354.16.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1'], 'normal_contains': ['48.a1', '48.b1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '432.354', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 58381831
    {'ambient': '432.354', 'aut_centralizer_order': 216, 'aut_label': '18.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 216, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.c1', '6.f1', '9.b1'], 'contains': ['36.a1', '36.b1', '54.a1'], 'core': '18.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7055, 7125, 6477, 673], 'generators': [162, 216, 72, 108], 'label': '432.354.18.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1', 'normal_contained_in': ['6.b1', '6.c1'], 'normal_contains': ['36.a1', '36.b1', '54.a1'], 'normalizer': '1.a1', 'old_label': '18.a1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381832
    {'ambient': '432.354', 'aut_centralizer_order': 24, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 432, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.e1', '9.a1'], 'contains': ['36.c1', '36.e1', '36.f1', '54.b1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7852, -1, 8057, -1], 'generators': [141, 108, 216, 146], 'label': '432.354.18.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381833
    {'ambient': '432.354', 'aut_centralizer_order': 12, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 72, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.e1', '9.b1'], 'contains': ['36.a1', '36.d1', '36.g1', '54.b1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5957, -1, 5031, -1], 'generators': [213, 108, 216, 72], 'label': '432.354.18.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.c1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 58381834
    {'ambient': '432.354', 'aut_centralizer_order': 144, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 432, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '9.a1'], 'contains': ['36.e1', '36.h1', '54.a1'], 'core': '54.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9006, -1, 9197, -1], 'generators': [54, 216, 2, 108], 'label': '432.354.18.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.d1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381835
    {'ambient': '432.354', 'aut_centralizer_order': 12, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 432, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.g1', '9.a1'], 'contains': ['36.f1', '36.h1', '54.c1'], 'core': '108.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9763, -1, 9772, -1], 'generators': [3, 54, 2, 108], 'label': '432.354.18.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.e1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 58381836
    {'ambient': '432.354', 'aut_centralizer_order': 6, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.38', 'aut_weyl_index': 72, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.d1', '6.g1', '9.b1'], 'contains': ['36.b1', '36.g1', '54.c1'], 'core': '36.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [8345, -1, 6960, -1], 'generators': [3, 162, 108, 72], 'label': '432.354.18.f1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.f1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 58381837
    {'ambient': '432.354', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '432.362', 'aut_weyl_index': 8, 'centralizer': '108.a1', 'complements': ['216.a1', '216.c1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '6.d1', '6.g1'], 'core': '2.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [6874, 7884, 4935, 6220], 'generators': [3, 72, 96, 54, 2, 108], 'label': '432.354.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '6.d1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '216.111', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 58381858
    {'ambient': '432.354', 'aut_centralizer_order': 576, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '3.1', 'aut_weyl_index': 1152, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.e1', '24.f1'], 'contains': ['144.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [108, -1, 2921, -1], 'generators': [170], 'label': '432.354.48.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '48.c1', 'projective_image': '432.354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381838
    {'ambient': '432.354', 'aut_centralizer_order': 288, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '6.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.a1', '12.f1'], 'contains': ['48.a1', '72.a1', '72.c1'], 'core': '24.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2648, 509, 3964, 6443], 'generators': [216, 2, 72], 'label': '432.354.24.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1'], 'normal_contains': ['48.a1', '72.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '216.54', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381839
    {'ambient': '432.354', 'aut_centralizer_order': 288, 'aut_label': '24.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 576, 'centralizer': '6.c1', 'complements': ['18.e1'], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.b1', '12.g1'], 'contains': ['48.b1', '72.a1'], 'core': '24.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1314, 2133, 1617, 7481], 'generators': [216, 168, 72], 'label': '432.354.24.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': ['8.a1', '12.b1'], 'normal_contains': ['48.b1', '72.a1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '216.54', 'quotient_action_image': '6.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381840
    {'ambient': '432.354', 'aut_centralizer_order': 576, 'aut_label': '24.c1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '6.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '12.a1', '12.d1', '12.i1'], 'contains': ['48.a1', '72.b1', '72.d1'], 'core': '24.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4916, 3101, 5806, 4365], 'generators': [108, 2, 72], 'label': '432.354.24.c1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.c1', 'normal_contained_in': ['8.b1', '12.a1', '12.d1'], 'normal_contains': ['48.a1', '72.b1'], 'normalizer': '1.a1', 'old_label': '24.c1', 'projective_image': '216.111', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381841
    {'ambient': '432.354', 'aut_centralizer_order': 576, 'aut_label': '24.d1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 576, 'centralizer': '6.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '12.b1', '12.c1', '12.e1'], 'contains': ['48.b1', '72.b1'], 'core': '24.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [3946, 4448, 2921, 5404], 'generators': [108, 168, 72], 'label': '432.354.24.d1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '24.d1', 'normal_contained_in': ['8.b1', '12.b1', '12.c1', '12.e1'], 'normal_contains': ['48.b1', '72.b1'], 'normalizer': '1.a1', 'old_label': '24.d1', 'projective_image': '216.111', 'quotient_action_image': '6.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381842
    {'ambient': '432.354', 'aut_centralizer_order': 288, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '3.1', 'aut_weyl_index': 1152, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.h1'], 'contains': ['48.c1', '72.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [304, -1, 2583, -1], 'generators': [216, 170, 72], 'label': '432.354.24.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '24.e1', 'projective_image': '216.54', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381843
    {'ambient': '432.354', 'aut_centralizer_order': 576, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '3.1', 'aut_weyl_index': 1152, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '12.h1', '12.j1'], 'contains': ['48.c1', '72.b1'], 'core': '72.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2047, -1, 3259, -1], 'generators': [108, 170, 72], 'label': '432.354.24.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '24.f1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381844
    {'ambient': '432.354', 'aut_centralizer_order': 24, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '12.f1', '12.i1'], 'contains': ['48.a1', '72.e1', '72.f1'], 'core': '48.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3193, -1, 4486, -1], 'generators': [141, 2, 72], 'label': '432.354.24.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '24.g1', 'projective_image': '432.354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381845
    {'ambient': '432.354', 'aut_centralizer_order': 8, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '54.6', 'aut_weyl_index': 64, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '12.c1', '12.g1'], 'contains': ['48.b1', '72.f1'], 'core': '48.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [993, -1, 1924, -1], 'generators': [213, 96, 72], 'label': '432.354.24.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.h1', 'projective_image': '432.354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381846
    {'ambient': '432.354', 'aut_centralizer_order': 6, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.138', 'aut_weyl_index': 54, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.b1'], 'contains': ['54.a1', '54.b1', '54.c1'], 'core': '54.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9459, -1, 8621, -1], 'generators': [3, 54, 216], 'label': '432.354.27.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '27.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 58381847
    {'ambient': '432.354', 'aut_centralizer_order': 864, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.b1', '12.h1', '18.a1', '18.c1'], 'contains': ['72.a1', '72.b1', '108.a1'], 'core': '36.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4407, 4507, 5008, 3103], 'generators': [108, 216, 72], 'label': '432.354.36.a1', 'mobius_quo': -2, 'mobius_sub': 6, 'normal_closure': '36.a1', 'normal_contained_in': ['12.a1', '12.b1', '18.a1'], 'normal_contains': ['72.a1', '72.b1', '108.a1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381848
    {'ambient': '432.354', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '3456.rl', 'aut_weyl_index': 1, 'centralizer': '108.a1', 'complements': ['144.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.c1', '6.d1', '9.b1'], 'core': '3.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7423, 8567, 3462, 4903], 'generators': [3, 72, 96, 54, 216, 108], 'label': '432.354.3.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.a1', '6.c1', '6.d1'], 'normalizer': '1.a1', 'old_label': '3.a1', 'projective_image': '108.26', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 58381849
    {'ambient': '432.354', 'aut_centralizer_order': 432, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.e1', '12.j1', '18.a1', '18.f1'], 'contains': ['72.b1', '108.b1'], 'core': '36.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6490, 5475, 6235, 2064], 'generators': [162, 72, 108], 'label': '432.354.36.b1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.b1', 'normal_contained_in': ['12.d1', '12.e1', '18.a1'], 'normal_contains': ['72.b1', '108.b1'], 'normalizer': '1.a1', 'old_label': '36.b1', 'projective_image': '216.111', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381850
    {'ambient': '432.354', 'aut_centralizer_order': 24, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.f1', '18.b1'], 'contains': ['72.c1', '72.e1', '108.c1'], 'core': '216.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5107, -1, 6665, -1], 'generators': [141, 216, 146], 'label': '432.354.36.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '36.c1', 'projective_image': '216.54', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381851
    {'ambient': '432.354', 'aut_centralizer_order': 12, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.f1', '12.g1', '18.c1'], 'contains': ['72.a1', '72.f1', '108.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2436, -1, 3566, -1], 'generators': [213, 216, 72], 'label': '432.354.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '36.d1', 'projective_image': '216.54', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381852
    {'ambient': '432.354', 'aut_centralizer_order': 576, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '18.b1', '18.d1'], 'contains': ['72.c1', '72.d1', '108.a1'], 'core': '108.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6939, -1, 7501, -1], 'generators': [108, 216, 2], 'label': '432.354.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.e1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381853
    {'ambient': '432.354', 'aut_centralizer_order': 48, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.i1', '18.b1', '18.e1'], 'contains': ['72.d1', '72.e1', '108.d1'], 'core': '216.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [7484, -1, 8023, -1], 'generators': [141, 108, 146], 'label': '432.354.36.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.f1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381854
    {'ambient': '432.354', 'aut_centralizer_order': 24, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.c1', '12.i1', '18.c1', '18.f1'], 'contains': ['72.b1', '72.f1', '108.d1'], 'core': '72.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5524, -1, 5407, -1], 'generators': [213, 108, 72], 'label': '432.354.36.g1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.g1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 58381855
    {'ambient': '432.354', 'aut_centralizer_order': 288, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '18.d1', '18.e1'], 'contains': ['72.d1', '108.b1'], 'core': '108.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8638, -1, 9250, -1], 'generators': [54, 2, 108], 'label': '432.354.36.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.h1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381856
    {'ambient': '432.354', 'aut_centralizer_order': 576, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '6.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.a1', '24.c1', '24.g1'], 'contains': ['144.a1', '144.b1'], 'core': '48.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2740, 1260, 4513, 6266], 'generators': [2, 72], 'label': '432.354.48.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': ['16.a1', '24.a1', '24.c1'], 'normal_contains': ['144.a1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '432.354', 'quotient_action_image': '6.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381857
    {'ambient': '432.354', 'aut_centralizer_order': 576, 'aut_label': '48.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 576, 'centralizer': '6.c1', 'complements': ['9.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.b1', '24.d1', '24.h1'], 'contains': ['144.a1'], 'core': '48.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [937, 1943, 2238, 7296], 'generators': [168], 'label': '432.354.48.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': ['16.a1', '24.b1', '24.d1'], 'normal_contains': ['144.a1'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '432.354', 'quotient_action_image': '6.2', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381859
    {'ambient': '432.354', 'aut_centralizer_order': 3, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.12882', 'aut_weyl_index': 9, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.b1', '6.e1', '6.g1', '9.a1', '9.b1'], 'core': '6.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9006, -1, 6692, -1], 'generators': [3, 72, 108, 162, 216, 2], 'label': '432.354.3.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '3.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 58381860
    {'ambient': '432.354', 'aut_centralizer_order': 432, 'aut_label': '54.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 432, 'centralizer': '2.b1', 'complements': ['8.c1'], 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.d1', '27.a1'], 'contains': ['108.a1', '108.b1'], 'core': '54.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8561, 6209, 8545, 1025], 'generators': [54, 216], 'label': '432.354.54.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.a1', 'normal_contained_in': ['18.a1'], 'normal_contains': ['108.a1', '108.b1'], 'normalizer': '1.a1', 'old_label': '54.a1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '27.4', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381861
    {'ambient': '432.354', 'aut_centralizer_order': 24, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 432, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1', '18.c1', '27.a1'], 'contains': ['108.a1', '108.c1', '108.d1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7027, -1, 7083, -1], 'generators': [213, 108, 216], 'label': '432.354.54.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381862
    {'ambient': '432.354', 'aut_centralizer_order': 12, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.3', 'aut_weyl_index': 432, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.e1', '18.f1', '27.a1'], 'contains': ['108.b1', '108.d1'], 'core': '108.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9042, -1, 8943, -1], 'generators': [3, 54], 'label': '432.354.54.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.c1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 58381863
    {'ambient': '432.354', 'aut_centralizer_order': 864, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '24.b1', '24.e1', '36.a1', '36.d1'], 'contains': ['144.a1', '216.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2347, 2435, 3941, 5237], 'generators': [216, 72], 'label': '432.354.72.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': ['24.a1', '24.b1', '36.a1'], 'normal_contains': ['144.a1', '216.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '216.54', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.8', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381864
    {'ambient': '432.354', 'aut_centralizer_order': 1728, 'aut_label': '72.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.d1', '24.f1', '36.a1', '36.b1', '36.g1'], 'contains': ['144.a1', '216.b1'], 'core': '72.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4046, 3886, 5207, 4225], 'generators': [108, 72], 'label': '432.354.72.b1', 'mobius_quo': 1, 'mobius_sub': -24, 'normal_closure': '72.b1', 'normal_contained_in': ['24.c1', '24.d1', '36.a1', '36.b1'], 'normal_contains': ['144.a1', '216.b1'], 'normalizer': '1.a1', 'old_label': '72.b1', 'projective_image': '216.111', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.14', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381865
    {'ambient': '432.354', 'aut_centralizer_order': 576, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '36.c1', '36.e1'], 'contains': ['144.b1', '216.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5112, -1, 6389, -1], 'generators': [216, 2], 'label': '432.354.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.c1', 'projective_image': '216.54', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381866
    {'ambient': '432.354', 'aut_centralizer_order': 1152, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '36.e1', '36.f1', '36.h1'], 'contains': ['144.b1', '216.b1'], 'core': '216.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6318, -1, 7570, -1], 'generators': [108, 2], 'label': '432.354.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.d1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381867
    {'ambient': '432.354', 'aut_centralizer_order': 48, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.g1', '36.c1', '36.f1'], 'contains': ['144.b1', '216.c1'], 'core': '432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4695, -1, 6665, -1], 'generators': [141, 146], 'label': '432.354.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '72.e1', 'projective_image': '432.354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381868
    {'ambient': '432.354', 'aut_centralizer_order': 24, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.g1', '24.h1', '36.d1', '36.g1'], 'contains': ['144.a1', '216.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2912, -1, 4218, -1], 'generators': [213, 72], 'label': '432.354.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '72.f1', 'projective_image': '432.354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381869
    {'ambient': '432.354', 'aut_centralizer_order': 1728, 'aut_label': '108.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.e1', '54.a1', '54.b1'], 'contains': ['216.a1', '216.b1'], 'core': '108.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5921, 4733, 6960, 3242], 'generators': [108, 216], 'label': '432.354.108.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '108.a1', 'normal_contained_in': ['36.a1', '54.a1'], 'normal_contains': ['216.a1', '216.b1'], 'normalizer': '1.a1', 'old_label': '108.a1', 'projective_image': '108.26', 'quotient_action_image': '1.1', 'quotient_action_kernel': '108.26', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381870
    {'ambient': '432.354', 'aut_centralizer_order': 96, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '36.12', 'aut_weyl_index': 96, 'centralizer': '18.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b1', '12.a1', '12.b1', '12.h1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3125, 2850, 2020, 6192], 'generators': [108, 72, 216, 2, 168], 'label': '432.354.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b1', '12.a1', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 58381871
    {'ambient': '432.354', 'aut_centralizer_order': 864, 'aut_label': '108.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.b1', 'complements': ['4.d1'], 'conjugacy_class_count': 2, 'contained_in': ['36.b1', '36.h1', '54.a1', '54.c1'], 'contains': ['216.b1'], 'core': '108.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8212, 5458, 8545, 2064], 'generators': [54], 'label': '432.354.108.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '108.b1', 'normal_contained_in': ['36.b1', '54.a1'], 'normal_contains': ['216.b1'], 'normalizer': '1.a1', 'old_label': '108.b1', 'projective_image': '216.111', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.11', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381872
    {'ambient': '432.354', 'aut_centralizer_order': 24, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.c1', '36.d1', '54.b1'], 'contains': ['216.a1', '216.c1'], 'core': '216.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5392, -1, 6093, -1], 'generators': [213, 216], 'label': '432.354.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '108.c1', 'projective_image': '216.54', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381873
    {'ambient': '432.354', 'aut_centralizer_order': 48, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.f1', '36.g1', '54.b1', '54.c1'], 'contains': ['216.b1', '216.c1'], 'core': '216.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [6799, -1, 7275, -1], 'generators': [213, 108], 'label': '432.354.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.d1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381874
    {'ambient': '432.354', 'aut_centralizer_order': 1728, 'aut_label': '144.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '48.b1', '48.c1', '72.a1', '72.b1', '72.f1'], 'contains': ['432.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2583, 2435, 4218, 5237], 'generators': [72], 'label': '432.354.144.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': ['48.a1', '48.b1', '72.a1', '72.b1'], 'normal_contains': ['432.a1'], 'normalizer': '1.a1', 'old_label': '144.a1', 'projective_image': '432.354', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.36', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381875
    {'ambient': '432.354', 'aut_centralizer_order': 1152, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '72.c1', '72.d1', '72.e1'], 'contains': ['432.a1'], 'core': '432.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4731, -1, 6653, -1], 'generators': [2], 'label': '432.354.144.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.b1', 'projective_image': '432.354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381876
    {'ambient': '432.354', 'aut_centralizer_order': 1728, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '1.a1', 'complements': ['2.c1'], 'conjugacy_class_count': 2, 'contained_in': ['72.a1', '72.c1', '108.a1', '108.c1'], 'contains': ['432.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5240, 3739, 6101, 4559], 'generators': [216], 'label': '432.354.216.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': ['72.a1', '108.a1'], 'normal_contains': ['432.a1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '216.54', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.54', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381877
    {'ambient': '432.354', 'aut_centralizer_order': 3456, 'aut_label': '216.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.b1', '72.d1', '108.a1', '108.b1', '108.d1'], 'contains': ['432.a1'], 'core': '216.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6105, 4507, 7117, 3873], 'generators': [108], 'label': '432.354.216.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.b1', 'normal_contained_in': ['72.b1', '108.a1', '108.b1'], 'normal_contains': ['432.a1'], 'normalizer': '1.a1', 'old_label': '216.b1', 'projective_image': '216.111', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.111', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381878
    {'ambient': '432.354', 'aut_centralizer_order': 48, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.e1', '72.f1', '108.c1', '108.d1'], 'contains': ['432.a1'], 'core': '432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4952, -1, 6377, -1], 'generators': [213], 'label': '432.354.216.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.c1', 'projective_image': '432.354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381879
    {'ambient': '432.354', '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', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '144.b1', '216.a1', '216.b1', '216.c1'], 'contains': [], 'core': '432.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4952, 3739, 6377, 4559], 'generators': [], 'label': '432.354.432.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '432.a1', 'normal_contained_in': ['144.a1', '216.a1', '216.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '432.a1', 'projective_image': '432.354', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381880
    {'ambient': '432.354', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 32, 'centralizer': '108.a1', 'complements': ['108.c1'], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '2.c1'], 'contains': ['8.b1', '8.c1', '12.c1', '12.i1'], 'core': '4.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4010, 4724, 2702, 9309], 'generators': [141, 72, 108, 2, 96], 'label': '432.354.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.c1'], 'normal_contains': ['8.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '216.111', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 58381881
    {'ambient': '432.354', 'aut_centralizer_order': 48, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 96, 'centralizer': '18.a1', 'complements': ['108.c1'], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.c1'], 'contains': ['8.b1', '12.d1', '12.e1', '12.j1'], 'core': '4.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6014, 6486, 4935, 3715], 'generators': [54, 72, 2, 168, 108], 'label': '432.354.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.b1', '2.c1'], 'normal_contains': ['8.b1', '12.d1', '12.e1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '216.111', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '18.3'}