Abstract group data - 12996.bc

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• gps_groups •

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

  
  {'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 684, 'aut_gen_orders': [18, 6, 38, 19], 'aut_gens': [[1, 6, 36, 684], [4969, 11190, 10944, 180], [3973, 7926, 432, 5472], [11035, 3498, 648, 684], [12961, 402, 36, 684]], 'aut_group': '77976.p', 'aut_hash': 6883077926354377314, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 77976, 'aut_permdeg': 152, 'aut_perms': [291178586244846694189938893218518790804617666096757472580932076603402712293582134954482154823594750035327516607696271733739459152970987331543509380442399536877984813605481383095817346911128656690899490751018922417847136418643129484521478306138893381969580484977684367, 353509197727097281137243774037839461381221164853645916456527608479231913038076924884387399773666858782339155360004662124435206574820339528451602476674684293144688172006716332303947268860103832076156894475497139245662244870564726855234641441007566980418994500673737635, 1286652237635616499397432129692456145662723641984847532823381184604094404049901222503488076664997463692891470894116725417935319940818513656507895681684113674618573104380045668811563078368997038289862236213898270179801868405525801590632010687354683173300878483160304705, 94554020659048641260565264800319131453019692772382756530214549986700758068211766753848351686911626880136941237999499991724036322941707110285417738631443903117687650663868096546547453705911791303152186032794759061295646793868560352858108381917709967817186893779046377], 'aut_phi_ratio': 19.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 57, 2, 1], [2, 361, 1, 1], [3, 38, 1, 2], [3, 361, 1, 2], [3, 722, 1, 1], [6, 361, 1, 2], [6, 722, 1, 3], [6, 1083, 2, 2], [19, 12, 3, 1], [19, 18, 6, 1], [19, 36, 6, 1], [38, 342, 6, 1], [57, 228, 3, 2]], 'aut_supersolvable': False, 'aut_tex': 'D_{19}^2:(S_3\\times C_9)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 684, 'autcentquo_group': '77976.p', 'autcentquo_hash': 6883077926354377314, 'autcentquo_nilpotent': False, 'autcentquo_order': 77976, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'D_{19}^2:(S_3\\times C_9)', 'cc_stats': [[1, 1, 1], [2, 57, 2], [2, 361, 1], [3, 38, 2], [3, 361, 2], [3, 722, 1], [6, 361, 2], [6, 722, 3], [6, 1083, 4], [19, 12, 3], [19, 18, 6], [19, 36, 6], [38, 342, 6], [57, 228, 6]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '12996.bc', 'commutator_count': 1, 'commutator_label': '1083.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '19.1', '19.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 29, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 57, 1, 2], [2, 361, 1, 1], [3, 38, 2, 1], [3, 361, 2, 1], [3, 722, 1, 1], [6, 361, 2, 1], [6, 722, 1, 1], [6, 722, 2, 1], [6, 1083, 2, 2], [19, 12, 3, 1], [19, 18, 3, 2], [19, 36, 3, 2], [38, 342, 3, 2], [57, 228, 6, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 480, 'exponent': 114, 'exponents_of_order': [2, 2, 2], 'factors_of_aut_order': [2, 3, 19], 'factors_of_order': [2, 3, 19], 'faithful_reps': [[12, 0, 6], [12, 1, 3], [18, 1, 12], [36, 1, 6]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '12996.bc', 'hash': None, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 114, 'inner_gen_orders': [6, 6, 19, 19], 'inner_gens': [[1, 66, 12312, 288], [301, 6, 432, 5472], [721, 294, 36, 684], [1081, 8214, 36, 684]], 'inner_hash': 8995592235010807521, 'inner_nilpotent': False, 'inner_order': 12996, 'inner_split': False, 'inner_tex': 'C_{19}^2:(C_6\\times S_3)', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 36, 'irrQ_dim': 36, 'irrR_degree': 12, 'irrep_stats': [[1, 12], [2, 6], [12, 9], [18, 12], [36, 6]], 'label': '12996.bc', 'linC_count': 9, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 36, 'linQ_degree_count': 1, 'linQ_dim': 36, 'linQ_dim_count': 1, 'linR_count': 3, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C19^2:(C6*S3)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 21, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 45, 'number_divisions': 20, 'number_normal_subgroups': 15, 'number_subgroup_autclasses': 62, 'number_subgroup_classes': 84, 'number_subgroups': 11940, 'old_label': None, 'order': 12996, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 475], [3, 1520], [6, 7220], [19, 360], [38, 2052], [57, 1368]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6], 'outer_gen_pows': [2072], 'outer_gens': [[5527, 7050, 6840, 144]], 'outer_group': '6.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 6, 'outer_permdeg': 5, 'outer_perms': [28], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 38, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 2], [36, 1], [54, 4], [72, 1], [108, 2]], 'representations': {'PC': {'code': '64709682252263437336336437127710462754249732215843580742470173293015', 'gens': [1, 3, 5, 6], 'pres': [6, -2, -3, -2, -3, -19, 19, 12, 1190, 113138, 50, 8355, 88713, 369364, 5950, 2176, 1012, 10373, 135443, 32849, 14387]}, 'Perm': {'d': 38, 'gens': [325760407756940772815106166399797493993544423, 522235454627554246724509260026334396876569944]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{19}^2:(C_6\\times S_3)', 'transitive_degree': 38, '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: 171588351
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 29, 'group_order': 12996, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 171588362
    {'aut_label': '2A', 'centralizer': '57.a1.a1', 'counter': 2, 'group_counter': 29, 'group_order': 12996, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 3063, 'size': 57}
  • id: 171588373
    {'aut_label': '2A', 'centralizer': '57.a1.b1', 'counter': 3, 'group_counter': 29, 'group_order': 12996, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 4353, 'size': 57}
  • id: 171588384
    {'aut_label': '2C', 'centralizer': '361.a1.a1', 'counter': 4, 'group_counter': 29, 'group_order': 12996, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 12762, 'size': 361}
  • id: 171588391
    {'aut_label': '3A1', 'centralizer': '38.a1.a1', 'counter': 5, 'group_counter': 29, 'group_order': 12996, 'label': '3A1', 'order': 3, 'powers': [6, 1, 5], 'representative': 7660, 'size': 38}
  • id: 171588392
    {'aut_label': '3A-1', 'centralizer': '38.a1.a1', 'counter': 6, 'group_counter': 29, 'group_order': 12996, 'label': '3A-1', 'order': 3, 'powers': [5, 1, 6], 'representative': 12794, 'size': 38}
  • id: 171588393
    {'aut_label': '3B1', 'centralizer': '361.a1.a1', 'counter': 7, 'group_counter': 29, 'group_order': 12996, 'label': '3B1', 'order': 3, 'powers': [8, 1, 7], 'representative': 8284, 'size': 361}
  • id: 171588394
    {'aut_label': '3B-1', 'centralizer': '361.a1.a1', 'counter': 8, 'group_counter': 29, 'group_order': 12996, 'label': '3B-1', 'order': 3, 'powers': [7, 1, 8], 'representative': 1262, 'size': 361}
  • id: 171588395
    {'aut_label': '3C', 'centralizer': '722.b1.a1', 'counter': 9, 'group_counter': 29, 'group_order': 12996, 'label': '3C', 'order': 3, 'powers': [9, 1, 9], 'representative': 2640, 'size': 722}
  • id: 171588352
    {'aut_label': '6A1', 'centralizer': '361.a1.a1', 'counter': 10, 'group_counter': 29, 'group_order': 12996, 'label': '6A1', 'order': 6, 'powers': [8, 4, 10], 'representative': 2146, 'size': 361}
  • id: 171588353
    {'aut_label': '6A-1', 'centralizer': '361.a1.a1', 'counter': 11, 'group_counter': 29, 'group_order': 12996, 'label': '6A-1', 'order': 6, 'powers': [7, 4, 11], 'representative': 11648, 'size': 361}
  • id: 171588354
    {'aut_label': '6B', 'centralizer': '722.b1.a1', 'counter': 12, 'group_counter': 29, 'group_order': 12996, 'label': '6B', 'order': 6, 'powers': [9, 4, 12], 'representative': 9258, 'size': 722}
  • id: 171588355
    {'aut_label': '6C1', 'centralizer': '722.b1.a1', 'counter': 13, 'group_counter': 29, 'group_order': 12996, 'label': '6C1', 'order': 6, 'powers': [5, 4, 13], 'representative': 11804, 'size': 722}
  • id: 171588356
    {'aut_label': '6C-1', 'centralizer': '722.b1.a1', 'counter': 14, 'group_counter': 29, 'group_order': 12996, 'label': '6C-1', 'order': 6, 'powers': [6, 4, 14], 'representative': 3934, 'size': 722}
  • id: 171588357
    {'aut_label': '6D1', 'centralizer': '1083.a1.a1', 'counter': 15, 'group_counter': 29, 'group_order': 12996, 'label': '6D1', 'order': 6, 'powers': [7, 3, 15], 'representative': 2339, 'size': 1083}
  • id: 171588358
    {'aut_label': '6D-1', 'centralizer': '1083.a1.a1', 'counter': 16, 'group_counter': 29, 'group_order': 12996, 'label': '6D-1', 'order': 6, 'powers': [8, 3, 16], 'representative': 6151, 'size': 1083}
  • id: 171588359
    {'aut_label': '6D1', 'centralizer': '1083.a1.a1', 'counter': 17, 'group_counter': 29, 'group_order': 12996, 'label': '6E1', 'order': 6, 'powers': [7, 2, 17], 'representative': 9653, 'size': 1083}
  • id: 171588360
    {'aut_label': '6D-1', 'centralizer': '1083.a1.a1', 'counter': 18, 'group_counter': 29, 'group_order': 12996, 'label': '6E-1', 'order': 6, 'powers': [8, 2, 18], 'representative': 1441, 'size': 1083}
  • id: 171588361
    {'aut_label': '19A1', 'centralizer': '12.c1.a1', 'counter': 19, 'group_counter': 29, 'group_order': 12996, 'label': '19A1', 'order': 19, 'powers': [20, 20, 1], 'representative': 4788, 'size': 12}
  • id: 171588363
    {'aut_label': '19A1', 'centralizer': '12.c1.a1', 'counter': 20, 'group_counter': 29, 'group_order': 12996, 'label': '19A2', 'order': 19, 'powers': [21, 21, 1], 'representative': 9576, 'size': 12}
  • id: 171588364
    {'aut_label': '19A1', 'centralizer': '12.c1.a1', 'counter': 21, 'group_counter': 29, 'group_order': 12996, 'label': '19A4', 'order': 19, 'powers': [19, 19, 1], 'representative': 6156, 'size': 12}
  • id: 171588365
    {'aut_label': '19B1', 'centralizer': '18.b1.a1', 'counter': 22, 'group_counter': 29, 'group_order': 12996, 'label': '19B1', 'order': 19, 'powers': [23, 23, 1], 'representative': 6624, 'size': 18}
  • id: 171588366
    {'aut_label': '19B1', 'centralizer': '18.b1.a1', 'counter': 23, 'group_counter': 29, 'group_order': 12996, 'label': '19B2', 'order': 19, 'powers': [24, 24, 1], 'representative': 12564, 'size': 18}
  • id: 171588367
    {'aut_label': '19B1', 'centralizer': '18.b1.a1', 'counter': 24, 'group_counter': 29, 'group_order': 12996, 'label': '19B4', 'order': 19, 'powers': [22, 22, 1], 'representative': 12132, 'size': 18}
  • id: 171588368
    {'aut_label': '19B1', 'centralizer': '18.b1.b1', 'counter': 25, 'group_counter': 29, 'group_order': 12996, 'label': '19C1', 'order': 19, 'powers': [26, 26, 1], 'representative': 9432, 'size': 18}
  • id: 171588369
    {'aut_label': '19B1', 'centralizer': '18.b1.b1', 'counter': 26, 'group_counter': 29, 'group_order': 12996, 'label': '19C2', 'order': 19, 'powers': [27, 27, 1], 'representative': 5184, 'size': 18}
  • id: 171588370
    {'aut_label': '19B1', 'centralizer': '18.b1.b1', 'counter': 27, 'group_counter': 29, 'group_order': 12996, 'label': '19C4', 'order': 19, 'powers': [25, 25, 1], 'representative': 9684, 'size': 18}
  • id: 171588371
    {'aut_label': '19D1', 'centralizer': '36.a1.a1', 'counter': 28, 'group_counter': 29, 'group_order': 12996, 'label': '19D1', 'order': 19, 'powers': [29, 29, 1], 'representative': 1404, 'size': 36}
  • id: 171588372
    {'aut_label': '19D1', 'centralizer': '36.a1.a1', 'counter': 29, 'group_counter': 29, 'group_order': 12996, 'label': '19D2', 'order': 19, 'powers': [30, 30, 1], 'representative': 2808, 'size': 36}
  • id: 171588374
    {'aut_label': '19D1', 'centralizer': '36.a1.a1', 'counter': 30, 'group_counter': 29, 'group_order': 12996, 'label': '19D4', 'order': 19, 'powers': [28, 28, 1], 'representative': 6876, 'size': 36}
  • id: 171588375
    {'aut_label': '19D1', 'centralizer': '36.a1.a1', 'counter': 31, 'group_counter': 29, 'group_order': 12996, 'label': '19E1', 'order': 19, 'powers': [32, 32, 1], 'representative': 2772, 'size': 36}
  • id: 171588376
    {'aut_label': '19D1', 'centralizer': '36.a1.a1', 'counter': 32, 'group_counter': 29, 'group_order': 12996, 'label': '19E2', 'order': 19, 'powers': [33, 33, 1], 'representative': 3456, 'size': 36}
  • id: 171588377
    {'aut_label': '19D1', 'centralizer': '36.a1.a1', 'counter': 33, 'group_counter': 29, 'group_order': 12996, 'label': '19E4', 'order': 19, 'powers': [31, 31, 1], 'representative': 3564, 'size': 36}
  • id: 171588378
    {'aut_label': '38A1', 'centralizer': '342.a1.a1', 'counter': 34, 'group_counter': 29, 'group_order': 12996, 'label': '38A1', 'order': 38, 'powers': [22, 35, 2], 'representative': 12531, 'size': 342}
  • id: 171588379
    {'aut_label': '38A1', 'centralizer': '342.a1.a1', 'counter': 35, 'group_counter': 29, 'group_order': 12996, 'label': '38A3', 'order': 38, 'powers': [23, 36, 2], 'representative': 5475, 'size': 342}
  • id: 171588380
    {'aut_label': '38A1', 'centralizer': '342.a1.a1', 'counter': 36, 'group_counter': 29, 'group_order': 12996, 'label': '38A9', 'order': 38, 'powers': [24, 34, 2], 'representative': 10983, 'size': 342}
  • id: 171588381
    {'aut_label': '38A1', 'centralizer': '342.a1.b1', 'counter': 37, 'group_counter': 29, 'group_order': 12996, 'label': '38B1', 'order': 38, 'powers': [25, 38, 3], 'representative': 12513, 'size': 342}
  • id: 171588382
    {'aut_label': '38A1', 'centralizer': '342.a1.b1', 'counter': 38, 'group_counter': 29, 'group_order': 12996, 'label': '38B3', 'order': 38, 'powers': [26, 39, 3], 'representative': 8265, 'size': 342}
  • id: 171588383
    {'aut_label': '38A1', 'centralizer': '342.a1.b1', 'counter': 39, 'group_counter': 29, 'group_order': 12996, 'label': '38B9', 'order': 38, 'powers': [27, 37, 3], 'representative': 9201, 'size': 342}
  • id: 171588385
    {'aut_label': '57A1', 'centralizer': '228.a1.a1', 'counter': 40, 'group_counter': 29, 'group_order': 12996, 'label': '57A1', 'order': 57, 'powers': [42, 19, 6], 'representative': 9770, 'size': 228}
  • id: 171588386
    {'aut_label': '57A-1', 'centralizer': '228.a1.a1', 'counter': 41, 'group_counter': 29, 'group_order': 12996, 'label': '57A-1', 'order': 57, 'powers': [43, 19, 5], 'representative': 10828, 'size': 228}
  • id: 171588387
    {'aut_label': '57A-1', 'centralizer': '228.a1.a1', 'counter': 42, 'group_counter': 29, 'group_order': 12996, 'label': '57A2', 'order': 57, 'powers': [44, 20, 5], 'representative': 2620, 'size': 228}
  • id: 171588388
    {'aut_label': '57A1', 'centralizer': '228.a1.a1', 'counter': 43, 'group_counter': 29, 'group_order': 12996, 'label': '57A-2', 'order': 57, 'powers': [45, 20, 6], 'representative': 4982, 'size': 228}
  • id: 171588389
    {'aut_label': '57A1', 'centralizer': '228.a1.a1', 'counter': 44, 'group_counter': 29, 'group_order': 12996, 'label': '57A4', 'order': 57, 'powers': [41, 21, 6], 'representative': 1562, 'size': 228}
  • id: 171588390
    {'aut_label': '57A-1', 'centralizer': '228.a1.a1', 'counter': 45, 'group_counter': 29, 'group_order': 12996, 'label': '57A-4', 'order': 57, 'powers': [40, 21, 5], 'representative': 6040, 'size': 228}
• 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: 17321493
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.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], 'schur_index': 1}
  • id: 17321504
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.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], 'schur_index': 1}
  • id: 17321506
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.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], 'schur_index': 1}
  • id: 17321507
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.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], 'schur_index': 1}
  • id: 17321508
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 17321509
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.1f', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 17321510
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.1g', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -1, -1, -1, -1, 2, 1, 1, -2, 1, 1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 17321511
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -1, -1, -1, -1, 2, 1, 1, -2, 1, 1, 1, 1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 17321512
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 0, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 17321494
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 0, -2, -1, -1, 2, 2, -1, -2, -2, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 17321495
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.2c', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 0, 0, 4, 1, 1, -2, -2, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 17321496
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.2d', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 0, 0, -4, 1, 1, -2, -2, -2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 17321497
    {'cdim': 12, 'counter': 13, 'faithful': True, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.12a', 'multiplicity': 3, 'nt': [38, 28], 'qdim': 36, 'qvalues': [36, 0, 0, 0, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 17, 17, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 17321499
    {'cdim': 18, 'counter': 15, 'faithful': True, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.18a', 'multiplicity': 3, 'nt': [57, 0], 'qdim': 54, 'qvalues': [54, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, 16, 16, 16, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17321500
    {'cdim': 18, 'counter': 16, 'faithful': True, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.18b', 'multiplicity': 3, 'nt': [57, 0], 'qdim': 54, 'qvalues': [54, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, 16, 16, 16, -3, -3, -3, -3, -3, -3, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17321501
    {'cdim': 18, 'counter': 17, 'faithful': True, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.18c', 'multiplicity': 3, 'nt': [114, 0], 'qdim': 54, 'qvalues': [54, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, 16, 16, 16, -3, -3, -3, -3, -3, -3, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17321502
    {'cdim': 18, 'counter': 18, 'faithful': True, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.18d', 'multiplicity': 3, 'nt': [114, 0], 'qdim': 54, 'qvalues': [54, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, 16, 16, 16, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17321498
    {'cdim': 12, 'counter': 14, 'faithful': True, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.12b', 'multiplicity': 6, 'nt': [114, 0], 'qdim': 72, 'qvalues': [72, 0, 0, 0, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34, 34, 34, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 17321503
    {'cdim': 36, 'counter': 19, 'faithful': True, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.36a', 'multiplicity': 3, 'nt': [114, 0], 'qdim': 108, 'qvalues': [108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, 13, 13, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17321505
    {'cdim': 36, 'counter': 20, 'faithful': True, 'group': '12996.bc', 'group_order': 12996, 'image': None, 'label': '12996.bc.36b', 'multiplicity': 3, 'nt': [114, 0], 'qdim': 108, 'qvalues': [108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, -6, -6, -6, -6, -6, 13, 13, 13, -6, -6, -6, 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: 37946659
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12996, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 12996, 'label': '12996.bc.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]]]}
  • id: 37946670
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12996, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 6498, 'label': '12996.bc.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]]]}
  • id: 37946681
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12996, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 6498, 'label': '12996.bc.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]]]}
  • id: 37946692
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12996, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 6498, 'label': '12996.bc.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]]]}
  • id: 37946699
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12996, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 4332, 'label': '12996.bc.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 37946700
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12996, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 4332, 'label': '12996.bc.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 37946701
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12996, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 2166, 'label': '12996.bc.1f1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 37946702
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12996, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 2166, 'label': '12996.bc.1f2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 37946703
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12996, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.b1', 'kernel_order': 2166, 'label': '12996.bc.1g1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 37946660
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12996, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.b1', 'kernel_order': 2166, 'label': '12996.bc.1g2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 37946661
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12996, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 2166, 'label': '12996.bc.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 37946662
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12996, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 2166, 'label': '12996.bc.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 37946663
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 2166, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 2166, 'label': '12996.bc.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 37946664
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 2166, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 1083, 'label': '12996.bc.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 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]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 37946665
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 2166, 'counter': 15, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 722, 'label': '12996.bc.2c1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[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]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 37946666
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 2166, 'counter': 16, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 722, 'label': '12996.bc.2c2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[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]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 37946667
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 2166, 'counter': 17, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 361, 'label': '12996.bc.2d1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[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]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 37946668
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 2166, 'counter': 18, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 361, 'label': '12996.bc.2d2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[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]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 37946669
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 19, 'dim': 12, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.12a1', 'nt': [38, 28], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0], [1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]], [[6, 0], [1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]], [[6, 0], [1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]], [[2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[-1, 0], [-1, 2], [-1, 3], [-1, 5], [-1, -5], [-1, -3], [-1, -2]], [[-1, 0], [-1, 4], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-1, -4]], [[-1, 0], [-1, 1], [-1, 7], [-1, 8], [-1, -8], [-1, -7], [-1, -1]], [[-1, 0], [-1, 1], [-1, 7], [-1, 8], [-1, -8], [-1, -7], [-1, -1]], [[-1, 0], [-1, 2], [-1, 3], [-1, 5], [-1, -5], [-1, -3], [-1, -2]], [[-1, 0], [-1, 4], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]], [[1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]], [[1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]], [[1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]], [[1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]], [[1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]]]}
  • id: 37946671
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 20, 'cyclotomic_n': 19, 'dim': 12, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.12a2', 'nt': [38, 28], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0], [1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]], [[6, 0], [1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]], [[6, 0], [1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]], [[2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[-1, 0], [-1, 4], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-1, -4]], [[-1, 0], [-1, 1], [-1, 7], [-1, 8], [-1, -8], [-1, -7], [-1, -1]], [[-1, 0], [-1, 2], [-1, 3], [-1, 5], [-1, -5], [-1, -3], [-1, -2]], [[-1, 0], [-1, 2], [-1, 3], [-1, 5], [-1, -5], [-1, -3], [-1, -2]], [[-1, 0], [-1, 4], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-1, -4]], [[-1, 0], [-1, 1], [-1, 7], [-1, 8], [-1, -8], [-1, -7], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]], [[1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]], [[1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]], [[1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]], [[1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]], [[1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]]]}
  • id: 37946672
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 21, 'cyclotomic_n': 19, 'dim': 12, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.12a3', 'nt': [38, 28], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0], [1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]], [[6, 0], [1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]], [[6, 0], [1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]], [[2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[-1, 0], [-1, 1], [-1, 7], [-1, 8], [-1, -8], [-1, -7], [-1, -1]], [[-1, 0], [-1, 2], [-1, 3], [-1, 5], [-1, -5], [-1, -3], [-1, -2]], [[-1, 0], [-1, 4], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-1, -4]], [[-1, 0], [-1, 4], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-1, -4]], [[-1, 0], [-1, 1], [-1, 7], [-1, 8], [-1, -8], [-1, -7], [-1, -1]], [[-1, 0], [-1, 2], [-1, 3], [-1, 5], [-1, -5], [-1, -3], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]], [[1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]], [[1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]], [[1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]], [[1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]], [[1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]]]}
  • id: 37946673
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  • id: 37946674
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 23, 'cyclotomic_n': 57, 'dim': 12, 'faithful': True, 'field': [49, -42, 43, -8, 7, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 0, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.12b2', 'nt': [114, 6], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 19]], [[6, -19]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0], [-1, 1], [-1, 7], [1, 12], [1, 18], [-1, 20], [-1, 26], [1, 27], [1, -27]], [[5, 0], [1, 1], [1, 4], [-1, 6], [1, 7], [-1, 9], [1, 10], [-1, 12], [1, 13], [-1, 15], [-1, 18], [1, 20], [1, 23], [1, 26], [-1, 27], [1, -28], [-1, -27], [1, -25]], [[6, 0], [-1, 4], [1, 6], [1, 9], [-1, 10], [-1, 13], [1, 15], [-1, 23], [-1, -28], [-1, -25]], [[-2, 4], [2, 6], [2, 9], [-2, 10], [-2, 13], [2, 15], [-2, 23], [-2, -28], [-2, -25]], [[-2, 1], [-2, 7], [2, 12], [2, 18], [-2, 20], [-2, 26], [2, 27], [2, -27]], [[-2, 0], [2, 1], [2, 4], [-2, 6], [2, 7], [-2, 9], [2, 10], [-2, 12], [2, 13], [-2, 15], [-2, 18], [2, 20], [2, 23], [2, 26], [-2, 27], [2, -28], [-2, -27], [2, -25]], [[-2, 4], [2, 6], [2, 9], [-2, 10], [-2, 13], [2, 15], [-2, 23], [-2, -28], [-2, -25]], [[-2, 1], [-2, 7], [2, 12], [2, 18], [-2, 20], [-2, 26], [2, 27], [2, -27]], [[-2, 0], [2, 1], [2, 4], [-2, 6], [2, 7], [-2, 9], [2, 10], [-2, 12], [2, 13], [-2, 15], [-2, 18], [2, 20], [2, 23], [2, 26], [-2, 27], [2, -28], [-2, -27], [2, -25]], [[-1, 0], [1, 4], [-1, 6], [-1, 9], [1, 10], [1, 13], [-1, 15], [1, 23], [1, -28], [1, -25]], [[-1, 0], [1, 1], [1, 7], [-1, 12], [-1, 18], [1, 20], [1, 26], [-1, 27], [-1, -27]], [[-1, 1], [-1, 4], [1, 6], [-1, 7], [1, 9], [-1, 10], [1, 12], [-1, 13], [1, 15], [1, 18], [-1, 20], [-1, 23], [-1, 26], [1, 27], [-1, -28], [1, -27], [-1, -25]], [[-1, 1], [-1, 4], [1, 6], [-1, 7], [1, 9], [-1, 10], [1, 12], [-1, 13], [1, 15], [1, 18], [-1, 20], [-1, 23], [-1, 26], [1, 27], [-1, -28], [1, -27], [-1, -25]], [[-1, 0], [1, 4], [-1, 6], [-1, 9], [1, 10], [1, 13], [-1, 15], [1, 23], [1, -28], [1, -25]], [[-1, 0], [1, 1], [1, 7], [-1, 12], [-1, 18], [1, 20], [1, 26], [-1, 27], [-1, -27]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, 9], [-1, 15], [1, 23], [-1, 25], [-1, 28], [1, -28], [1, -25], [-1, -23]], [[1, 4], [1, 10], [1, 13], [1, 25], [1, 28], [1, -23]], [[-1, 0], [1, 1], [1, 2], [-1, 3], [1, 5], [-1, 6], [1, 7], [-1, 9], [-1, 12], [1, 14], [-1, 15], [1, 17], [-1, 18], [-1, 19], [1, 20], [-1, 22], [1, 23], [-1, 25], [1, 26], [-1, 27], [-1, 28], [1, -28], [-1, -27], [1, -25], [-1, -23], [1, -22]], [[1, 0], [-1, 2], [1, 3], [-1, 5], [1, 6], [1, 9], [-1, 14], [1, 15], [-1, 17], [1, 19], [1, 22], [-1, 23], [1, 25], [1, 28], [-1, -28], [-1, -25], [1, -23], [-1, -22]], [[1, 2], [-1, 3], [1, 5], [1, 14], [1, 17], [-1, 22], [1, -22]], [[1, 0], [-1, 1], [-1, 2], [1, 3], [-1, 4], [-1, 5], [1, 6], [-1, 7], [1, 9], [-1, 10], [1, 12], [-1, 13], [-1, 14], [1, 15], [-1, 17], [1, 18], [-1, 20], [1, 22], [-1, 23], [-1, 26], [1, 27], [-1, -28], [1, -27], [-1, -25], [-1, -22]]]}
  • id: 37946675
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  • id: 37946676
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  • id: 37946677
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 26, 'cyclotomic_n': 57, 'dim': 12, 'faithful': True, 'field': [49, -42, 43, -8, 7, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 0, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.12b5', 'nt': [114, 0], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, -19]], [[6, 19]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0], [-1, 4], [1, 6], [1, 9], [-1, 10], [-1, 13], [1, 15], [-1, 23], [-1, -28], [-1, -25]], [[6, 0], [-1, 1], [-1, 7], [1, 12], [1, 18], [-1, 20], [-1, 26], [1, 27], [1, -27]], [[5, 0], [1, 1], [1, 4], [-1, 6], [1, 7], [-1, 9], [1, 10], [-1, 12], [1, 13], [-1, 15], [-1, 18], [1, 20], [1, 23], [1, 26], [-1, 27], [1, -28], [-1, -27], [1, -25]], [[-2, 0], [2, 1], [2, 4], [-2, 6], [2, 7], [-2, 9], [2, 10], [-2, 12], [2, 13], [-2, 15], [-2, 18], [2, 20], [2, 23], [2, 26], [-2, 27], [2, -28], [-2, -27], [2, -25]], [[-2, 4], [2, 6], [2, 9], [-2, 10], [-2, 13], [2, 15], [-2, 23], [-2, -28], [-2, -25]], [[-2, 1], [-2, 7], [2, 12], [2, 18], [-2, 20], [-2, 26], [2, 27], [2, -27]], [[-2, 0], [2, 1], [2, 4], [-2, 6], [2, 7], [-2, 9], [2, 10], [-2, 12], [2, 13], [-2, 15], [-2, 18], [2, 20], [2, 23], [2, 26], [-2, 27], [2, -28], [-2, -27], [2, -25]], [[-2, 4], [2, 6], [2, 9], [-2, 10], [-2, 13], [2, 15], [-2, 23], [-2, -28], [-2, -25]], [[-2, 1], [-2, 7], [2, 12], [2, 18], [-2, 20], [-2, 26], [2, 27], [2, -27]], [[-1, 1], [-1, 4], [1, 6], [-1, 7], [1, 9], [-1, 10], [1, 12], [-1, 13], [1, 15], [1, 18], [-1, 20], [-1, 23], [-1, 26], [1, 27], [-1, -28], [1, -27], [-1, -25]], [[-1, 0], [1, 4], [-1, 6], [-1, 9], [1, 10], [1, 13], [-1, 15], [1, 23], [1, -28], [1, -25]], [[-1, 0], [1, 1], [1, 7], [-1, 12], [-1, 18], [1, 20], [1, 26], [-1, 27], [-1, -27]], [[-1, 0], [1, 1], [1, 7], [-1, 12], [-1, 18], [1, 20], [1, 26], [-1, 27], [-1, -27]], [[-1, 1], [-1, 4], [1, 6], [-1, 7], [1, 9], [-1, 10], [1, 12], [-1, 13], [1, 15], [1, 18], [-1, 20], [-1, 23], [-1, 26], [1, 27], [-1, -28], [1, -27], [-1, -25]], [[-1, 0], [1, 4], [-1, 6], [-1, 9], [1, 10], [1, 13], [-1, 15], [1, 23], [1, -28], [1, -25]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1], [-1, 2], [1, 3], [-1, 4], [-1, 5], [1, 6], [-1, 7], [1, 9], [-1, 10], [1, 12], [-1, 13], [-1, 14], [1, 15], [-1, 17], [1, 18], [-1, 20], [1, 22], [-1, 23], [-1, 26], [1, 27], [-1, -28], [1, -27], [-1, -25], [-1, -22]], [[1, 2], [-1, 3], [1, 5], [1, 14], [1, 17], [-1, 22], [1, -22]], [[-1, 6], [-1, 9], [-1, 15], [1, 23], [-1, 25], [-1, 28], [1, -28], [1, -25], [-1, -23]], [[1, 4], [1, 10], [1, 13], [1, 25], [1, 28], [1, -23]], [[-1, 0], [1, 1], [1, 2], [-1, 3], [1, 5], [-1, 6], [1, 7], [-1, 9], [-1, 12], [1, 14], [-1, 15], [1, 17], [-1, 18], [-1, 19], [1, 20], [-1, 22], [1, 23], [-1, 25], [1, 26], [-1, 27], [-1, 28], [1, -28], [-1, -27], [1, -25], [-1, -23], [1, -22]], [[1, 0], [-1, 2], [1, 3], [-1, 5], [1, 6], [1, 9], [-1, 14], [1, 15], [-1, 17], [1, 19], [1, 22], [-1, 23], [1, 25], [1, 28], [-1, -28], [-1, -25], [1, -23], [-1, -22]]]}
  • id: 37946678
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  • id: 37946679
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  • id: 37946680
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 29, 'cyclotomic_n': 19, 'dim': 18, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.18a2', 'nt': [57, 0], 'q_character': None, 'values': [[[18, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 7], [3, 8], [3, -8], [3, -7], [3, -1]], [[3, 2], [3, 3], [3, 5], [3, -5], [3, -3], [3, -2]], [[3, 4], [3, 6], [3, 9], [3, -9], [3, -6], [3, -4]], [[6, 0], [2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[6, 0], [2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[6, 0], [2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[-2, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[1, 2], [1, 3], [2, 4], [1, 5], [2, 6], [2, 9], [2, -9], [2, -6], [1, -5], [2, -4], [1, -3], [1, -2]], [[-2, 0], [-2, 2], [-2, 3], [-1, 4], [-2, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-2, -5], [-1, -4], [-2, -3], [-2, -2]], [[-1, 0], [1, 2], [1, 3], [-1, 4], [1, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [1, -5], [-1, -4], [1, -3], [1, -2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]], [[1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]], [[1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946682
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 30, 'cyclotomic_n': 19, 'dim': 18, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.18a3', 'nt': [57, 0], 'q_character': None, 'values': [[[18, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, 3], [3, 5], [3, -5], [3, -3], [3, -2]], [[3, 4], [3, 6], [3, 9], [3, -9], [3, -6], [3, -4]], [[3, 1], [3, 7], [3, 8], [3, -8], [3, -7], [3, -1]], [[6, 0], [2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[6, 0], [2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[6, 0], [2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[-2, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[-2, 0], [-2, 2], [-2, 3], [-1, 4], [-2, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-2, -5], [-1, -4], [-2, -3], [-2, -2]], [[-1, 0], [1, 2], [1, 3], [-1, 4], [1, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [1, -5], [-1, -4], [1, -3], [1, -2]], [[1, 2], [1, 3], [2, 4], [1, 5], [2, 6], [2, 9], [2, -9], [2, -6], [1, -5], [2, -4], [1, -3], [1, -2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]], [[1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]], [[1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946683
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 31, 'cyclotomic_n': 19, 'dim': 18, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.18b1', 'nt': [57, 0], 'q_character': None, 'values': [[[18, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, 6], [3, 9], [3, -9], [3, -6], [3, -4]], [[3, 1], [3, 7], [3, 8], [3, -8], [3, -7], [3, -1]], [[3, 2], [3, 3], [3, 5], [3, -5], [3, -3], [3, -2]], [[2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[-2, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[6, 0], [2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[6, 0], [2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[6, 0], [2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0], [-2, 2], [-2, 3], [-1, 4], [-2, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-2, -5], [-1, -4], [-2, -3], [-2, -2]], [[-1, 0], [1, 2], [1, 3], [-1, 4], [1, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [1, -5], [-1, -4], [1, -3], [1, -2]], [[1, 2], [1, 3], [2, 4], [1, 5], [2, 6], [2, 9], [2, -9], [2, -6], [1, -5], [2, -4], [1, -3], [1, -2]], [[1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]], [[1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]], [[1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946684
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 32, 'cyclotomic_n': 19, 'dim': 18, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.18b2', 'nt': [57, 0], 'q_character': None, 'values': [[[18, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 7], [3, 8], [3, -8], [3, -7], [3, -1]], [[3, 2], [3, 3], [3, 5], [3, -5], [3, -3], [3, -2]], [[3, 4], [3, 6], [3, 9], [3, -9], [3, -6], [3, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[-2, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[6, 0], [2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[6, 0], [2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[6, 0], [2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [1, 2], [1, 3], [-1, 4], [1, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [1, -5], [-1, -4], [1, -3], [1, -2]], [[1, 2], [1, 3], [2, 4], [1, 5], [2, 6], [2, 9], [2, -9], [2, -6], [1, -5], [2, -4], [1, -3], [1, -2]], [[-2, 0], [-2, 2], [-2, 3], [-1, 4], [-2, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-2, -5], [-1, -4], [-2, -3], [-2, -2]], [[1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]], [[1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]], [[1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946685
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 33, 'cyclotomic_n': 19, 'dim': 18, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.18b3', 'nt': [57, 0], 'q_character': None, 'values': [[[18, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, 3], [3, 5], [3, -5], [3, -3], [3, -2]], [[3, 4], [3, 6], [3, 9], [3, -9], [3, -6], [3, -4]], [[3, 1], [3, 7], [3, 8], [3, -8], [3, -7], [3, -1]], [[-2, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[6, 0], [2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[6, 0], [2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[6, 0], [2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2], [1, 3], [2, 4], [1, 5], [2, 6], [2, 9], [2, -9], [2, -6], [1, -5], [2, -4], [1, -3], [1, -2]], [[-2, 0], [-2, 2], [-2, 3], [-1, 4], [-2, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-2, -5], [-1, -4], [-2, -3], [-2, -2]], [[-1, 0], [1, 2], [1, 3], [-1, 4], [1, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [1, -5], [-1, -4], [1, -3], [1, -2]], [[1, 1], [1, 7], [1, 8], [1, -8], [1, -7], [1, -1]], [[1, 2], [1, 3], [1, 5], [1, -5], [1, -3], [1, -2]], [[1, 4], [1, 6], [1, 9], [1, -9], [1, -6], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946686
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 34, 'cyclotomic_n': 19, 'dim': 18, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.18c1', 'nt': [114, 0], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, 6], [3, 9], [3, -9], [3, -6], [3, -4]], [[3, 1], [3, 7], [3, 8], [3, -8], [3, -7], [3, -1]], [[3, 2], [3, 3], [3, 5], [3, -5], [3, -3], [3, -2]], [[2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[-2, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[6, 0], [2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[6, 0], [2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[6, 0], [2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0], [-2, 2], [-2, 3], [-1, 4], [-2, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-2, -5], [-1, -4], [-2, -3], [-2, -2]], [[-1, 0], [1, 2], [1, 3], [-1, 4], [1, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [1, -5], [-1, -4], [1, -3], [1, -2]], [[1, 2], [1, 3], [2, 4], [1, 5], [2, 6], [2, 9], [2, -9], [2, -6], [1, -5], [2, -4], [1, -3], [1, -2]], [[-1, 2], [-1, 3], [-1, 5], [-1, -5], [-1, -3], [-1, -2]], [[-1, 4], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-1, -4]], [[-1, 1], [-1, 7], [-1, 8], [-1, -8], [-1, -7], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946687
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 35, 'cyclotomic_n': 19, 'dim': 18, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.18c2', 'nt': [114, 0], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 7], [3, 8], [3, -8], [3, -7], [3, -1]], [[3, 2], [3, 3], [3, 5], [3, -5], [3, -3], [3, -2]], [[3, 4], [3, 6], [3, 9], [3, -9], [3, -6], [3, -4]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[-2, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[6, 0], [2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[6, 0], [2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[6, 0], [2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [1, 2], [1, 3], [-1, 4], [1, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [1, -5], [-1, -4], [1, -3], [1, -2]], [[1, 2], [1, 3], [2, 4], [1, 5], [2, 6], [2, 9], [2, -9], [2, -6], [1, -5], [2, -4], [1, -3], [1, -2]], [[-2, 0], [-2, 2], [-2, 3], [-1, 4], [-2, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-2, -5], [-1, -4], [-2, -3], [-2, -2]], [[-1, 4], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-1, -4]], [[-1, 1], [-1, 7], [-1, 8], [-1, -8], [-1, -7], [-1, -1]], [[-1, 2], [-1, 3], [-1, 5], [-1, -5], [-1, -3], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946688
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 36, 'cyclotomic_n': 19, 'dim': 18, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.18c3', 'nt': [114, 0], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, 3], [3, 5], [3, -5], [3, -3], [3, -2]], [[3, 4], [3, 6], [3, 9], [3, -9], [3, -6], [3, -4]], [[3, 1], [3, 7], [3, 8], [3, -8], [3, -7], [3, -1]], [[-2, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[6, 0], [2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[6, 0], [2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[6, 0], [2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2], [1, 3], [2, 4], [1, 5], [2, 6], [2, 9], [2, -9], [2, -6], [1, -5], [2, -4], [1, -3], [1, -2]], [[-2, 0], [-2, 2], [-2, 3], [-1, 4], [-2, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-2, -5], [-1, -4], [-2, -3], [-2, -2]], [[-1, 0], [1, 2], [1, 3], [-1, 4], [1, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [1, -5], [-1, -4], [1, -3], [1, -2]], [[-1, 1], [-1, 7], [-1, 8], [-1, -8], [-1, -7], [-1, -1]], [[-1, 2], [-1, 3], [-1, 5], [-1, -5], [-1, -3], [-1, -2]], [[-1, 4], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946689
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 37, 'cyclotomic_n': 19, 'dim': 18, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.18d1', 'nt': [114, 0], 'q_character': None, 'values': [[[18, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, 6], [3, 9], [3, -9], [3, -6], [3, -4]], [[3, 1], [3, 7], [3, 8], [3, -8], [3, -7], [3, -1]], [[3, 2], [3, 3], [3, 5], [3, -5], [3, -3], [3, -2]], [[6, 0], [2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[6, 0], [2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[6, 0], [2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[-2, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[-1, 0], [1, 2], [1, 3], [-1, 4], [1, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [1, -5], [-1, -4], [1, -3], [1, -2]], [[1, 2], [1, 3], [2, 4], [1, 5], [2, 6], [2, 9], [2, -9], [2, -6], [1, -5], [2, -4], [1, -3], [1, -2]], [[-2, 0], [-2, 2], [-2, 3], [-1, 4], [-2, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-2, -5], [-1, -4], [-2, -3], [-2, -2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 3], [-1, 5], [-1, -5], [-1, -3], [-1, -2]], [[-1, 4], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-1, -4]], [[-1, 1], [-1, 7], [-1, 8], [-1, -8], [-1, -7], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946690
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 38, 'cyclotomic_n': 19, 'dim': 18, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.18d2', 'nt': [114, 0], 'q_character': None, 'values': [[[18, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 7], [3, 8], [3, -8], [3, -7], [3, -1]], [[3, 2], [3, 3], [3, 5], [3, -5], [3, -3], [3, -2]], [[3, 4], [3, 6], [3, 9], [3, -9], [3, -6], [3, -4]], [[6, 0], [2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[6, 0], [2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[6, 0], [2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[-2, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[1, 2], [1, 3], [2, 4], [1, 5], [2, 6], [2, 9], [2, -9], [2, -6], [1, -5], [2, -4], [1, -3], [1, -2]], [[-2, 0], [-2, 2], [-2, 3], [-1, 4], [-2, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-2, -5], [-1, -4], [-2, -3], [-2, -2]], [[-1, 0], [1, 2], [1, 3], [-1, 4], [1, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [1, -5], [-1, -4], [1, -3], [1, -2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-1, -4]], [[-1, 1], [-1, 7], [-1, 8], [-1, -8], [-1, -7], [-1, -1]], [[-1, 2], [-1, 3], [-1, 5], [-1, -5], [-1, -3], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946691
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 39, 'cyclotomic_n': 19, 'dim': 18, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.18d3', 'nt': [114, 0], 'q_character': None, 'values': [[[18, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, 3], [3, 5], [3, -5], [3, -3], [3, -2]], [[3, 4], [3, 6], [3, 9], [3, -9], [3, -6], [3, -4]], [[3, 1], [3, 7], [3, 8], [3, -8], [3, -7], [3, -1]], [[6, 0], [2, 4], [2, 6], [2, 9], [2, -9], [2, -6], [2, -4]], [[6, 0], [2, 1], [2, 7], [2, 8], [2, -8], [2, -7], [2, -1]], [[6, 0], [2, 2], [2, 3], [2, 5], [2, -5], [2, -3], [2, -2]], [[-2, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[-1, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[-2, 0], [-2, 2], [-2, 3], [-1, 4], [-2, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-2, -5], [-1, -4], [-2, -3], [-2, -2]], [[-1, 0], [1, 2], [1, 3], [-1, 4], [1, 5], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [1, -5], [-1, -4], [1, -3], [1, -2]], [[1, 2], [1, 3], [2, 4], [1, 5], [2, 6], [2, 9], [2, -9], [2, -6], [1, -5], [2, -4], [1, -3], [1, -2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 7], [-1, 8], [-1, -8], [-1, -7], [-1, -1]], [[-1, 2], [-1, 3], [-1, 5], [-1, -5], [-1, -3], [-1, -2]], [[-1, 4], [-1, 6], [-1, 9], [-1, -9], [-1, -6], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946693
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 40, 'cyclotomic_n': 19, 'dim': 36, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.36a1', 'nt': [114, 0], 'q_character': None, 'values': [[[36, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 2], [-3, 3], [-3, 5], [-3, -5], [-3, -3], [-3, -2]], [[-3, 0], [-3, 4], [-3, 6], [-3, 9], [-3, -9], [-3, -6], [-3, -4]], [[-3, 0], [-3, 1], [-3, 7], [-3, 8], [-3, -8], [-3, -7], [-3, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0], [-4, 2], [-4, 3], [-2, 4], [-4, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-4, -5], [-2, -4], [-4, -3], [-4, -2]], [[-2, 0], [2, 2], [2, 3], [-2, 4], [2, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [2, -5], [-2, -4], [2, -3], [2, -2]], [[2, 2], [2, 3], [4, 4], [2, 5], [4, 6], [4, 9], [4, -9], [4, -6], [2, -5], [4, -4], [2, -3], [2, -2]], [[-3, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[-1, 0], [2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[-2, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[6, 0], [3, 2], [3, 3], [2, 4], [3, 5], [2, 6], [2, 9], [2, -9], [2, -6], [3, -5], [2, -4], [3, -3], [3, -2]], [[4, 0], [-2, 2], [-2, 3], [1, 4], [-2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-2, -5], [1, -4], [-2, -3], [-2, -2]], [[3, 0], [-1, 2], [-1, 3], [-3, 4], [-1, 5], [-3, 6], [-3, 9], [-3, -9], [-3, -6], [-1, -5], [-3, -4], [-1, -3], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946694
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 41, 'cyclotomic_n': 19, 'dim': 36, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.36a2', 'nt': [114, 0], 'q_character': None, 'values': [[[36, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 1], [-3, 7], [-3, 8], [-3, -8], [-3, -7], [-3, -1]], [[-3, 0], [-3, 2], [-3, 3], [-3, 5], [-3, -5], [-3, -3], [-3, -2]], [[-3, 0], [-3, 4], [-3, 6], [-3, 9], [-3, -9], [-3, -6], [-3, -4]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 2], [2, 3], [4, 4], [2, 5], [4, 6], [4, 9], [4, -9], [4, -6], [2, -5], [4, -4], [2, -3], [2, -2]], [[-4, 0], [-4, 2], [-4, 3], [-2, 4], [-4, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-4, -5], [-2, -4], [-4, -3], [-4, -2]], [[-2, 0], [2, 2], [2, 3], [-2, 4], [2, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [2, -5], [-2, -4], [2, -3], [2, -2]], [[-2, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[-3, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[-1, 0], [2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[3, 0], [-1, 2], [-1, 3], [-3, 4], [-1, 5], [-3, 6], [-3, 9], [-3, -9], [-3, -6], [-1, -5], [-3, -4], [-1, -3], [-1, -2]], [[6, 0], [3, 2], [3, 3], [2, 4], [3, 5], [2, 6], [2, 9], [2, -9], [2, -6], [3, -5], [2, -4], [3, -3], [3, -2]], [[4, 0], [-2, 2], [-2, 3], [1, 4], [-2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-2, -5], [1, -4], [-2, -3], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946695
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 42, 'cyclotomic_n': 19, 'dim': 36, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.36a3', 'nt': [114, 0], 'q_character': None, 'values': [[[36, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 4], [-3, 6], [-3, 9], [-3, -9], [-3, -6], [-3, -4]], [[-3, 0], [-3, 1], [-3, 7], [-3, 8], [-3, -8], [-3, -7], [-3, -1]], [[-3, 0], [-3, 2], [-3, 3], [-3, 5], [-3, -5], [-3, -3], [-3, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0], [2, 2], [2, 3], [-2, 4], [2, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [2, -5], [-2, -4], [2, -3], [2, -2]], [[2, 2], [2, 3], [4, 4], [2, 5], [4, 6], [4, 9], [4, -9], [4, -6], [2, -5], [4, -4], [2, -3], [2, -2]], [[-4, 0], [-4, 2], [-4, 3], [-2, 4], [-4, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-4, -5], [-2, -4], [-4, -3], [-4, -2]], [[-1, 0], [2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[-2, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[-3, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[4, 0], [-2, 2], [-2, 3], [1, 4], [-2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-2, -5], [1, -4], [-2, -3], [-2, -2]], [[3, 0], [-1, 2], [-1, 3], [-3, 4], [-1, 5], [-3, 6], [-3, 9], [-3, -9], [-3, -6], [-1, -5], [-3, -4], [-1, -3], [-1, -2]], [[6, 0], [3, 2], [3, 3], [2, 4], [3, 5], [2, 6], [2, 9], [2, -9], [2, -6], [3, -5], [2, -4], [3, -3], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946696
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 43, 'cyclotomic_n': 19, 'dim': 36, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.36b1', 'nt': [114, 0], 'q_character': None, 'values': [[[36, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 2], [-3, 3], [-3, 5], [-3, -5], [-3, -3], [-3, -2]], [[-3, 0], [-3, 4], [-3, 6], [-3, 9], [-3, -9], [-3, -6], [-3, -4]], [[-3, 0], [-3, 1], [-3, 7], [-3, 8], [-3, -8], [-3, -7], [-3, -1]], [[-4, 0], [-4, 2], [-4, 3], [-2, 4], [-4, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-4, -5], [-2, -4], [-4, -3], [-4, -2]], [[-2, 0], [2, 2], [2, 3], [-2, 4], [2, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [2, -5], [-2, -4], [2, -3], [2, -2]], [[2, 2], [2, 3], [4, 4], [2, 5], [4, 6], [4, 9], [4, -9], [4, -6], [2, -5], [4, -4], [2, -3], [2, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0], [-2, 2], [-2, 3], [1, 4], [-2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-2, -5], [1, -4], [-2, -3], [-2, -2]], [[3, 0], [-1, 2], [-1, 3], [-3, 4], [-1, 5], [-3, 6], [-3, 9], [-3, -9], [-3, -6], [-1, -5], [-3, -4], [-1, -3], [-1, -2]], [[6, 0], [3, 2], [3, 3], [2, 4], [3, 5], [2, 6], [2, 9], [2, -9], [2, -6], [3, -5], [2, -4], [3, -3], [3, -2]], [[-2, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[-3, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[-1, 0], [2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946697
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 44, 'cyclotomic_n': 19, 'dim': 36, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.36b2', 'nt': [114, 0], 'q_character': None, 'values': [[[36, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 1], [-3, 7], [-3, 8], [-3, -8], [-3, -7], [-3, -1]], [[-3, 0], [-3, 2], [-3, 3], [-3, 5], [-3, -5], [-3, -3], [-3, -2]], [[-3, 0], [-3, 4], [-3, 6], [-3, 9], [-3, -9], [-3, -6], [-3, -4]], [[2, 2], [2, 3], [4, 4], [2, 5], [4, 6], [4, 9], [4, -9], [4, -6], [2, -5], [4, -4], [2, -3], [2, -2]], [[-4, 0], [-4, 2], [-4, 3], [-2, 4], [-4, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-4, -5], [-2, -4], [-4, -3], [-4, -2]], [[-2, 0], [2, 2], [2, 3], [-2, 4], [2, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [2, -5], [-2, -4], [2, -3], [2, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[6, 0], [3, 2], [3, 3], [2, 4], [3, 5], [2, 6], [2, 9], [2, -9], [2, -6], [3, -5], [2, -4], [3, -3], [3, -2]], [[4, 0], [-2, 2], [-2, 3], [1, 4], [-2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-2, -5], [1, -4], [-2, -3], [-2, -2]], [[3, 0], [-1, 2], [-1, 3], [-3, 4], [-1, 5], [-3, 6], [-3, 9], [-3, -9], [-3, -6], [-1, -5], [-3, -4], [-1, -3], [-1, -2]], [[-1, 0], [2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[-2, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[-3, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37946698
    {'center': '12996.a1.a1', 'center_index': 12996, 'center_order': 1, 'counter': 45, 'cyclotomic_n': 19, 'dim': 36, 'faithful': True, 'field': [7, -6, -1, 1], 'group': '12996.bc', 'group_counter': 29, 'group_order': 12996, 'image': None, 'image_isoclass': '12996.bc', 'image_order': 12996, 'indicator': 1, 'kernel': '12996.a1.a1', 'kernel_order': 1, 'label': '12996.bc.36b3', 'nt': [114, 0], 'q_character': None, 'values': [[[36, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 4], [-3, 6], [-3, 9], [-3, -9], [-3, -6], [-3, -4]], [[-3, 0], [-3, 1], [-3, 7], [-3, 8], [-3, -8], [-3, -7], [-3, -1]], [[-3, 0], [-3, 2], [-3, 3], [-3, 5], [-3, -5], [-3, -3], [-3, -2]], [[-2, 0], [2, 2], [2, 3], [-2, 4], [2, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [2, -5], [-2, -4], [2, -3], [2, -2]], [[2, 2], [2, 3], [4, 4], [2, 5], [4, 6], [4, 9], [4, -9], [4, -6], [2, -5], [4, -4], [2, -3], [2, -2]], [[-4, 0], [-4, 2], [-4, 3], [-2, 4], [-4, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-4, -5], [-2, -4], [-4, -3], [-4, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0], [-1, 2], [-1, 3], [-3, 4], [-1, 5], [-3, 6], [-3, 9], [-3, -9], [-3, -6], [-1, -5], [-3, -4], [-1, -3], [-1, -2]], [[6, 0], [3, 2], [3, 3], [2, 4], [3, 5], [2, 6], [2, 9], [2, -9], [2, -6], [3, -5], [2, -4], [3, -3], [3, -2]], [[4, 0], [-2, 2], [-2, 3], [1, 4], [-2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-2, -5], [1, -4], [-2, -3], [-2, -2]], [[-3, 0], [-1, 2], [-1, 3], [-2, 4], [-1, 5], [-2, 6], [-2, 9], [-2, -9], [-2, -6], [-1, -5], [-2, -4], [-1, -3], [-1, -2]], [[-1, 0], [2, 2], [2, 3], [1, 4], [2, 5], [1, 6], [1, 9], [1, -9], [1, -6], [2, -5], [1, -4], [2, -3], [2, -2]], [[-2, 0], [-1, 2], [-1, 3], [1, 4], [-1, 5], [1, 6], [1, 9], [1, -9], [1, -6], [-1, -5], [1, -4], [-1, -3], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 262842035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 12996, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 114, 'label': '12996.bc.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': None, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12996.bc', 'subgroup_hash': 8995592235010807521, 'subgroup_order': 12996, 'subgroup_tex': 'C_{19}^2:(C_6\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 262842046
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6498, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12996.bc.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': None, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2613459789052328731, 'subgroup_order': 6498, 'subgroup_tex': 'C_{19}^2:(C_3\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 262842057
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6498, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12996.bc.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': None, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2613459789052328731, 'subgroup_order': 6498, 'subgroup_tex': 'C_{19}^2:(C_3\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 262842068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 6498, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12996.bc.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': None, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5349043168595766166, 'subgroup_order': 6498, 'subgroup_tex': 'C_{19}^2:(C_3\\times C_6)', 'supersolvable': True, 'sylow': 0}
  • id: 262842079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 4332, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12996.bc.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': None, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5060185839156683504, 'subgroup_order': 4332, 'subgroup_tex': 'C_{19}^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 262842090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2166, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7523251478204693230, 'subgroup_order': 4332, 'subgroup_tex': 'C_{19}^2:(C_2\\times C_6)', 'supersolvable': True, 'sylow': 0}
  • id: 262842101
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 3249, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 57, 'label': '12996.bc.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': None, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3249.21', 'subgroup_hash': 21, 'subgroup_order': 3249, 'subgroup_tex': '(C_{19}:C_3)^2', 'supersolvable': True, 'sylow': 0}
  • id: 262842112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2166, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12996.bc.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', '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': None, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2166.11', 'subgroup_hash': 11, 'subgroup_order': 2166, 'subgroup_tex': 'C_{19}^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 262842118
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2166, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12996.bc.6.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': None, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2166.11', 'subgroup_hash': 11, 'subgroup_order': 2166, 'subgroup_tex': 'C_{19}^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 262842036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2166, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12996.bc.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': None, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2166.b', 'subgroup_hash': 9, 'subgroup_order': 2166, 'subgroup_tex': 'C_{19}^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842037
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2166, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12996.bc.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': None, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2166.10', 'subgroup_hash': 10, 'subgroup_order': 2166, 'subgroup_tex': 'C_{19}^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842038
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1083, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2166.7', 'subgroup_hash': 7, 'subgroup_order': 2166, 'subgroup_tex': 'C_{19}^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1083, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '2166.7', 'subgroup_hash': 7, 'subgroup_order': 2166, 'subgroup_tex': 'C_{19}^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 722, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2166.6', 'subgroup_hash': 6, 'subgroup_order': 2166, 'subgroup_tex': 'C_{19}^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842041
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 722, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 38, 'label': '12996.bc.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1444.9', 'subgroup_hash': 9, 'subgroup_order': 1444, 'subgroup_tex': 'D_{19}^2', 'supersolvable': True, 'sylow': 0}
  • id: 262842042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1083, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12996.bc.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': None, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1083.4', 'subgroup_hash': 4, 'subgroup_order': 1083, 'subgroup_tex': 'C_{19}^2:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 262842043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1083, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12996.bc.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', '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': None, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1083.5', 'subgroup_hash': 5, 'subgroup_order': 1083, 'subgroup_tex': 'C_{19}^2:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 262842044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 19, 'characteristic': False, 'core_order': 361, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1083.3', 'subgroup_hash': 3, 'subgroup_order': 1083, 'subgroup_tex': 'C_{19}:C_{57}', 'supersolvable': True, 'sylow': 0}
  • id: 262842045
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 722, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12996.bc.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': None, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '722.4', 'subgroup_hash': 4, 'subgroup_order': 722, 'subgroup_tex': 'C_{19}:D_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842047
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 19, 'characteristic': False, 'core_order': 361, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '722.3', 'subgroup_hash': 3, 'subgroup_order': 722, 'subgroup_tex': 'C_{19}\\times D_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 19, 'characteristic': False, 'core_order': 361, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.18.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '722.3', 'subgroup_hash': 3, 'subgroup_order': 722, 'subgroup_tex': 'C_{19}\\times D_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842049
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 361, 'characteristic': True, 'core_order': 361, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 19, 'label': '12996.bc.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, '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': None, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S', 'D2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '361.2', 'subgroup_hash': 2, 'subgroup_order': 361, 'subgroup_tex': 'C_{19}^2', 'supersolvable': True, 'sylow': 19}
  • id: 262842050
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.38.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '38.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 38, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '342.9', 'subgroup_hash': 9, 'subgroup_order': 342, 'subgroup_tex': 'C_{57}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842051
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.57.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '57.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 57, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '228.7', 'subgroup_hash': 7, 'subgroup_order': 228, 'subgroup_tex': 'C_{38}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842052
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.57.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '57.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 57, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '228.7', 'subgroup_hash': 7, 'subgroup_order': 228, 'subgroup_tex': 'C_{38}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842053
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.76.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '76.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 76, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '171.4', 'subgroup_hash': 4, 'subgroup_order': 171, 'subgroup_tex': 'C_{57}:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 262842054
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.114.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '114.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 114, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '114.2', 'subgroup_hash': 2, 'subgroup_order': 114, 'subgroup_tex': 'C_{19}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842055
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.114.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '114.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 114, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '114.2', 'subgroup_hash': 2, 'subgroup_order': 114, 'subgroup_tex': 'C_{19}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842056
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.114.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '114.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 114, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '114.1', 'subgroup_hash': 1, 'subgroup_order': 114, 'subgroup_tex': 'C_{19}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842058
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.114.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '114.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 114, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '114.1', 'subgroup_hash': 1, 'subgroup_order': 114, 'subgroup_tex': 'C_{19}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842059
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.114.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '114.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 114, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '114.4', 'subgroup_hash': 4, 'subgroup_order': 114, 'subgroup_tex': 'C_3\\times D_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842060
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.114.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '114.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 114, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '114.1', 'subgroup_hash': 1, 'subgroup_order': 114, 'subgroup_tex': 'C_{19}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842061
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.114.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '114.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 114, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '114.1', 'subgroup_hash': 1, 'subgroup_order': 114, 'subgroup_tex': 'C_{19}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842062
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.114.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '114.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 114, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '114.1', 'subgroup_hash': 1, 'subgroup_order': 114, 'subgroup_tex': 'C_{19}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842063
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.114.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '114.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 114, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '114.1', 'subgroup_hash': 1, 'subgroup_order': 114, 'subgroup_tex': 'C_{19}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842064
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.114.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '114.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 114, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '114.1', 'subgroup_hash': 1, 'subgroup_order': 114, 'subgroup_tex': 'C_{19}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842065
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.114.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '114.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 114, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '114.1', 'subgroup_hash': 1, 'subgroup_order': 114, 'subgroup_tex': 'C_{19}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842066
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.114.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '114.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 114, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '114.1', 'subgroup_hash': 1, 'subgroup_order': 114, 'subgroup_tex': 'C_{19}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842067
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.171.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '171.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 171, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '76.3', 'subgroup_hash': 3, 'subgroup_order': 76, 'subgroup_tex': 'D_{38}', 'supersolvable': True, 'sylow': 0}
  • id: 262842069
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.171.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '171.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 171, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '76.3', 'subgroup_hash': 3, 'subgroup_order': 76, 'subgroup_tex': 'D_{38}', 'supersolvable': True, 'sylow': 0}
  • id: 262842070
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 57, 'characteristic': False, 'core_order': 1, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.228.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '228.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 228, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '57.2', 'subgroup_hash': 2, 'subgroup_order': 57, 'subgroup_tex': 'C_{57}', 'supersolvable': True, 'sylow': 0}
  • id: 262842071
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 57, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.228.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '228.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 228, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '57.1', 'subgroup_hash': 1, 'subgroup_order': 57, 'subgroup_tex': 'C_{19}:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 262842072
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.228.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '228.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 228, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '57.1', 'subgroup_hash': 1, 'subgroup_order': 57, 'subgroup_tex': 'C_{19}:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 262842073
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.228.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '228.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 228, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '57.1', 'subgroup_hash': 1, 'subgroup_order': 57, 'subgroup_tex': 'C_{19}:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 262842074
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.228.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '228.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 228, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '57.1', 'subgroup_hash': 1, 'subgroup_order': 57, 'subgroup_tex': 'C_{19}:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 262842075
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.228.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '228.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 228, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '57.1', 'subgroup_hash': 1, 'subgroup_order': 57, 'subgroup_tex': 'C_{19}:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 262842076
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.228.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '228.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 228, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '57.1', 'subgroup_hash': 1, 'subgroup_order': 57, 'subgroup_tex': 'C_{19}:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 262842077
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.228.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '228.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 228, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '57.1', 'subgroup_hash': 1, 'subgroup_order': 57, 'subgroup_tex': 'C_{19}:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 262842078
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 38, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.342.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '342.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 342, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '38.2', 'subgroup_hash': 2, 'subgroup_order': 38, 'subgroup_tex': 'C_{38}', 'supersolvable': True, 'sylow': 0}
  • id: 262842080
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 38, 'characteristic': False, 'core_order': 1, 'counter': 50, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.342.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '342.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 342, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '38.2', 'subgroup_hash': 2, 'subgroup_order': 38, 'subgroup_tex': 'C_{38}', 'supersolvable': True, 'sylow': 0}
  • id: 262842081
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 38, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.342.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '342.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 342, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '38.1', 'subgroup_hash': 1, 'subgroup_order': 38, 'subgroup_tex': 'D_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842082
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 38, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.342.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '342.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 342, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '38.1', 'subgroup_hash': 1, 'subgroup_order': 38, 'subgroup_tex': 'D_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842083
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.342.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '342.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 342, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '38.1', 'subgroup_hash': 1, 'subgroup_order': 38, 'subgroup_tex': 'D_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842084
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.342.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '342.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 342, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '38.1', 'subgroup_hash': 1, 'subgroup_order': 38, 'subgroup_tex': 'D_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842085
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.342.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '342.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 342, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '38.1', 'subgroup_hash': 1, 'subgroup_order': 38, 'subgroup_tex': 'D_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842086
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.342.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '342.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 342, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '38.1', 'subgroup_hash': 1, 'subgroup_order': 38, 'subgroup_tex': 'D_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842087
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.342.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '342.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 342, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '38.1', 'subgroup_hash': 1, 'subgroup_order': 38, 'subgroup_tex': 'D_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '12996.bc.361.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '361.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 361, 'quotient_simple': 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: 262842089
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 1083, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.684.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '684.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 684, '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': '19.1', 'subgroup_hash': 1, 'subgroup_order': 19, 'subgroup_tex': 'C_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842091
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 722, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.684.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '684.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 684, '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': '19.1', 'subgroup_hash': 1, 'subgroup_order': 19, 'subgroup_tex': 'C_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842092
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 722, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.684.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '684.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 684, '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': '19.1', 'subgroup_hash': 1, 'subgroup_order': 19, 'subgroup_tex': 'C_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842093
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 361, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.684.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '684.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 684, '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': '19.1', 'subgroup_hash': 1, 'subgroup_order': 19, 'subgroup_tex': 'C_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842094
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 361, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.684.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '684.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 684, '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': '19.1', 'subgroup_hash': 1, 'subgroup_order': 19, 'subgroup_tex': 'C_{19}', 'supersolvable': True, 'sylow': 0}
  • id: 262842095
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.722.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '722.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 722, 'quotient_simple': 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: 262842096
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.722.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '722.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 722, 'quotient_simple': 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: 262842097
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.722.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '722.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 722, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262842098
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.1083.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1083.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1083, 'quotient_simple': 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: 262842099
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.1083.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1083.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1083, 'quotient_simple': 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: 262842100
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '12996.bc.1444.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1444.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1444, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 262842102
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.2166.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2166.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2166, 'quotient_simple': 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: 262842103
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.2166.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2166.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2166, 'quotient_simple': 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: 262842104
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.2166.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2166.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2166, 'quotient_simple': 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: 262842105
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12996.bc.2166.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2166.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2166, 'quotient_simple': 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: 262842106
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.2166.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2166.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2166, 'quotient_simple': 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: 262842107
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.2166.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2166.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2166, 'quotient_simple': 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: 262842108
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.2166.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2166.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2166, 'quotient_simple': 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: 262842109
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '12996.bc.3249.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3249.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3249, 'quotient_simple': 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': 2}
  • id: 262842110
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 342, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.4332.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4332.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4332, '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: 262842111
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.4332.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4332.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4332, '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: 262842113
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.4332.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4332.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4332, '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: 262842114
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 228, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.6498.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6498.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6498, '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: 262842115
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 228, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.6498.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6498.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6498, '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: 262842116
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12996.bc.6498.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6498.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6498, '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: 262842117
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12996.bc', 'ambient_counter': 29, 'ambient_order': 12996, 'ambient_tex': 'C_{19}^2:(C_6\\times S_3)', 'central': True, 'central_factor': False, 'centralizer_order': 12996, 'characteristic': True, 'core_order': 1, 'counter': 84, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '12996.bc.12996.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12996.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '12996.bc', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8995592235010807521, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 12996, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': None, 'quotient_tex': 'C_{19}^2:(C_6\\times S_3)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D3', 'C5'], '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: 262842035
    {'ambient': '12996.bc', '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': '12996.a1.a1', 'complements': ['12996.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '3.a1.a1', '3.b1.a1', '361.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4858, 6069, 6788, 5834, 3887, 5743, 3943, 4459], 'generators': [5772, 8244, 684, 8390, 234, 5379], 'label': '12996.bc.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.b1', '2.a1.a1', '2.b1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842036
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': ['2166.b1.a1', '2166.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '18.a1.a1', '114.e1.a1', '114.f1.a1', '114.f1.b1', '114.g1.a1', '114.g1.b1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6242, 1255, 5705, 1260, 4723, 1363, 5289, 8335], 'generators': [2250, 8390, 684, 4824], 'label': '12996.bc.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842037
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': ['2166.a1.b1', '2166.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '18.a1.a1', '114.h1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4002, 4136, 7590, 3346, 5245, 6464, 2972, 4661], 'generators': [2250, 7320, 684, 4824], 'label': '12996.bc.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '12996.bc', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842038
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '18.b1.a1', '114.a1.a1', '114.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7875, -1, 2094, -1, 1928, -1, 6731, -1], 'generators': [5379, 8390, 684, 720], 'label': '12996.bc.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.d1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842039
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.b1.a1'], 'contains': ['12.a1.a1', '18.b1.b1', '114.a1.b1', '114.b1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7875, -1, 2776, -1, 1928, -1, 8708, -1], 'generators': [10869, 8390, 684, 12348], 'label': '12996.bc.6.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.d1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842040
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.c1.a1', '18.a1.a1', '114.c1.a1', '114.d1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1377, -1, 9190, -1, 8563, -1, 1049, -1], 'generators': [2250, 2114, 684, 4824], 'label': '12996.bc.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '6.e1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842041
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.b1.b1', '171.a1.a1', '171.a1.b1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9086, -1, 4128, -1, 2394, -1, 7082, -1], 'generators': [939, 2250, 684, 7560], 'label': '12996.bc.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842042
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': ['1083.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.d1.a1', '6.d1.b1'], 'contains': ['36.a1.a1', '228.c1.a1', '228.d1.a1', '228.d1.b1', '228.e1.a1', '228.e1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6312, 3867, 2776, 1260, 4723, 1539, 5643, 7347], 'generators': [8390, 4824, 684], 'label': '12996.bc.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.a1'], 'normal_contains': ['36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842043
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': ['1083.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.a1.b1', '6.c1.a1'], 'contains': ['36.a1.a1', '228.f1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4002, 6748, 7383, 4672, 5768, 6464, 3089, 3800], 'generators': [7320, 5508, 684], 'label': '12996.bc.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.b1', '6.a1.a1', '6.c1.a1'], 'normal_contains': ['36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': '12.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842044
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '684.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.e1.a1'], 'contains': ['36.a1.a1', '228.a1.a1', '228.b1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1377, -1, 9190, -1, 8563, -1, 1049, -1], 'generators': [2114, 4824, 684], 'label': '12996.bc.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.c1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '342.9'}
  • id: 262842045
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': ['722.a1.b1', '722.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.a1', '6.e1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '342.c1.a1', '342.d1.a1', '342.d1.b1', '342.e1.a1', '342.e1.b1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5226, 2036, 6359, 2943, 5245, 4002, 4935, 5573], 'generators': [2250, 4824, 684], 'label': '12996.bc.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.b1.a1', '6.c1.a1'], 'normal_contains': ['36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': '18.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842046
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': ['6498.b1.a1', '6498.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '6.d1.a1', '722.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4858, 8745, 5087, 4866, 3211, 5743, 3469, 5865], 'generators': [8244, 684, 7248, 2114, 5379], 'label': '12996.bc.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842047
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '684.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '342.a1.a1', '342.b1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7812, -1, 3785, -1, 1808, -1, 6728, -1], 'generators': [939, 684, 7560], 'label': '12996.bc.18.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '228.7'}
  • id: 262842048
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '684.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '6.d1.b1', '9.a1.a1'], 'contains': ['36.a1.a1', '342.a1.b1', '342.b1.b1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7812, -1, 4489, -1, 1808, -1, 8926, -1], 'generators': [11061, 684, 8244], 'label': '12996.bc.18.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.b1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.b1', 'subgroup_fusion': None, 'weyl_group': '228.7'}
  • id: 262842049
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': ['361.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '18.a1.a1', '18.b1.a1', '18.b1.b1'], 'contains': ['684.a1.a1', '684.b1.a1', '684.b1.b1', '684.c1.a1', '684.c1.b1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5281, 3867, 5095, 2943, 5354, 4002, 5444, 5573], 'generators': [4824, 684], 'label': '12996.bc.36.a1.a1', 'mobius_quo': -1, 'mobius_sub': 6, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.b1.a1', '18.a1.a1'], 'normal_contains': ['12996.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': '36.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 262842050
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '38.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4332.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['76.a1.a1', '114.c1.a1', '114.d1.a1', '114.e1.a1', '114.h1.a1', '722.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': '38T28', 'count': 38, 'diagramx': [2413, -1, 8729, -1, 7205, -1, 2039, -1], 'generators': [2250, 8390, 684, 7320], 'label': '12996.bc.38.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '38.a1.a1', 'old_label': '38.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '38.a1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842051
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '57.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['114.a1.a1', '114.b1.b1', '114.f1.a1', '171.a1.a1', '1083.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [9583, -1, 1951, -1, 1304, -1, 7498, -1], 'generators': [2499, 306, 12348, 8390], 'label': '12996.bc.57.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.a1', 'old_label': '57.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '57.a1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842052
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '57.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['114.a1.b1', '114.b1.a1', '114.f1.b1', '171.a1.b1', '1083.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [9583, -1, 890, -1, 1304, -1, 8031, -1], 'generators': [10455, 90, 720, 8390], 'label': '12996.bc.57.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.b1', 'old_label': '57.a1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '57.a1.b1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842053
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '76.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4332.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '38.a1.a1'], 'contains': ['228.a1.a1', '228.b1.a1', '228.c1.a1', '228.f1.a1', '1444.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 38, 'diagramx': [1940, -1, 8851, -1, 7791, -1, 1612, -1], 'generators': [2114, 7320, 684], 'label': '12996.bc.76.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '38.a1.a1', 'old_label': '76.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '76.a1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842054
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '114.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '57.a1.a1'], 'contains': ['228.d1.a1', '342.a1.a1', '2166.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [9300, -1, 1544, -1, 774, -1, 7236, -1], 'generators': [5379, 10262, 12348], 'label': '12996.bc.114.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.a1', 'old_label': '114.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '114.a1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842055
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '114.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '57.a1.b1'], 'contains': ['228.d1.b1', '342.a1.b1', '2166.a1.b1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [9300, -1, 671, -1, 774, -1, 9761, -1], 'generators': [10869, 6122, 720], 'label': '12996.bc.114.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.b1', 'old_label': '114.a1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '114.a1.b1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842056
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '114.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '57.a1.b1'], 'contains': ['228.d1.b1', '342.b1.a1', '2166.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [8139, -1, 163, -1, 188, -1, 8034, -1], 'generators': [5379, 1298, 720], 'label': '12996.bc.114.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.b1', 'old_label': '114.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '114.b1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842057
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': ['6498.b1.a1', '6498.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.b1', '6.d1.b1', '722.a1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4858, 8745, 7270, 8740, 3211, 5743, 4557, 3065], 'generators': [4824, 684, 7248, 2114, 10869], 'label': '12996.bc.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '12996.bc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842058
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '114.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '57.a1.a1'], 'contains': ['228.d1.a1', '342.b1.b1', '2166.a1.b1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [8139, -1, 2052, -1, 188, -1, 9334, -1], 'generators': [10869, 1694, 12348], 'label': '12996.bc.114.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.a1', 'old_label': '114.b1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '114.b1.b1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842059
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '114.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4332.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '38.a1.a1'], 'contains': ['228.a1.a1', '342.c1.a1', '2166.c1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 38, 'diagramx': [1338, -1, 9834, -1, 9728, -1, 524, -1], 'generators': [2250, 2114, 36], 'label': '12996.bc.114.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '38.a1.a1', 'old_label': '114.c1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '114.c1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842060
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '114.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4332.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '38.a1.a1'], 'contains': ['228.b1.a1', '342.c1.a1', '2166.c1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 38, 'diagramx': [252, -1, 9130, -1, 9198, -1, 137, -1], 'generators': [2250, 2114, 684], 'label': '12996.bc.114.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '38.a1.a1', 'old_label': '114.d1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '114.d1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842061
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '114.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4332.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '38.a1.a1'], 'contains': ['228.c1.a1', '342.c1.a1', '2166.d1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 38, 'diagramx': [4534, -1, 7351, -1, 6761, -1, 2735, -1], 'generators': [2250, 8390, 684], 'label': '12996.bc.114.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '38.a1.a1', 'old_label': '114.e1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '114.e1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842062
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '114.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '57.a1.a1'], 'contains': ['228.d1.a1', '342.d1.a1', '2166.d1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [7432, -1, 3933, -1, 2875, -1, 5996, -1], 'generators': [2250, 8390, 12348], 'label': '12996.bc.114.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.a1', 'old_label': '114.f1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '114.f1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842063
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '114.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '57.a1.b1'], 'contains': ['228.d1.b1', '342.d1.b1', '2166.d1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [7432, -1, 2809, -1, 2875, -1, 6320, -1], 'generators': [2250, 8390, 4824], 'label': '12996.bc.114.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.b1', 'old_label': '114.f1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '114.f1.b1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842064
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '114.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['228.e1.a1', '342.e1.a1', '2166.d1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 114, 'diagramx': [5889, -1, 5857, -1, 4238, -1, 5289, -1], 'generators': [2250, 8390, 2088], 'label': '12996.bc.114.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '114.g1.a1', 'old_label': '114.g1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '114.g1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842065
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '114.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['228.e1.b1', '342.e1.b1', '2166.d1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 114, 'diagramx': [5889, -1, 5472, -1, 4238, -1, 4582, -1], 'generators': [2250, 8390, 2772], 'label': '12996.bc.114.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '114.g1.b1', 'old_label': '114.g1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '114.g1.b1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842066
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '114.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4332.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '38.a1.a1'], 'contains': ['228.f1.a1', '342.c1.a1', '2166.e1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 38, 'diagramx': [2802, -1, 8231, -1, 7205, -1, 2039, -1], 'generators': [2250, 7320, 684], 'label': '12996.bc.114.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '38.a1.a1', 'old_label': '114.h1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '114.h1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842067
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '171.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '57.a1.a1'], 'contains': ['342.a1.a1', '342.b1.b1', '342.d1.a1', '3249.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [9748, -1, 3348, -1, 1304, -1, 8316, -1], 'generators': [12747, 2250, 5508], 'label': '12996.bc.171.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.a1', 'old_label': '171.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '171.a1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842068
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': ['6498.a1.b1', '6498.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.b1.a1', '6.c1.a1', '6.e1.a1', '38.a1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3294, 3354, 8017, 1542, 5514, 1821, 2719, 8689], 'generators': [4824, 684, 7320, 8390, 2250], 'label': '12996.bc.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.b1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842069
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '171.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '57.a1.b1'], 'contains': ['342.a1.b1', '342.b1.a1', '342.d1.b1', '3249.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [9748, -1, 1951, -1, 1304, -1, 8558, -1], 'generators': [4251, 2250, 7560], 'label': '12996.bc.171.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.b1', 'old_label': '171.a1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '171.a1.b1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842070
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '228.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '228.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '76.a1.a1', '114.c1.a1'], 'contains': ['684.a1.a1', '4332.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 38, 'diagramx': [1148, -1, 9837, -1, 8347, -1, 1851, -1], 'generators': [2114, 36], 'label': '12996.bc.228.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '38.a1.a1', 'old_label': '228.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '228.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 262842071
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '228.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '228.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '76.a1.a1', '114.d1.a1'], 'contains': ['684.a1.a1', '4332.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [252, -1, 9233, -1, 7690, -1, 1372, -1], 'generators': [2114, 684], 'label': '12996.bc.228.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '228.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '228.b1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842072
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '228.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4332.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '76.a1.a1', '114.e1.a1'], 'contains': ['684.a1.a1', '4332.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 38, 'diagramx': [4504, -1, 7351, -1, 6369, -1, 3564, -1], 'generators': [8390, 684], 'label': '12996.bc.228.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '38.a1.a1', 'old_label': '228.c1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '228.c1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842073
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '228.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '114.a1.a1', '114.b1.b1', '114.f1.a1'], 'contains': ['684.b1.a1', '4332.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [7781, -1, 2624, -1, 2756, -1, 6562, -1], 'generators': [8390, 12348], 'label': '12996.bc.228.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.a1', 'old_label': '228.d1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '228.d1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842074
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '228.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '114.a1.b1', '114.b1.a1', '114.f1.b1'], 'contains': ['684.b1.b1', '4332.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [7781, -1, 1130, -1, 2756, -1, 7084, -1], 'generators': [8390, 4824], 'label': '12996.bc.228.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.b1', 'old_label': '228.d1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '228.d1.b1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842075
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '228.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '114.g1.a1'], 'contains': ['684.c1.a1', '4332.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 114, 'diagramx': [6238, -1, 5243, -1, 4596, -1, 5754, -1], 'generators': [8390, 2088], 'label': '12996.bc.228.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '114.g1.a1', 'old_label': '228.e1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '228.e1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842076
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '228.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '114.g1.b1'], 'contains': ['684.c1.b1', '4332.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 114, 'diagramx': [6238, -1, 4732, -1, 4596, -1, 4935, -1], 'generators': [8390, 2772], 'label': '12996.bc.228.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '114.g1.b1', 'old_label': '228.e1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '228.e1.b1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842077
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '228.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4332.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '76.a1.a1', '114.h1.a1'], 'contains': ['684.a1.a1', '4332.c1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 38, 'diagramx': [2423, -1, 8353, -1, 6813, -1, 2819, -1], 'generators': [7320, 684], 'label': '12996.bc.228.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '38.a1.a1', 'old_label': '228.f1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '228.f1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842078
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '342.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '342.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '114.a1.a1', '171.a1.a1'], 'contains': ['684.b1.a1', '6498.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [9499, -1, 3446, -1, 1954, -1, 7367, -1], 'generators': [939, 5508], 'label': '12996.bc.342.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.a1', 'old_label': '342.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '342.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 262842079
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': ['4332.b1.a1', '4332.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.a1.b1', '6.c1.a1', '9.a1.a1', '1083.b1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5545, 6069, 6563, 7087, 3887, 8927, 4065, 773], 'generators': [7560, 684, 6348, 2250, 939], 'label': '12996.bc.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.b1', '6.a1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842080
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '342.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '342.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.b1', '114.a1.b1', '171.a1.b1'], 'contains': ['684.b1.b1', '6498.a1.b1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [9499, -1, 2255, -1, 1954, -1, 8558, -1], 'generators': [11061, 4824], 'label': '12996.bc.342.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.b1', 'old_label': '342.a1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '342.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 262842081
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '342.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '342.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '114.b1.a1', '171.a1.b1'], 'contains': ['684.b1.b1', '6498.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8458, -1, 1967, -1, 1622, -1, 7832, -1], 'generators': [4251, 7560], 'label': '12996.bc.342.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '342.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '342.b1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842082
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '342.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '342.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.b1', '114.b1.b1', '171.a1.a1'], 'contains': ['684.b1.a1', '6498.a1.b1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8458, -1, 3733, -1, 1622, -1, 8316, -1], 'generators': [11061, 8244], 'label': '12996.bc.342.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '342.b1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '342.b1.b1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842083
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '342.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4332.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '114.c1.a1', '114.d1.a1', '114.e1.a1', '114.h1.a1'], 'contains': ['684.a1.a1', '6498.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 38, 'diagramx': [3035, -1, 8240, -1, 7201, -1, 2536, -1], 'generators': [2250, 684], 'label': '12996.bc.342.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '38.a1.a1', 'old_label': '342.c1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '342.c1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842084
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '342.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '114.f1.a1', '171.a1.a1'], 'contains': ['684.b1.a1', '6498.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [7572, -1, 4147, -1, 3454, -1, 6037, -1], 'generators': [2250, 12348], 'label': '12996.bc.342.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.a1', 'old_label': '342.d1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '342.d1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842085
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '342.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6498.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '114.f1.b1', '171.a1.b1'], 'contains': ['684.b1.b1', '6498.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [7572, -1, 2666, -1, 3454, -1, 6279, -1], 'generators': [2250, 4824], 'label': '12996.bc.342.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.b1', 'old_label': '342.d1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '342.d1.b1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842086
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '342.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '114.g1.a1'], 'contains': ['684.c1.a1', '6498.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 114, 'diagramx': [5595, -1, 5945, -1, 4984, -1, 4653, -1], 'generators': [2250, 2088], 'label': '12996.bc.342.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '114.g1.a1', 'old_label': '342.e1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '342.e1.a1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842087
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '342.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '114.g1.b1'], 'contains': ['684.c1.b1', '6498.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 114, 'diagramx': [5595, -1, 6232, -1, 4984, -1, 4411, -1], 'generators': [2250, 2772], 'label': '12996.bc.342.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '114.g1.b1', 'old_label': '342.e1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '342.e1.b1', 'subgroup_fusion': None, 'weyl_group': '114.1'}
  • id: 262842088
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '361.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2166.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['722.a1.a1', '722.a1.b1', '722.b1.a1', '1083.a1.a1', '1083.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 361, 'diagramx': [3787, -1, 6847, -1, 4208, -1, 3831, -1], 'generators': [2499, 2250, 2114, 7320], 'label': '12996.bc.361.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '361.a1.a1', 'old_label': '361.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '361.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 262842089
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '684.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '228.a1.a1', '228.b1.a1', '228.c1.a1', '228.f1.a1', '342.c1.a1'], 'contains': ['12996.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2218, -1, 8486, -1, 6813, -1, 2819, -1], 'generators': [684], 'label': '12996.bc.684.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '684.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '684.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 262842090
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.d1.a1', '6.d1.b1', '9.a1.a1', '57.a1.a1', '57.a1.b1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8075, -1, 2776, -1, 2379, -1, 7082, -1], 'generators': [720, 684, 8390, 234, 5379], 'label': '12996.bc.3.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842091
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '684.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '228.d1.a1', '342.a1.a1', '342.b1.b1', '342.d1.a1'], 'contains': ['12996.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8454, -1, 3907, -1, 3100, -1, 6298, -1], 'generators': [12348], 'label': '12996.bc.684.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '684.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '684.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 262842092
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '684.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '228.d1.b1', '342.a1.b1', '342.b1.a1', '342.d1.b1'], 'contains': ['12996.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8454, -1, 2032, -1, 3100, -1, 7062, -1], 'generators': [4824], 'label': '12996.bc.684.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '684.b1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '684.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 262842093
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '684.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '228.e1.a1', '342.e1.a1'], 'contains': ['12996.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5535, -1, 5049, -1, 5223, -1, 5444, -1], 'generators': [2088], 'label': '12996.bc.684.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '684.c1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '684.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 262842094
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '684.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '228.e1.b1', '342.e1.b1'], 'contains': ['12996.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5535, -1, 5334, -1, 5223, -1, 5071, -1], 'generators': [2772], 'label': '12996.bc.684.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '684.c1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '684.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 262842095
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '722.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2166.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '361.a1.a1'], 'contains': ['1444.a1.a1', '2166.a1.a1', '2166.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 361, 'diagramx': [4051, -1, 6365, -1, 3349, -1, 3567, -1], 'generators': [5379, 3482, 8724], 'label': '12996.bc.722.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '361.a1.a1', 'old_label': '722.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '722.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 262842096
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '722.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2166.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '361.a1.a1'], 'contains': ['1444.a1.a1', '2166.a1.b1', '2166.b1.b1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 361, 'diagramx': [4051, -1, 7050, -1, 3349, -1, 4236, -1], 'generators': [10869, 11690, 3756], 'label': '12996.bc.722.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '361.a1.a1', 'old_label': '722.a1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '722.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 262842097
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '722.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '722.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['38.a1.a1', '361.a1.a1'], 'contains': ['1444.a1.a1', '2166.c1.a1', '2166.d1.a1', '2166.e1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 361, 'diagramx': [3184, -1, 7736, -1, 6283, -1, 2387, -1], 'generators': [2250, 8390, 7320], 'label': '12996.bc.722.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '361.a1.a1', 'old_label': '722.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '722.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262842098
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '1083.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1083.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['57.a1.a1', '57.a1.b1', '361.a1.a1'], 'contains': ['2166.a1.a1', '2166.a1.b1', '2166.d1.a1', '3249.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 1083, 'diagramx': [7104, -1, 1350, -1, 2398, -1, 7685, -1], 'generators': [2499, 2250, 8390], 'label': '12996.bc.1083.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1083.a1.a1', 'old_label': '1083.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1083.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262842099
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '1083.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2166.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '361.a1.a1'], 'contains': ['2166.b1.a1', '2166.b1.b1', '2166.e1.a1', '3249.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 361, 'diagramx': [4634, -1, 6714, -1, 3880, -1, 3850, -1], 'generators': [12747, 2250, 7320], 'label': '12996.bc.1083.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '361.a1.a1', 'old_label': '1083.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1083.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 262842100
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '1444.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '722.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['76.a1.a1', '722.a1.a1', '722.a1.b1', '722.b1.a1'], 'contains': ['4332.a1.a1', '4332.b1.a1', '4332.c1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 361, 'diagramx': [2926, -1, 7649, -1, 5992, -1, 3290, -1], 'generators': [2114, 7320], 'label': '12996.bc.1444.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '361.a1.a1', 'old_label': '1444.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1444.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262842101
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': ['3249.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '76.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3080, 6069, 8160, 3227, 5787, 3914, 2577, 6498], 'generators': [2114, 7320, 684, 5508], 'label': '12996.bc.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.b1', '2.a1.a1', '2.b1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842102
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '2166.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1083.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['114.a1.a1', '114.b1.a1', '722.a1.a1', '1083.a1.a1'], 'contains': ['4332.b1.a1', '6498.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 1083, 'diagramx': [7298, -1, 1230, -1, 2398, -1, 6823, -1], 'generators': [5379, 6374], 'label': '12996.bc.2166.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1083.a1.a1', 'old_label': '2166.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2166.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262842103
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '2166.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1083.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['114.a1.b1', '114.b1.b1', '722.a1.b1', '1083.a1.a1'], 'contains': ['4332.b1.a1', '6498.a1.b1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 1083, 'diagramx': [7298, -1, 2203, -1, 2398, -1, 8053, -1], 'generators': [10869, 6878], 'label': '12996.bc.2166.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1083.a1.a1', 'old_label': '2166.a1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2166.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262842104
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '2166.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2166.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '722.a1.a1', '1083.b1.a1'], 'contains': ['4332.c1.a1', '6498.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 361, 'diagramx': [4339, -1, 6452, -1, 3756, -1, 3826, -1], 'generators': [3, 6852], 'label': '12996.bc.2166.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '361.a1.a1', 'old_label': '2166.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2166.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 262842105
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '2166.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2166.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '722.a1.b1', '1083.b1.a1'], 'contains': ['4332.c1.a1', '6498.a1.b1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 361, 'diagramx': [4339, -1, 7031, -1, 3756, -1, 4022, -1], 'generators': [12033, 6996], 'label': '12996.bc.2166.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '361.a1.a1', 'old_label': '2166.b1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2166.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 262842106
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '2166.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '722.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['114.c1.a1', '114.d1.a1', '722.b1.a1'], 'contains': ['4332.a1.a1', '6498.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 722, 'diagramx': [1482, -1, 8894, -1, 8048, -1, 1633, -1], 'generators': [2250, 2114], 'label': '12996.bc.2166.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '722.b1.a1', 'old_label': '2166.c1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2166.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262842107
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '2166.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '361.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['114.e1.a1', '114.f1.a1', '114.f1.b1', '114.g1.a1', '114.g1.b1', '722.b1.a1', '1083.a1.a1'], 'contains': ['4332.b1.a1', '6498.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 361, 'diagramx': [5805, -1, 5469, -1, 4238, -1, 5197, -1], 'generators': [2250, 8390], 'label': '12996.bc.2166.d1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '361.a1.a1', 'old_label': '2166.d1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2166.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262842108
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '2166.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '722.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['114.h1.a1', '722.b1.a1', '1083.b1.a1'], 'contains': ['4332.c1.a1', '6498.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 361, 'diagramx': [3747, -1, 7578, -1, 5701, -1, 3080, -1], 'generators': [2250, 7320], 'label': '12996.bc.2166.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '361.a1.a1', 'old_label': '2166.e1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2166.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262842109
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '3249.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1083.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['171.a1.a1', '171.a1.b1', '1083.a1.a1', '1083.b1.a1'], 'contains': ['6498.a1.a1', '6498.a1.b1', '6498.b1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 1083, 'diagramx': [7114, -1, 2872, -1, 3133, -1, 7598, -1], 'generators': [12747, 2250], 'label': '12996.bc.3249.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1083.a1.a1', 'old_label': '3249.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3249.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262842110
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '4332.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '38.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['228.a1.a1', '228.b1.a1', '1444.a1.a1', '2166.c1.a1'], 'contains': ['12996.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 38, 'diagramx': [1482, -1, 8894, -1, 7690, -1, 1851, -1], 'generators': [2114], 'label': '12996.bc.4332.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '38.a1.a1', 'old_label': '4332.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4332.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262842111
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '4332.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '361.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['228.c1.a1', '228.d1.a1', '228.d1.b1', '228.e1.a1', '228.e1.b1', '1444.a1.a1', '2166.a1.a1', '2166.a1.b1', '2166.d1.a1'], 'contains': ['12996.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 361, 'diagramx': [5805, -1, 4421, -1, 4596, -1, 5708, -1], 'generators': [8390], 'label': '12996.bc.4332.b1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '361.a1.a1', 'old_label': '4332.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4332.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262842112
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': ['2166.d1.a1', '2166.c1.a1', '2166.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '18.b1.a1', '2166.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5545, 8579, 5252, 5999, 3551, 8927, 3352, 2888], 'generators': [939, 6348, 684, 12348], 'label': '12996.bc.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 262842113
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '4332.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '722.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['228.f1.a1', '1444.a1.a1', '2166.b1.a1', '2166.b1.b1', '2166.e1.a1'], 'contains': ['12996.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 361, 'diagramx': [3200, -1, 7196, -1, 5701, -1, 3556, -1], 'generators': [7320], 'label': '12996.bc.4332.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '361.a1.a1', 'old_label': '4332.c1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4332.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262842114
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '6498.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '57.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['342.a1.a1', '342.b1.a1', '2166.a1.a1', '2166.b1.a1', '3249.a1.a1'], 'contains': ['12996.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [7503, -1, 2507, -1, 2790, -1, 6834, -1], 'generators': [3], 'label': '12996.bc.6498.a1.a1', 'mobius_quo': None, 'mobius_sub': 19, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.a1', 'old_label': '6498.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6498.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262842115
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '6498.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '57.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['342.a1.b1', '342.b1.b1', '2166.a1.b1', '2166.b1.b1', '3249.a1.a1'], 'contains': ['12996.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 57, 'diagramx': [7503, -1, 3102, -1, 2790, -1, 7824, -1], 'generators': [12033], 'label': '12996.bc.6498.a1.b1', 'mobius_quo': None, 'mobius_sub': 19, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '57.a1.b1', 'old_label': '6498.a1.b1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6498.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262842116
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '6498.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '361.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['342.c1.a1', '342.d1.a1', '342.d1.b1', '342.e1.a1', '342.e1.b1', '2166.c1.a1', '2166.d1.a1', '2166.e1.a1', '3249.a1.a1'], 'contains': ['12996.a1.a1'], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 361, 'diagramx': [4574, -1, 5715, -1, 4924, -1, 4753, -1], 'generators': [2250], 'label': '12996.bc.6498.b1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '361.a1.a1', 'old_label': '6498.b1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6498.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262842117
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '12996.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['684.a1.a1', '684.b1.a1', '684.b1.b1', '684.c1.a1', '684.c1.b1', '4332.a1.a1', '4332.b1.a1', '4332.c1.a1', '6498.a1.a1', '6498.a1.b1', '6498.b1.a1'], 'contains': [], 'core': '12996.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4908, 3867, 4729, 2943, 5074, 4002, 5444, 5573], 'generators': [], 'label': '12996.bc.12996.a1.a1', 'mobius_quo': 1, 'mobius_sub': -2166, 'normal_closure': '12996.a1.a1', 'normal_contained_in': ['36.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '12996.a1.a1', 'projective_image': '12996.bc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12996.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262842118
    {'ambient': '12996.bc', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12996.a1.a1', 'complements': ['2166.d1.a1', '2166.c1.a1', '2166.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.b1.a1', '18.b1.b1', '2166.b1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5545, 8579, 7138, 8070, 3551, 8927, 4310, 1127], 'generators': [11061, 5160, 684, 720], 'label': '12996.bc.6.a1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.b1', 'normal_contained_in': ['2.a1.b1', '3.a1.a1'], 'normal_contains': ['12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.b1', 'projective_image': '12996.bc', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}