Abstract group data - 2400.bt

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [2, 20, 4, 2, 4, 2, 60, 2], 'aut_gens': [[122109387504, 77355542572, 130509168233, 147999673081, 148051235266, 116250388725], [122109387504, 77355542572, 60215928797, 147999673081, 42634393514, 116250388725], [5078828170, 77355542572, 66075318946, 147999673081, 122230481386, 151807329271], [122109387504, 113732510846, 92911416209, 75245970908, 1322734790, 43496295927], [122109387504, 77355542572, 71992911941, 147999673081, 24801160490, 116250388725], [5078828170, 29953804004, 87052026055, 111623017307, 38920487444, 115430282997], [5078828170, 40978887423, 108369567715, 38868924509, 111674579617, 42676190199], [5078828170, 12581083359, 103672680970, 147999673081, 102142146747, 151807329271], [5078828170, 77355542572, 130509168233, 147999673081, 24801160490, 151807329271]], 'aut_group': '19200.bj', 'aut_hash': 7188633043150786832, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 19200, 'aut_permdeg': 40, 'aut_perms': [253312846115475057493232496895076042579295413733, 790452548108827236261397032166563936580818014134, 398543359480943729697896347917605376056839531113, 353223867849215885972922208049971536524584138295, 407833444209382133252187284337502207718386887184, 97179909648855351984364163108684214723721121103, 134922383901032257881937333088546884049027910495, 5770753944467775514874717034639165089583836465], 'aut_phi_ratio': 30.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 150, 2, 1], [3, 20, 1, 1], [4, 5, 4, 1], [4, 30, 1, 2], [5, 2, 2, 1], [5, 12, 2, 1], [5, 24, 4, 1], [6, 20, 1, 1], [6, 20, 2, 1], [10, 2, 2, 1], [10, 2, 4, 1], [10, 12, 2, 1], [10, 12, 4, 1], [10, 24, 4, 1], [10, 24, 8, 1], [12, 100, 4, 1], [15, 40, 2, 1], [20, 60, 2, 2], [20, 60, 8, 1], [30, 40, 2, 1], [30, 40, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_4\\times F_5\\times S_5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.3', 'autcent_hash': 3, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '2400.db', 'autcentquo_hash': 3070016846447328869, 'autcentquo_nilpotent': False, 'autcentquo_order': 2400, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\times S_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 150, 2], [3, 20, 1], [4, 5, 4], [4, 30, 2], [5, 2, 2], [5, 12, 2], [5, 24, 4], [6, 20, 3], [10, 2, 6], [10, 12, 6], [10, 24, 12], [12, 100, 4], [15, 40, 2], [20, 60, 12], [30, 40, 6]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '600.146', 'commutator_count': 1, 'commutator_label': '600.54', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '5.1', '60.5'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 46, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['1200.481', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 150, 1, 2], [3, 20, 1, 1], [4, 5, 2, 2], [4, 30, 1, 2], [5, 2, 2, 1], [5, 12, 2, 1], [5, 24, 2, 2], [6, 20, 1, 3], [10, 2, 2, 3], [10, 12, 2, 3], [10, 24, 2, 6], [12, 100, 2, 2], [15, 40, 2, 1], [20, 60, 2, 2], [20, 60, 4, 2], [30, 40, 2, 3]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 57, 'exponent': 60, 'exponents_of_order': [5, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '1200.944', 'hash': 6351781673999964458, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [1, 15, 2, 5, 2, 5], 'inner_gens': [[122109387504, 77355542572, 130509168233, 147999673081, 148051235266, 116250388725], [122109387504, 77355542572, 92911416209, 147999673081, 30556644004, 116250388725], [122109387504, 40978887423, 130509168233, 38868924509, 148051235266, 7119249528], [122109387504, 77355542572, 50675370281, 147999673081, 75297533218, 116250388725], [122109387504, 21929326699, 130509168233, 38868924509, 148051235266, 7119249528], [122109387504, 77355542572, 87052026055, 147999673081, 38920487444, 116250388725]], 'inner_hash': 146, 'inner_nilpotent': False, 'inner_order': 600, 'inner_split': False, 'inner_tex': 'D_5\\times A_5', 'inner_used': [2, 3, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4], [2, 12], [3, 8], [4, 16], [5, 4], [6, 12], [8, 8], [10, 4], [12, 4]], 'label': '2400.bt', 'linC_count': 16, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 8, 'linQ_dim': 9, 'linQ_dim_count': 8, 'linR_count': 16, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'SL(2,5):D10', 'ngens': 6, '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, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 26, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 72, 'number_divisions': 40, 'number_normal_subgroups': 20, 'number_subgroup_autclasses': 138, 'number_subgroup_classes': 232, 'number_subgroups': 5980, 'old_label': None, 'order': 2400, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 303], [3, 20], [4, 80], [5, 124], [6, 60], [10, 372], [12, 400], [15, 80], [20, 720], [30, 240]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [130509168233, 7089953025, 7089953025, 30527346876], 'outer_gens': [[122109387504, 4601837899, 130509168233, 111623017307, 148051235266, 79873342326], [122109387504, 59195525983, 71992911941, 111623017307, 24754285370, 79873342326], [5078828170, 59195525983, 71992911941, 111623017307, 148098110386, 115430282997], [5078828170, 59195525983, 118732185089, 111623017307, 42587518394, 115430282997]], 'outer_group': '32.46', 'outer_hash': 46, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [7, 23, 11543, 16567], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 31, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 6], [5, 4], [6, 4], [8, 8], [12, 6], [16, 4], [20, 2], [24, 2]], 'representations': {'GLFp': {'d': 4, 'p': 5, 'gens': [122109387504, 77355542572, 130509168233, 147999673081, 148051235266, 116250388725]}, 'Perm': {'d': 31, 'gens': [292725929225504590146332350192230, 565917939345389685165176183195329, 841515720257750107397704921901215, 565917939345389685165176183193601, 565917939345389685165176183196120, 539393489113882869654087476465694]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\SL(2,5):D_{10}', 'transitive_degree': 240, '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: 155798499
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 46, 'group_order': 2400, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 30527346876, 'size': 1}
  • id: 155798510
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 46, 'group_order': 2400, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 5078828170, 'size': 1}
  • id: 155798521
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 46, 'group_order': 2400, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 122109387504, 'size': 1}
  • id: 155798532
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 46, 'group_order': 2400, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 1271171980, 'size': 1}
  • id: 155798543
    {'aut_label': '2D', 'centralizer': '150.a1.a1', 'counter': 5, 'group_counter': 46, 'group_order': 2400, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 40478052989, 'size': 150}
  • id: 155798554
    {'aut_label': '2D', 'centralizer': '150.a1.a1', 'counter': 6, 'group_counter': 46, 'group_order': 2400, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 104588083197, 'size': 150}
  • id: 155798565
    {'aut_label': '3A', 'centralizer': '20.c1.a1', 'counter': 7, 'group_counter': 46, 'group_order': 2400, 'label': '3A', 'order': 3, 'powers': [7, 1, 7], 'representative': 22859104683, 'size': 20}
  • id: 155798569
    {'aut_label': '4A1', 'centralizer': '5.b1.a1', 'counter': 8, 'group_counter': 46, 'group_order': 2400, 'label': '4A1', 'order': 4, 'powers': [4, 9, 8], 'representative': 87052026055, 'size': 5}
  • id: 155798570
    {'aut_label': '4A1', 'centralizer': '5.b1.a1', 'counter': 9, 'group_counter': 46, 'group_order': 2400, 'label': '4A-1', 'order': 4, 'powers': [4, 8, 9], 'representative': 28535769768, 'size': 5}
  • id: 155798500
    {'aut_label': '4A1', 'centralizer': '5.b1.a1', 'counter': 10, 'group_counter': 46, 'group_order': 2400, 'label': '4B1', 'order': 4, 'powers': [4, 11, 10], 'representative': 82355139310, 'size': 5}
  • id: 155798501
    {'aut_label': '4A1', 'centralizer': '5.b1.a1', 'counter': 11, 'group_counter': 46, 'group_order': 2400, 'label': '4B-1', 'order': 4, 'powers': [4, 10, 11], 'representative': 23838883023, 'size': 5}
  • id: 155798502
    {'aut_label': '4C', 'centralizer': '30.b1.a1', 'counter': 12, 'group_counter': 46, 'group_order': 2400, 'label': '4C', 'order': 4, 'powers': [4, 12, 12], 'representative': 20421058009, 'size': 30}
  • id: 155798503
    {'aut_label': '4D', 'centralizer': '30.b1.a1', 'counter': 13, 'group_counter': 46, 'group_order': 2400, 'label': '4D', 'order': 4, 'powers': [4, 13, 13], 'representative': 105535439803, 'size': 30}
  • id: 155798504
    {'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 14, 'group_counter': 46, 'group_order': 2400, 'label': '5A1', 'order': 5, 'powers': [15, 15, 1], 'representative': 140879192328, 'size': 2}
  • id: 155798505
    {'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 15, 'group_counter': 46, 'group_order': 2400, 'label': '5A2', 'order': 5, 'powers': [14, 14, 1], 'representative': 68125099525, 'size': 2}
  • id: 155798506
    {'aut_label': '5B1', 'centralizer': '12.b1.a1', 'counter': 16, 'group_counter': 46, 'group_order': 2400, 'label': '5B1', 'order': 5, 'powers': [17, 17, 1], 'representative': 30677737886, 'size': 12}
  • id: 155798507
    {'aut_label': '5B1', 'centralizer': '12.b1.a1', 'counter': 17, 'group_counter': 46, 'group_order': 2400, 'label': '5B2', 'order': 5, 'powers': [16, 16, 1], 'representative': 30583987646, 'size': 12}
  • id: 155798508
    {'aut_label': '5C1', 'centralizer': '24.b1.a1', 'counter': 18, 'group_counter': 46, 'group_order': 2400, 'label': '5C1', 'order': 5, 'powers': [19, 19, 1], 'representative': 92294956504, 'size': 24}
  • id: 155798509
    {'aut_label': '5C1', 'centralizer': '24.b1.a1', 'counter': 19, 'group_counter': 46, 'group_order': 2400, 'label': '5C2', 'order': 5, 'powers': [18, 18, 1], 'representative': 253972377, 'size': 24}
  • id: 155798511
    {'aut_label': '5C1', 'centralizer': '24.b1.a1', 'counter': 20, 'group_counter': 46, 'group_order': 2400, 'label': '5D1', 'order': 5, 'powers': [21, 21, 1], 'representative': 98398552779, 'size': 24}
  • id: 155798512
    {'aut_label': '5C1', 'centralizer': '24.b1.a1', 'counter': 21, 'group_counter': 46, 'group_order': 2400, 'label': '5D2', 'order': 5, 'powers': [20, 20, 1], 'representative': 12461161802, 'size': 24}
  • id: 155798513
    {'aut_label': '6A', 'centralizer': '20.c1.a1', 'counter': 22, 'group_counter': 46, 'group_order': 2400, 'label': '6A', 'order': 6, 'powers': [7, 4, 22], 'representative': 110631910891, 'size': 20}
  • id: 155798514
    {'aut_label': '6B', 'centralizer': '20.c1.a1', 'counter': 23, 'group_counter': 46, 'group_order': 2400, 'label': '6B', 'order': 6, 'powers': [7, 2, 23], 'representative': 73755296014, 'size': 20}
  • id: 155798515
    {'aut_label': '6B', 'centralizer': '20.c1.a1', 'counter': 24, 'group_counter': 46, 'group_order': 2400, 'label': '6C', 'order': 6, 'powers': [7, 3, 24], 'representative': 73763499155, 'size': 20}
  • id: 155798516
    {'aut_label': '10A1', 'centralizer': '2.a1.a1', 'counter': 25, 'group_counter': 46, 'group_order': 2400, 'label': '10A1', 'order': 10, 'powers': [14, 26, 4], 'representative': 147999673081, 'size': 2}
  • id: 155798517
    {'aut_label': '10A1', 'centralizer': '2.a1.a1', 'counter': 26, 'group_counter': 46, 'group_order': 2400, 'label': '10A3', 'order': 10, 'powers': [15, 25, 4], 'representative': 75245970908, 'size': 2}
  • id: 155798518
    {'aut_label': '10B1', 'centralizer': '2.a1.a1', 'counter': 27, 'group_counter': 46, 'group_order': 2400, 'label': '10B1', 'order': 10, 'powers': [14, 28, 2], 'representative': 42676190199, 'size': 2}
  • id: 155798519
    {'aut_label': '10B1', 'centralizer': '2.a1.a1', 'counter': 28, 'group_counter': 46, 'group_order': 2400, 'label': '10B3', 'order': 10, 'powers': [15, 27, 2], 'representative': 115430282997, 'size': 2}
  • id: 155798520
    {'aut_label': '10B1', 'centralizer': '2.a1.a1', 'counter': 29, 'group_counter': 46, 'group_order': 2400, 'label': '10C1', 'order': 10, 'powers': [14, 30, 3], 'representative': 7119249528, 'size': 2}
  • id: 155798522
    {'aut_label': '10B1', 'centralizer': '2.a1.a1', 'counter': 30, 'group_counter': 46, 'group_order': 2400, 'label': '10C3', 'order': 10, 'powers': [15, 29, 3], 'representative': 79873342326, 'size': 2}
  • id: 155798523
    {'aut_label': '10D1', 'centralizer': '12.b1.a1', 'counter': 31, 'group_counter': 46, 'group_order': 2400, 'label': '10D1', 'order': 10, 'powers': [16, 32, 2], 'representative': 5031953650, 'size': 12}
  • id: 155798524
    {'aut_label': '10D1', 'centralizer': '12.b1.a1', 'counter': 32, 'group_counter': 46, 'group_order': 2400, 'label': '10D3', 'order': 10, 'powers': [17, 31, 2], 'representative': 4985078530, 'size': 12}
  • id: 155798525
    {'aut_label': '10D1', 'centralizer': '12.b1.a1', 'counter': 33, 'group_counter': 46, 'group_order': 2400, 'label': '10E1', 'order': 10, 'powers': [16, 34, 3], 'representative': 122306653634, 'size': 12}
  • id: 155798526
    {'aut_label': '10D1', 'centralizer': '12.b1.a1', 'counter': 34, 'group_counter': 46, 'group_order': 2400, 'label': '10E3', 'order': 10, 'powers': [17, 33, 3], 'representative': 122259778514, 'size': 12}
  • id: 155798527
    {'aut_label': '10F1', 'centralizer': '12.b1.a1', 'counter': 35, 'group_counter': 46, 'group_order': 2400, 'label': '10F1', 'order': 10, 'powers': [16, 36, 4], 'representative': 27898544480, 'size': 12}
  • id: 155798528
    {'aut_label': '10F1', 'centralizer': '12.b1.a1', 'counter': 36, 'group_counter': 46, 'group_order': 2400, 'label': '10F3', 'order': 10, 'powers': [17, 35, 4], 'representative': 17661070730, 'size': 12}
  • id: 155798529
    {'aut_label': '10G1', 'centralizer': '24.b1.a1', 'counter': 37, 'group_counter': 46, 'group_order': 2400, 'label': '10G1', 'order': 10, 'powers': [18, 38, 3], 'representative': 91836013000, 'size': 24}
  • id: 155798530
    {'aut_label': '10G1', 'centralizer': '24.b1.a1', 'counter': 38, 'group_counter': 46, 'group_order': 2400, 'label': '10G3', 'order': 10, 'powers': [19, 37, 3], 'representative': 61562559751, 'size': 24}
  • id: 155798531
    {'aut_label': '10H1', 'centralizer': '24.b1.a1', 'counter': 39, 'group_counter': 46, 'group_order': 2400, 'label': '10H1', 'order': 10, 'powers': [18, 40, 4], 'representative': 7374768130, 'size': 24}
  • id: 155798533
    {'aut_label': '10H1', 'centralizer': '24.b1.a1', 'counter': 40, 'group_counter': 46, 'group_order': 2400, 'label': '10H3', 'order': 10, 'powers': [19, 39, 4], 'representative': 13478361280, 'size': 24}
  • id: 155798534
    {'aut_label': '10G1', 'centralizer': '24.b1.a1', 'counter': 41, 'group_counter': 46, 'group_order': 2400, 'label': '10I1', 'order': 10, 'powers': [18, 42, 2], 'representative': 29492813145, 'size': 24}
  • id: 155798535
    {'aut_label': '10G1', 'centralizer': '24.b1.a1', 'counter': 42, 'group_counter': 46, 'group_order': 2400, 'label': '10I3', 'order': 10, 'powers': [19, 41, 2], 'representative': 17285626970, 'size': 24}
  • id: 155798536
    {'aut_label': '10G1', 'centralizer': '24.b1.a1', 'counter': 43, 'group_counter': 46, 'group_order': 2400, 'label': '10J1', 'order': 10, 'powers': [20, 44, 3], 'representative': 104043202425, 'size': 24}
  • id: 155798537
    {'aut_label': '10G1', 'centralizer': '24.b1.a1', 'counter': 44, 'group_counter': 46, 'group_order': 2400, 'label': '10J3', 'order': 10, 'powers': [21, 43, 3], 'representative': 110146795575, 'size': 24}
  • id: 155798538
    {'aut_label': '10G1', 'centralizer': '24.b1.a1', 'counter': 45, 'group_counter': 46, 'group_order': 2400, 'label': '10K1', 'order': 10, 'powers': [20, 46, 2], 'representative': 26542229300, 'size': 24}
  • id: 155798539
    {'aut_label': '10G1', 'centralizer': '24.b1.a1', 'counter': 46, 'group_counter': 46, 'group_order': 2400, 'label': '10K3', 'order': 10, 'powers': [21, 45, 2], 'representative': 121533876022, 'size': 24}
  • id: 155798540
    {'aut_label': '10H1', 'centralizer': '24.b1.a1', 'counter': 47, 'group_counter': 46, 'group_order': 2400, 'label': '10L1', 'order': 10, 'powers': [20, 48, 4], 'representative': 11604352700, 'size': 24}
  • id: 155798541
    {'aut_label': '10H1', 'centralizer': '24.b1.a1', 'counter': 48, 'group_counter': 46, 'group_order': 2400, 'label': '10L3', 'order': 10, 'powers': [21, 47, 4], 'representative': 117726219832, 'size': 24}
  • id: 155798542
    {'aut_label': '12A1', 'centralizer': '100.b1.a1', 'counter': 49, 'group_counter': 46, 'group_order': 2400, 'label': '12A1', 'order': 12, 'powers': [22, 8, 49], 'representative': 51755148650, 'size': 100}
  • id: 155798544
    {'aut_label': '12A1', 'centralizer': '100.b1.a1', 'counter': 50, 'group_counter': 46, 'group_order': 2400, 'label': '12A-1', 'order': 12, 'powers': [22, 9, 50], 'representative': 22252879884, 'size': 100}
  • id: 155798545
    {'aut_label': '12A1', 'centralizer': '100.b1.a1', 'counter': 51, 'group_counter': 46, 'group_order': 2400, 'label': '12B1', 'order': 12, 'powers': [22, 11, 51], 'representative': 122741847365, 'size': 100}
  • id: 155798546
    {'aut_label': '12A1', 'centralizer': '100.b1.a1', 'counter': 52, 'group_counter': 46, 'group_order': 2400, 'label': '12B-1', 'order': 12, 'powers': [22, 10, 52], 'representative': 5514037886, 'size': 100}
  • id: 155798547
    {'aut_label': '15A1', 'centralizer': '40.b1.a1', 'counter': 53, 'group_counter': 46, 'group_order': 2400, 'label': '15A1', 'order': 15, 'powers': [54, 14, 7], 'representative': 141928892394, 'size': 40}
  • id: 155798548
    {'aut_label': '15A1', 'centralizer': '40.b1.a1', 'counter': 54, 'group_counter': 46, 'group_order': 2400, 'label': '15A2', 'order': 15, 'powers': [53, 15, 7], 'representative': 65095619356, 'size': 40}
  • id: 155798549
    {'aut_label': '20A1', 'centralizer': '60.f1.a1', 'counter': 55, 'group_counter': 46, 'group_order': 2400, 'label': '20A1', 'order': 20, 'powers': [25, 56, 12], 'representative': 62657181432, 'size': 60}
  • id: 155798550
    {'aut_label': '20A1', 'centralizer': '60.f1.a1', 'counter': 56, 'group_counter': 46, 'group_order': 2400, 'label': '20A3', 'order': 20, 'powers': [26, 55, 12], 'representative': 22296629694, 'size': 60}
  • id: 155798551
    {'aut_label': '20B1', 'centralizer': '60.f1.a1', 'counter': 57, 'group_counter': 46, 'group_order': 2400, 'label': '20B1', 'order': 20, 'powers': [26, 58, 13], 'representative': 141912486202, 'size': 60}
  • id: 155798552
    {'aut_label': '20B1', 'centralizer': '60.f1.a1', 'counter': 58, 'group_counter': 46, 'group_order': 2400, 'label': '20B3', 'order': 20, 'powers': [25, 57, 13], 'representative': 36624693130, 'size': 60}
  • id: 155798553
    {'aut_label': '20C1', 'centralizer': '60.e1.a1', 'counter': 59, 'group_counter': 46, 'group_order': 2400, 'label': '20C1', 'order': 20, 'powers': [35, 61, 8], 'representative': 61653184805, 'size': 60}
  • id: 155798555
    {'aut_label': '20C1', 'centralizer': '60.e1.a1', 'counter': 60, 'group_counter': 46, 'group_order': 2400, 'label': '20C-1', 'order': 20, 'powers': [35, 62, 9], 'representative': 3136928518, 'size': 60}
  • id: 155798556
    {'aut_label': '20C1', 'centralizer': '60.e1.a1', 'counter': 61, 'group_counter': 46, 'group_order': 2400, 'label': '20C3', 'order': 20, 'powers': [36, 59, 9], 'representative': 8257621643, 'size': 60}
  • id: 155798557
    {'aut_label': '20C1', 'centralizer': '60.e1.a1', 'counter': 62, 'group_counter': 46, 'group_order': 2400, 'label': '20C-3', 'order': 20, 'powers': [36, 60, 8], 'representative': 72875424805, 'size': 60}
  • id: 155798558
    {'aut_label': '20C1', 'centralizer': '60.e1.a1', 'counter': 63, 'group_counter': 46, 'group_order': 2400, 'label': '20D1', 'order': 20, 'powers': [35, 65, 10], 'representative': 29045119497, 'size': 60}
  • id: 155798559
    {'aut_label': '20C1', 'centralizer': '60.e1.a1', 'counter': 64, 'group_counter': 46, 'group_order': 2400, 'label': '20D-1', 'order': 20, 'powers': [35, 66, 11], 'representative': 116771050680, 'size': 60}
  • id: 155798560
    {'aut_label': '20C1', 'centralizer': '60.e1.a1', 'counter': 65, 'group_counter': 46, 'group_order': 2400, 'label': '20D3', 'order': 20, 'powers': [36, 63, 11], 'representative': 32945015867, 'size': 60}
  • id: 155798561
    {'aut_label': '20C1', 'centralizer': '60.e1.a1', 'counter': 66, 'group_counter': 46, 'group_order': 2400, 'label': '20D-3', 'order': 20, 'powers': [36, 64, 10], 'representative': 97514397034, 'size': 60}
  • id: 155798562
    {'aut_label': '30A1', 'centralizer': '40.b1.a1', 'counter': 67, 'group_counter': 46, 'group_order': 2400, 'label': '30A1', 'order': 30, 'powers': [53, 25, 22], 'representative': 126869400125, 'size': 40}
  • id: 155798563
    {'aut_label': '30A1', 'centralizer': '40.b1.a1', 'counter': 68, 'group_counter': 46, 'group_order': 2400, 'label': '30A7', 'order': 30, 'powers': [54, 26, 22], 'representative': 142976185800, 'size': 40}
  • id: 155798564
    {'aut_label': '30B1', 'centralizer': '40.b1.a1', 'counter': 69, 'group_counter': 46, 'group_order': 2400, 'label': '30B1', 'order': 30, 'powers': [53, 27, 23], 'representative': 33345928625, 'size': 40}
  • id: 155798566
    {'aut_label': '30B1', 'centralizer': '40.b1.a1', 'counter': 70, 'group_counter': 46, 'group_order': 2400, 'label': '30B7', 'order': 30, 'powers': [54, 28, 23], 'representative': 46488677450, 'size': 40}
  • id: 155798567
    {'aut_label': '30B1', 'centralizer': '40.b1.a1', 'counter': 71, 'group_counter': 46, 'group_order': 2400, 'label': '30C1', 'order': 30, 'powers': [53, 29, 24], 'representative': 62595853625, 'size': 40}
  • id: 155798568
    {'aut_label': '30B1', 'centralizer': '40.b1.a1', 'counter': 72, 'group_counter': 46, 'group_order': 2400, 'label': '30C7', 'order': 30, 'powers': [54, 30, 24], 'representative': 66722219325, 'size': 40}
• 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: 15175665
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15175676
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 15175687
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 15175698
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15175700
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.2a', 'multiplicity': 2, 'nt': [5, 2], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, 0, 0, 0, 0, 4, 4, -1, -1, 4, 4, -1, -1, -1, -1, 4, 4, 4, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 15175701
    {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.2b', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 4, 0, 0, 0, 0, -4, 4, -1, -1, 4, 4, -1, -1, -1, -1, 4, -4, -4, 1, 1, 1, -1, 1, -1, -4, -4, 4, -4, -4, 4, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 0, 1, -1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 15175669
    {'cdim': 4, 'counter': 13, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.4a', 'multiplicity': 1, 'nt': [5, 4], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 1, 4, 4, 4, 4, 0, 0, 4, 4, -1, -1, -1, -1, -1, -1, 1, 1, 1, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 0, 0, 0, -1, -1, -1, -1, -1, -1, 0, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15175670
    {'cdim': 4, 'counter': 14, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.4b', 'multiplicity': 1, 'nt': [10, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 1, -4, -4, 4, 4, 0, 0, 4, 4, -1, -1, -1, -1, -1, -1, 1, -1, -1, -4, -4, -4, 4, -4, 4, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, -1, 1, -1, -1, 0, -1, -1, 1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 15175671
    {'cdim': 4, 'counter': 15, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.4c', 'multiplicity': 1, 'nt': [10, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 1, 4, 4, -4, -4, 0, 0, 4, 4, -1, -1, -1, -1, -1, -1, 1, -1, -1, -4, -4, -4, 4, -4, 4, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 0, 0, 0, -1, -1, 1, -1, 1, 1, 0, 1, -1, 1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 15175672
    {'cdim': 4, 'counter': 16, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.4d', 'multiplicity': 1, 'nt': [10, 11], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 1, -4, -4, -4, -4, 0, 0, 4, 4, -1, -1, -1, -1, -1, -1, 1, 1, 1, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15175680
    {'cdim': 5, 'counter': 23, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.5a', 'multiplicity': 1, 'nt': [6, 12], 'qdim': 5, 'qvalues': [5, 5, 5, 5, 1, 1, -1, 5, 5, 5, 5, 1, 1, 5, 5, 0, 0, 0, 0, 0, 0, -1, -1, -1, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 15175681
    {'cdim': 5, 'counter': 24, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.5b', 'multiplicity': 1, 'nt': [12, 75], 'qdim': 5, 'qvalues': [5, 5, -5, -5, -1, 1, -1, -5, -5, 5, 5, -1, 1, 5, 5, 0, 0, 0, 0, 0, 0, -1, 1, 1, -5, -5, -5, 5, -5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, -1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 15175682
    {'cdim': 5, 'counter': 25, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.5c', 'multiplicity': 1, 'nt': [12, 75], 'qdim': 5, 'qvalues': [5, 5, -5, -5, 1, -1, -1, 5, 5, -5, -5, -1, 1, 5, 5, 0, 0, 0, 0, 0, 0, -1, 1, 1, -5, -5, -5, 5, -5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, -1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 15175683
    {'cdim': 5, 'counter': 26, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.5d', 'multiplicity': 1, 'nt': [12, 75], 'qdim': 5, 'qvalues': [5, 5, 5, 5, -1, -1, -1, -5, -5, -5, -5, 1, 1, 5, 5, 0, 0, 0, 0, 0, 0, -1, -1, -1, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 15175704
    {'cdim': 3, 'counter': 9, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.3a', 'multiplicity': 2, 'nt': [12, 33], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, 0, 6, 6, 6, 6, -2, -2, 6, 6, 1, 1, 1, 1, 1, 1, 0, 0, 0, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15175666
    {'cdim': 3, 'counter': 10, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.3b', 'multiplicity': 2, 'nt': [12, 76], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -2, 2, 0, 6, 6, -6, -6, 2, -2, 6, 6, 1, 1, 1, 1, 1, 1, 0, 0, 0, -6, -6, -6, 6, -6, 6, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 2, -2, -2, 1, 1, -1, 1, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15175667
    {'cdim': 3, 'counter': 11, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.3c', 'multiplicity': 2, 'nt': [12, 76], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 2, -2, 0, -6, -6, 6, 6, 2, -2, 6, 6, 1, 1, 1, 1, 1, 1, 0, 0, 0, -6, -6, -6, 6, -6, 6, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, 2, -2, -2, -1, -1, 1, -1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15175668
    {'cdim': 3, 'counter': 12, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.3d', 'multiplicity': 2, 'nt': [12, 76], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 2, 2, 0, -6, -6, -6, -6, -2, -2, 6, 6, 1, 1, 1, 1, 1, 1, 0, 0, 0, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -2, -2, -2, -1, -1, -1, -1, -1, -1, -2, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15175702
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.2c', 'multiplicity': 4, 'nt': [120, 0], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, -4, 0, 0, 0, 0, 0, 0, 8, 8, -2, -2, -2, -2, -2, -2, 4, 4, -4, 8, 8, -8, -8, -8, -8, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, -2, -2, 2, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -4, -4, 4], 'schur_index': 1}
  • id: 15175703
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.2d', 'multiplicity': 4, 'nt': [120, 0], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, -4, 0, 0, 0, 0, 0, 0, 8, 8, -2, -2, -2, -2, -2, -2, 4, -4, 4, -8, -8, 8, -8, 8, -8, 2, 2, 2, -2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, 4, 4], 'schur_index': 1}
  • id: 15175673
    {'cdim': 4, 'counter': 17, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.4e', 'multiplicity': 2, 'nt': [40, 188], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 2, 0, 0, 0, 0, 0, 0, 8, 8, -2, -2, -2, -2, -2, -2, -2, -2, 2, 8, 8, -8, -8, -8, -8, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, -2], 'schur_index': 1}
  • id: 15175674
    {'cdim': 4, 'counter': 18, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.4f', 'multiplicity': 2, 'nt': [40, 188], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 2, 0, 0, 0, 0, 0, 0, 8, 8, -2, -2, -2, -2, -2, -2, -2, 2, -2, -8, -8, 8, -8, 8, -8, 2, 2, 2, -2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, -2, -2], 'schur_index': 1}
  • id: 15175675
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.4g', 'multiplicity': 2, 'nt': [120, 0], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 3, 3, 4, 4, -4, -2, -2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, -3, 2, 3, -2, 2, 2, -3, -3, 2, 3, -2, -3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 15175677
    {'cdim': 4, 'counter': 20, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.4h', 'multiplicity': 2, 'nt': [120, 0], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 3, 3, -2, -2, 4, 4, -4, -2, -2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, -3, -2, 3, -3, -3, 2, 2, -3, -2, 3, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 15175678
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.4i', 'multiplicity': 2, 'nt': [120, 0], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 3, 3, 4, -4, 4, 2, 2, -2, 2, -2, 2, 2, 2, 2, -2, -2, 2, -3, -2, -3, 2, 2, 2, 3, -3, -2, -3, 2, 3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 15175679
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.4j', 'multiplicity': 2, 'nt': [120, 0], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 3, 3, -2, -2, 4, -4, 4, 2, 2, -2, 2, -2, 2, 2, 2, 2, -2, -2, 2, 2, 3, 2, -3, -3, -3, -2, 2, 3, 2, -3, -2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 15175684
    {'cdim': 6, 'counter': 27, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.6a', 'multiplicity': 2, 'nt': [24, 576], 'qdim': 12, 'qvalues': [12, -12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, 2, 2, 2, 2, 2, 2, 0, 0, 0, 12, 12, -12, -12, -12, -12, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15175685
    {'cdim': 6, 'counter': 28, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.6b', 'multiplicity': 2, 'nt': [24, 576], 'qdim': 12, 'qvalues': [12, -12, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, 2, 2, 2, 2, 2, 2, 0, 0, 0, -12, -12, 12, -12, 12, -12, -2, -2, -2, 2, 2, -2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15175686
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.6c', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 12, 'qvalues': [12, 12, -12, -12, 0, 0, 0, 0, 0, 0, 0, 4, -4, -3, -3, 2, 2, -3, -3, 2, 2, 0, 0, 0, 3, 3, 3, -3, 3, -3, -2, -2, 2, -2, -2, 2, 2, 3, -2, 3, -3, -3, -2, 2, 3, -2, 3, -2, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15175688
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.6d', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 12, 'qvalues': [12, 12, -12, -12, 0, 0, 0, 0, 0, 0, 0, 4, -4, -3, -3, 2, 2, 2, 2, -3, -3, 0, 0, 0, 3, 3, 3, -3, 3, -3, -2, -2, 2, -2, -2, 2, -3, -2, 3, -2, 2, 2, 3, -3, -2, 3, -2, 3, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15175689
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.6e', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, -4, -4, -3, -3, 2, 2, -3, -3, 2, 2, 0, 0, 0, -3, -3, -3, -3, -3, -3, 2, 2, 2, 2, 2, 2, 2, -3, 2, -3, -3, -3, 2, 2, -3, 2, -3, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15175690
    {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.6f', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, -4, -4, -3, -3, 2, 2, 2, 2, -3, -3, 0, 0, 0, -3, -3, -3, -3, -3, -3, 2, 2, 2, 2, 2, 2, -3, 2, -3, 2, 2, 2, -3, -3, 2, -3, 2, -3, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15175691
    {'cdim': 8, 'counter': 33, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.8a', 'multiplicity': 2, 'nt': [25, 46], 'qdim': 16, 'qvalues': [16, 16, 16, 16, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 1, 1, 1, 1, 4, 4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 15175692
    {'cdim': 8, 'counter': 34, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.8b', 'multiplicity': 2, 'nt': [50, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 1, 1, 1, 1, 4, -4, -4, 4, 4, 4, -4, 4, -4, 4, 4, -4, 4, 4, -4, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 15175693
    {'cdim': 8, 'counter': 35, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.8c', 'multiplicity': 2, 'nt': [120, 0], 'qdim': 16, 'qvalues': [16, -16, -16, 16, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 1, 1, 1, 1, -4, -4, 4, -4, -4, 4, 4, 4, 4, -4, -4, 4, 4, 4, 4, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 15175694
    {'cdim': 8, 'counter': 36, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.8d', 'multiplicity': 2, 'nt': [120, 0], 'qdim': 16, 'qvalues': [16, -16, 16, -16, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 1, 1, 1, 1, -4, 4, -4, 4, 4, -4, 4, -4, 4, 4, 4, 4, -4, -4, 4, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 15175695
    {'cdim': 10, 'counter': 37, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.10a', 'multiplicity': 2, 'nt': [30, 128], 'qdim': 20, 'qvalues': [20, 20, 20, 20, 0, 0, -4, 0, 0, 0, 0, 4, 4, -5, -5, 0, 0, 0, 0, 0, 0, -4, -4, -4, -5, -5, -5, -5, -5, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15175696
    {'cdim': 10, 'counter': 38, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.10b', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 20, 'qvalues': [20, 20, -20, -20, 0, 0, -4, 0, 0, 0, 0, -4, 4, -5, -5, 0, 0, 0, 0, 0, 0, -4, 4, 4, 5, 5, 5, -5, 5, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 15175697
    {'cdim': 12, 'counter': 39, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.12a', 'multiplicity': 2, 'nt': [120, 0], 'qdim': 24, 'qvalues': [24, -24, -24, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 4, 4, -1, -1, -1, -1, 0, 0, 0, -6, -6, 6, 6, 6, 6, 4, 4, -4, -4, -4, -4, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15175699
    {'cdim': 12, 'counter': 40, 'faithful': False, 'group': '2400.bt', 'group_order': 2400, 'image': None, 'label': '2400.bt.12b', 'multiplicity': 2, 'nt': [120, 0], 'qdim': 24, 'qvalues': [24, -24, 24, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 4, 4, -1, -1, -1, -1, 0, 0, 0, 6, 6, -6, 6, -6, 6, -4, -4, -4, 4, 4, -4, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 34931180
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2400, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 2400, 'label': '2400.bt.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34931191
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2400, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 1200, 'label': '2400.bt.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 34931202
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2400, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 1200, 'label': '2400.bt.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 34931213
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2400, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 1200, 'label': '2400.bt.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34931224
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 240, 'counter': 5, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 240, 'label': '2400.bt.2a1', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 34931235
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 240, 'counter': 6, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 240, 'label': '2400.bt.2a2', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 34931246
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 240, 'counter': 7, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 120, 'label': '2400.bt.2b1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]]]}
  • id: 34931250
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 240, 'counter': 8, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 120, 'label': '2400.bt.2b2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 34931251
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 9, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.b1', 'kernel_order': 10, 'label': '2400.bt.2c1', 'nt': [120, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 5]], [[2, 5]], [[2, 5]], [[-2, 5]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 3], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 5], [1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[-1, 3], [-1, 7]], [[1, 3], [1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[1, 3], [1, 7]], [[0, 0]], [[1, 3], [-1, 5], [1, 7]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 34931181
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 10, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.b1', 'kernel_order': 10, 'label': '2400.bt.2c2', 'nt': [120, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 5]], [[-2, 5]], [[-2, 5]], [[2, 5]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 5], [-1, 7]], [[1, 3], [-1, 5], [1, 7]], [[1, 3], [1, 7]], [[-1, 3], [-1, 7]], [[1, 3], [-1, 5], [1, 7]], [[-1, 3], [-1, 7]], [[0, 0]], [[-1, 3], [1, 5], [-1, 7]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 34931182
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 11, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.b1', 'kernel_order': 10, 'label': '2400.bt.2c3', 'nt': [120, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 5]], [[2, 5]], [[2, 5]], [[-2, 5]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[-1, 0]], [[1, 3], [-1, 5], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 7]], [[1, 3], [1, 7]], [[1, 3], [-1, 5], [1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[1, 3], [1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[0, 0]], [[-1, 3], [-1, 7]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 34931183
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 12, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.b1', 'kernel_order': 10, 'label': '2400.bt.2c4', 'nt': [120, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 5]], [[-2, 5]], [[-2, 5]], [[2, 5]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 3], [1, 5], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, 7]], [[-1, 3], [-1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[1, 3], [-1, 5], [1, 7]], [[-1, 3], [-1, 7]], [[1, 3], [-1, 5], [1, 7]], [[0, 0]], [[1, 3], [1, 7]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 34931184
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 13, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 10, 'label': '2400.bt.2d1', 'nt': [120, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 5]], [[2, 5]], [[-2, 5]], [[2, 5]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 3], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 5], [1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[1, 3], [1, 7]], [[1, 3], [1, 7]], [[1, 3], [-1, 5], [1, 7]], [[-1, 3], [-1, 7]], [[0, 0]], [[-1, 3], [1, 5], [-1, 7]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34931185
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 14, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 10, 'label': '2400.bt.2d2', 'nt': [120, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 5]], [[-2, 5]], [[2, 5]], [[-2, 5]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 5], [-1, 7]], [[1, 3], [-1, 5], [1, 7]], [[-1, 3], [-1, 7]], [[-1, 3], [-1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[1, 3], [1, 7]], [[0, 0]], [[1, 3], [-1, 5], [1, 7]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34931186
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 15, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 10, 'label': '2400.bt.2d3', 'nt': [120, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 5]], [[2, 5]], [[-2, 5]], [[2, 5]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 0]], [[1, 3], [-1, 5], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 7]], [[1, 3], [1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[-1, 3], [-1, 7]], [[1, 3], [-1, 5], [1, 7]], [[0, 0]], [[1, 3], [1, 7]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34931187
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 16, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 10, 'label': '2400.bt.2d4', 'nt': [120, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 5]], [[-2, 5]], [[2, 5]], [[-2, 5]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 3], [1, 5], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, 7]], [[-1, 3], [-1, 7]], [[1, 3], [-1, 5], [1, 7]], [[1, 3], [-1, 5], [1, 7]], [[1, 3], [1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[0, 0]], [[-1, 3], [-1, 7]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34931188
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 17, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 40, 'label': '2400.bt.3a1', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931189
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 18, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 40, 'label': '2400.bt.3a2', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931190
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 19, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.b1.a1', 'kernel_order': 20, 'label': '2400.bt.3b1', 'nt': [12, 76], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931192
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 20, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.b1.a1', 'kernel_order': 20, 'label': '2400.bt.3b2', 'nt': [12, 76], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931193
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 21, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.b1.b1', 'kernel_order': 20, 'label': '2400.bt.3c1', 'nt': [12, 76], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931194
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 22, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.b1.b1', 'kernel_order': 20, 'label': '2400.bt.3c2', 'nt': [12, 76], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931195
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 23, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 20, 'label': '2400.bt.3d1', 'nt': [12, 76], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931196
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 24, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 20, 'label': '2400.bt.3d2', 'nt': [12, 76], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931197
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 40, 'label': '2400.bt.4a', 'nt': [5, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34931198
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 26, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.b1.b1', 'kernel_order': 20, 'label': '2400.bt.4b', 'nt': [10, 11], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 34931199
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 27, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.b1.a1', 'kernel_order': 20, 'label': '2400.bt.4c', 'nt': [10, 11], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 34931200
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 28, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 20, 'label': '2400.bt.4d', 'nt': [10, 11], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34931201
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 29, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.b1', 'kernel_order': 10, 'label': '2400.bt.4e1', 'nt': [40, 188], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-4, 1]], [[4, 1]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 34931203
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 30, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.b1', 'kernel_order': 10, 'label': '2400.bt.4e2', 'nt': [40, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 1]], [[-4, 1]], [[-4, 1]], [[4, 1]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 34931204
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 31, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 10, 'label': '2400.bt.4f1', 'nt': [40, 188], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-4, 1]], [[4, 1]], [[-4, 1]], [[4, 1]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 34931205
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 32, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 10, 'label': '2400.bt.4f2', 'nt': [40, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 1]], [[-4, 1]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 34931206
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 33, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.b1', 'kernel_order': 2, 'label': '2400.bt.4g1', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 0]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-1, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-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]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]]]}
  • id: 34931207
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 34, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.b1', 'kernel_order': 2, 'label': '2400.bt.4g2', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 0]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 34931208
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 35, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.b1', 'kernel_order': 2, 'label': '2400.bt.4h1', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-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]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]]]}
  • id: 34931209
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 36, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.b1', 'kernel_order': 2, 'label': '2400.bt.4h2', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 34931210
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 37, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.a1', 'kernel_order': 2, 'label': '2400.bt.4i1', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 0]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0], [1, 2], [1, -2]], [[-1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-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]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 34931211
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 38, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.a1', 'kernel_order': 2, 'label': '2400.bt.4i2', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 0]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-1, 0], [1, 2], [1, -2]], [[-1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[2, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 34931212
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 39, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.a1', 'kernel_order': 2, 'label': '2400.bt.4j1', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[1, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-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]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 34931214
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 40, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.a1', 'kernel_order': 2, 'label': '2400.bt.4j2', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 34931215
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 41, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 40, 'label': '2400.bt.5a', 'nt': [6, 12], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 34931216
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 42, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.b1.b1', 'kernel_order': 20, 'label': '2400.bt.5b', 'nt': [12, 75], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-5, 0]], [[-5, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-5, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[-5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 34931217
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 43, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.b1.a1', 'kernel_order': 20, 'label': '2400.bt.5c', 'nt': [12, 75], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-5, 0]], [[-5, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[-5, 0]], [[-5, 0]], [[-1, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-5, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[-5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 34931218
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 44, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 20, 'label': '2400.bt.5d', 'nt': [12, 75], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-5, 0]], [[-5, 0]], [[-5, 0]], [[-5, 0]], [[1, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 34931219
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 45, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.b1', 'kernel_order': 10, 'label': '2400.bt.6a1', 'nt': [24, 576], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[6, 1]], [[6, 1]], [[-6, 1]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931220
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 46, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.b1', 'kernel_order': 10, 'label': '2400.bt.6a2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[-6, 1]], [[-6, 1]], [[6, 1]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931221
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 47, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 10, 'label': '2400.bt.6b1', 'nt': [24, 576], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[6, 1]], [[-6, 1]], [[6, 1]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931222
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 40, 'counter': 48, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '240.93', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 10, 'label': '2400.bt.6b2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[-6, 1]], [[6, 1]], [[-6, 1]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931223
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 49, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.944', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.b1.a1', 'kernel_order': 2, 'label': '2400.bt.6c1', 'nt': [60, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[3, 2], [3, -2]], [[-3, 2], [-3, -2]], [[3, 1], [3, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931225
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 50, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.944', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.b1.a1', 'kernel_order': 2, 'label': '2400.bt.6c2', 'nt': [60, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[3, 1], [3, -1]], [[-3, 1], [-3, -1]], [[3, 2], [3, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931226
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 51, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.944', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.b1.a1', 'kernel_order': 2, 'label': '2400.bt.6d1', 'nt': [60, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[1, 0]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[3, 2], [3, -2]], [[-3, 2], [-3, -2]], [[3, 1], [3, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0], [1, 2], [1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931227
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 52, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.944', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.b1.a1', 'kernel_order': 2, 'label': '2400.bt.6d2', 'nt': [60, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[1, 0]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[3, 1], [3, -1]], [[-3, 1], [-3, -1]], [[3, 2], [3, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-1, 0], [1, 2], [1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931228
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 53, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '600.146', 'image_order': 600, 'indicator': 1, 'kernel': '600.a1.a1', 'kernel_order': 4, 'label': '2400.bt.6e1', 'nt': [60, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931229
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 54, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '600.146', 'image_order': 600, 'indicator': 1, 'kernel': '600.a1.a1', 'kernel_order': 4, 'label': '2400.bt.6e2', 'nt': [60, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931230
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 55, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '600.146', 'image_order': 600, 'indicator': 1, 'kernel': '600.a1.a1', 'kernel_order': 4, 'label': '2400.bt.6f1', 'nt': [60, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[1, 0]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931231
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 56, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '600.146', 'image_order': 600, 'indicator': 1, 'kernel': '600.a1.a1', 'kernel_order': 4, 'label': '2400.bt.6f2', 'nt': [60, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[1, 0]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931232
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 57, 'cyclotomic_n': 5, 'dim': 8, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '600.146', 'image_order': 600, 'indicator': 1, 'kernel': '600.a1.a1', 'kernel_order': 4, 'label': '2400.bt.8a1', 'nt': [25, 46], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [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]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 34931233
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 58, 'cyclotomic_n': 5, 'dim': 8, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '600.146', 'image_order': 600, 'indicator': 1, 'kernel': '600.a1.a1', 'kernel_order': 4, 'label': '2400.bt.8a2', 'nt': [25, 46], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 34931234
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 59, 'cyclotomic_n': 5, 'dim': 8, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.944', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.b1.a1', 'kernel_order': 2, 'label': '2400.bt.8b1', 'nt': [50, 0], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[4, 2], [4, -2]], [[-4, 2], [-4, -2]], [[4, 1], [4, -1]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [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]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]]]}
  • id: 34931236
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 60, 'cyclotomic_n': 5, 'dim': 8, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.944', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.b1.a1', 'kernel_order': 2, 'label': '2400.bt.8b2', 'nt': [50, 0], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[4, 1], [4, -1]], [[-4, 1], [-4, -1]], [[4, 2], [4, -2]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 34931237
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 61, 'cyclotomic_n': 5, 'dim': 8, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.b1', 'kernel_order': 2, 'label': '2400.bt.8c1', 'nt': [120, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [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]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 34931238
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 62, 'cyclotomic_n': 5, 'dim': 8, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.b1', 'kernel_order': 2, 'label': '2400.bt.8c2', 'nt': [120, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 34931239
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 63, 'cyclotomic_n': 5, 'dim': 8, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.a1', 'kernel_order': 2, 'label': '2400.bt.8d1', 'nt': [120, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[4, 1], [4, -1]], [[-4, 2], [-4, -2]], [[4, 2], [4, -2]], [[-4, 1], [-4, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [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]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 34931240
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 64, 'cyclotomic_n': 5, 'dim': 8, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.a1', 'kernel_order': 2, 'label': '2400.bt.8d2', 'nt': [120, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[4, 2], [4, -2]], [[-4, 1], [-4, -1]], [[4, 1], [4, -1]], [[-4, 2], [-4, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 34931241
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 65, 'cyclotomic_n': 5, 'dim': 10, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '600.146', 'image_order': 600, 'indicator': 1, 'kernel': '600.a1.a1', 'kernel_order': 4, 'label': '2400.bt.10a1', 'nt': [30, 128], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[5, 2], [5, -2]], [[5, 1], [5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[5, 1], [5, -1]], [[5, 2], [5, -2]], [[5, 1], [5, -1]], [[5, 2], [5, -2]], [[5, 2], [5, -2]], [[5, 1], [5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 34931242
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 66, 'cyclotomic_n': 5, 'dim': 10, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '600.146', 'image_order': 600, 'indicator': 1, 'kernel': '600.a1.a1', 'kernel_order': 4, 'label': '2400.bt.10a2', 'nt': [30, 128], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[5, 1], [5, -1]], [[5, 2], [5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[5, 2], [5, -2]], [[5, 1], [5, -1]], [[5, 2], [5, -2]], [[5, 1], [5, -1]], [[5, 1], [5, -1]], [[5, 2], [5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 34931243
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 67, 'cyclotomic_n': 5, 'dim': 10, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.944', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.b1.a1', 'kernel_order': 2, 'label': '2400.bt.10b1', 'nt': [60, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[-10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[5, 2], [5, -2]], [[5, 1], [5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[5, 2], [5, -2]], [[-5, 2], [-5, -2]], [[5, 1], [5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 34931244
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 68, 'cyclotomic_n': 5, 'dim': 10, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.944', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.b1.a1', 'kernel_order': 2, 'label': '2400.bt.10b2', 'nt': [60, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[-10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[5, 1], [5, -1]], [[5, 2], [5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[5, 1], [5, -1]], [[-5, 1], [-5, -1]], [[5, 2], [5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 34931245
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 69, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.b1', 'kernel_order': 2, 'label': '2400.bt.12a1', 'nt': [120, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 2], [6, -2]], [[6, 1], [6, -1]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1], [6, -1]], [[6, 2], [6, -2]], [[-6, 1], [-6, -1]], [[-6, 2], [-6, -2]], [[-6, 2], [-6, -2]], [[-6, 1], [-6, -1]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931247
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 70, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.b1', 'kernel_order': 2, 'label': '2400.bt.12a2', 'nt': [120, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1], [6, -1]], [[6, 2], [6, -2]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 2], [6, -2]], [[6, 1], [6, -1]], [[-6, 2], [-6, -2]], [[-6, 1], [-6, -1]], [[-6, 1], [-6, -1]], [[-6, 2], [-6, -2]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931248
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 71, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.a1', 'kernel_order': 2, 'label': '2400.bt.12b1', 'nt': [120, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 2], [6, -2]], [[6, 1], [6, -1]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1], [-6, -1]], [[-6, 2], [-6, -2]], [[6, 1], [6, -1]], [[-6, 2], [-6, -2]], [[6, 2], [6, -2]], [[-6, 1], [-6, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34931249
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 4, 'counter': 72, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '2400.bt', 'group_counter': 46, 'group_order': 2400, 'image': None, 'image_isoclass': '1200.481', 'image_order': 1200, 'indicator': 1, 'kernel': '1200.a1.a1', 'kernel_order': 2, 'label': '2400.bt.12b2', 'nt': [120, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1], [6, -1]], [[6, 2], [6, -2]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 2], [-6, -2]], [[-6, 1], [-6, -1]], [[6, 2], [6, -2]], [[-6, 1], [-6, -1]], [[6, 1], [6, -1]], [[-6, 2], [-6, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 171720086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 2400, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '2400.bt.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': False, 'special_labels': ['L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2400.bt', 'subgroup_hash': 6351781673999964458, 'subgroup_order': 2400, 'subgroup_tex': '\\SL(2,5):D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 171720197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 1200, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2400.bt.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1200.484', 'subgroup_hash': 484, 'subgroup_order': 1200, 'subgroup_tex': 'C_{10}\\times \\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 171720241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1200, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2400.bt.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1200.481', 'subgroup_hash': 481, 'subgroup_order': 1200, 'subgroup_tex': '\\SL(2,5):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 171720252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1200, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2400.bt.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.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': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1200.481', 'subgroup_hash': 481, 'subgroup_order': 1200, 'subgroup_tex': '\\SL(2,5):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 171720263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 600, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2400.bt.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': ['D', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '600.54', 'subgroup_hash': 54, 'subgroup_order': 600, 'subgroup_tex': 'C_5\\times \\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 171720274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 40, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.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': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1038', 'subgroup_hash': 1038, 'subgroup_order': 480, 'subgroup_tex': '\\SL(2,3):D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 171720285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 240, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.5.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.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': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.955', 'subgroup_hash': 955, 'subgroup_order': 480, 'subgroup_tex': '\\SL(2,5):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 171720296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 40, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.6.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '400.175', 'subgroup_hash': 175, 'subgroup_order': 400, 'subgroup_tex': 'C_{10}^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 171720307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': True, 'core_order': 240, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2400.bt.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.94', 'subgroup_hash': 94, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times \\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 171720087
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 40, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.10.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.144', 'subgroup_hash': 144, 'subgroup_order': 240, 'subgroup_tex': 'D_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.153', 'subgroup_hash': 153, 'subgroup_order': 240, 'subgroup_tex': 'C_{10}\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 171720109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.10.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.108', 'subgroup_hash': 108, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,3):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 171720120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.10.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.108', 'subgroup_hash': 108, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,3):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 171720131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 120, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.10.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.93', 'subgroup_hash': 93, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,5):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 171720142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 120, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.10.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.93', 'subgroup_hash': 93, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,5):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 171720153
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '200.51', 'subgroup_hash': 51, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720164
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 40, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '200.30', 'subgroup_hash': 30, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720175
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '200.30', 'subgroup_hash': 30, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720186
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '200.23', 'subgroup_hash': 23, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720198
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '200.23', 'subgroup_hash': 23, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720209
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.23', 'subgroup_hash': 23, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720220
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '200.23', 'subgroup_hash': 23, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 40, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.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': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.221', 'subgroup_hash': 221, 'subgroup_order': 160, 'subgroup_tex': 'Q_8:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': True, 'core_order': 120, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2400.bt.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': '20.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}', 'simple': False, 'solvable': False, 'special_labels': ['PC', 'D2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.5', 'subgroup_hash': 5, 'subgroup_order': 120, 'subgroup_tex': '\\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 171720236
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.46', 'subgroup_hash': 46, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 171720237
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 40, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.19', 'subgroup_hash': 19, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 171720238
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720239
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.20.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.10', 'subgroup_hash': 10, 'subgroup_order': 120, 'subgroup_tex': 'D_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.20.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.10', 'subgroup_hash': 10, 'subgroup_order': 120, 'subgroup_tex': 'D_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720242
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.20.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.10', 'subgroup_hash': 10, 'subgroup_order': 120, 'subgroup_tex': 'D_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720243
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.20.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.10', 'subgroup_hash': 10, 'subgroup_order': 120, 'subgroup_tex': 'D_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.20.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.15', 'subgroup_hash': 15, 'subgroup_order': 120, 'subgroup_tex': 'C_5\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 171720245
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720246
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.24.a1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720248
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.24.a1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720249
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 20, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.16', 'subgroup_hash': 16, 'subgroup_order': 100, 'subgroup_tex': 'C_{10}^2', 'supersolvable': True, 'sylow': 0}
  • id: 171720250
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720253
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.6', 'subgroup_hash': 6, 'subgroup_order': 100, 'subgroup_tex': 'C_5:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720254
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.6', 'subgroup_hash': 6, 'subgroup_order': 100, 'subgroup_tex': 'C_5:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720255
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.6', 'subgroup_hash': 6, 'subgroup_order': 100, 'subgroup_tex': 'C_5:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720256
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.6', 'subgroup_hash': 6, 'subgroup_order': 100, 'subgroup_tex': 'C_5:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '2400.bt.25.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '25.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': 25, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.200', 'subgroup_hash': 200, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 171720258
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.36', 'subgroup_hash': 36, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720259
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 40, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.36', 'subgroup_hash': 36, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.37', 'subgroup_hash': 37, 'subgroup_order': 80, 'subgroup_tex': 'C_2\\times D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.47', 'subgroup_hash': 47, 'subgroup_order': 80, 'subgroup_tex': 'Q_8\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.30.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.42', 'subgroup_hash': 42, 'subgroup_order': 80, 'subgroup_tex': 'D_{20}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 171720264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.30.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.42', 'subgroup_hash': 42, 'subgroup_order': 80, 'subgroup_tex': 'D_{20}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 171720265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.30.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.42', 'subgroup_hash': 42, 'subgroup_order': 80, 'subgroup_tex': 'D_{20}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 171720266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.30.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.42', 'subgroup_hash': 42, 'subgroup_order': 80, 'subgroup_tex': 'D_{20}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 171720267
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 171720268
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.40.a1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.a1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 171720269
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.40.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 171720270
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.40.a1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.a1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 171720271
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 20, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 171720272
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 171720273
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.40.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 171720275
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 20, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.40.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.2', 'subgroup_hash': 2, 'subgroup_order': 60, 'subgroup_tex': 'C_5:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 171720276
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 20, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.40.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.2', 'subgroup_hash': 2, 'subgroup_order': 60, 'subgroup_tex': 'C_5:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 171720277
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.40.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720278
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.40.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720279
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 10, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720280
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 10, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.48.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720281
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 10, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720282
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720283
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.48.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.c1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720284
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.48.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720286
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.48.c1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.c1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.50.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 171720288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.50.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 171720289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.50.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 171720290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.50.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 171720291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': True, 'core_order': 40, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2400.bt.60.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'A_5', 'simple': False, 'solvable': True, 'special_labels': ['R', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '40.7', 'subgroup_hash': 7, 'subgroup_order': 40, 'subgroup_tex': 'C_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720292
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720297
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720298
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 20, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.7', 'subgroup_hash': 7, 'subgroup_order': 40, 'subgroup_tex': 'C_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720300
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720301
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720302
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720303
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720305
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.j1.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.l1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.l1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.11', 'subgroup_hash': 11, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 171720314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.60.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.11', 'subgroup_hash': 11, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 171720315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '2400.bt.75.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '75.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': 75, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 171720316
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 10, 'counter': 98, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 171720317
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 10, 'counter': 99, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.80.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 171720088
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 10, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.80.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 171720089
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.80.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 171720090
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.80.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.c1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 171720091
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.80.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 171720092
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.80.c1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.c1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 171720093
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 5, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 5, 'label': '2400.bt.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 5}
  • id: 171720094
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.100.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 171720095
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.100.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 171720096
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.100.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720097
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.100.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 171720099
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.100.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 171720100
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.100.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 171720101
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.100.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 171720102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.100.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 171720103
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 1200, 'characteristic': True, 'core_order': 20, 'counter': 114, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2400.bt.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_5', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720104
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 20, 'counter': 115, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2400.bt.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720105
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 20, 'counter': 116, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2400.bt.120.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '120.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720107
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720108
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.d1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.d1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.d1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.d1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.e1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.e1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.e1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720117
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720118
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.e1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.e1.c2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720119
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720121
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.e1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.e1.d2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720122
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 200, 'characteristic': False, 'core_order': 4, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720123
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720124
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 4, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720125
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720126
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720127
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720128
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720129
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720130
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.j1.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720132
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.j1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.j1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720133
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.j1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.j1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720134
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 142, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.120.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720135
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 143, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.120.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720136
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 144, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.120.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720137
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720138
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 146, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.120.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 171720139
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.120.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720140
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.150.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.150.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.150.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 171720144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.150.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 171720145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.150.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 171720146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.150.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 171720147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.150.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 171720148
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 155, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 171720149
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.200.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': 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: 171720150
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.200.a1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.a1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': 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: 171720151
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.200.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': 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: 171720152
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.200.a1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.a1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': 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: 171720154
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 4, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.200.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': 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: 171720155
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.200.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': 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: 171720156
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.200.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': 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: 171720157
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 163, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.200.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 171720158
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 164, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.200.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 171720159
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.200.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720160
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.200.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720161
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 1200, 'characteristic': False, 'core_order': 10, 'counter': 167, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2400.bt.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.93', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 93, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\SL(2,5):C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720162
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 1200, 'characteristic': False, 'core_order': 10, 'counter': 168, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2400.bt.240.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.93', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 93, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\SL(2,5):C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720163
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 1200, 'characteristic': True, 'core_order': 10, 'counter': 169, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2400.bt.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.190', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 190, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times A_5', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720165
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 200, 'characteristic': False, 'core_order': 2, 'counter': 170, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720166
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 200, 'characteristic': False, 'core_order': 2, 'counter': 171, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.240.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720167
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 2, 'counter': 172, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720168
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 2, 'counter': 173, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.240.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720169
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 2, 'counter': 174, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.240.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720170
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 2, 'counter': 175, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.240.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720171
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 200, 'characteristic': False, 'core_order': 2, 'counter': 176, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.240.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720172
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 2, 'counter': 177, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.240.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720173
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 2, 'counter': 178, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.240.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 171720174
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720176
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720177
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720178
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.h1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720179
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720180
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.h1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.h1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720181
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720182
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.i1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720183
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720184
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.i1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.i1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720185
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720187
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.i1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.i1.c2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720188
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.i1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720189
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.240.i1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.i1.d2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720190
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.300.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 171720191
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 4, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.300.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720192
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.300.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720193
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.300.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720194
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.300.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720195
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.300.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720196
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.300.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.300.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.300.f1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.f1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.300.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.300.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.300.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 171720204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.300.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 171720205
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 206, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.400.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': 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: 171720206
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 207, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.400.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': 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: 171720207
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 208, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.400.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': 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: 171720208
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.400.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': 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: 171720210
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.400.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '400.c1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 400, 'quotient_simple': 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: 171720211
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.400.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': 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: 171720212
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.400.c1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '400.c1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 400, 'quotient_simple': 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: 171720213
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 1200, 'characteristic': True, 'core_order': 5, 'counter': 213, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2400.bt.480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '480.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '480.955', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 955, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 480, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\SL(2,5):C_2^2', 'simple': True, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720214
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 200, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.480.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720215
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.480.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720216
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 1, 'counter': 216, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.480.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 171720217
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 2400, 'characteristic': True, 'core_order': 4, 'counter': 217, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2400.bt.600.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '600.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '600.146', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 146, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 600, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'D_5\\times A_5', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 171720218
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.600.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 171720219
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.600.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 171720221
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.600.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 171720222
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2400.bt.600.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 171720223
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 2, 'counter': 222, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.600.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720224
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 2, 'counter': 223, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.600.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720225
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 2, 'counter': 224, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.600.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720226
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 2, 'counter': 225, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.600.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 171720227
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 226, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '2400.bt.800.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '800.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': 800, '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': 3}
  • id: 171720228
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 2400, 'characteristic': False, 'core_order': 2, 'counter': 227, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '2400.bt.1200.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1200.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1200.481', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 481, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1200, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\SL(2,5):D_5', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 171720229
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 2400, 'characteristic': False, 'core_order': 2, 'counter': 228, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '2400.bt.1200.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1200.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1200.481', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 481, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1200, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\SL(2,5):D_5', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 171720230
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 2400, 'characteristic': True, 'core_order': 2, 'counter': 229, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2400.bt.1200.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1200.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1200.944', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 944, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1200, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'D_{10}\\times A_5', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 171720232
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 230, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.1200.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1200.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': 1200, '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: 171720233
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 231, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2400.bt.1200.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1200.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': 1200, '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: 171720234
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2400.bt', 'ambient_counter': 46, 'ambient_order': 2400, 'ambient_tex': '\\SL(2,5):D_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 2400, 'characteristic': True, 'core_order': 1, 'counter': 232, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '2400.bt.2400.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2400.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '2400.bt', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6351781673999964458, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 2400, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\SL(2,5):D_{10}', 'simple': False, 'solvable': True, 'special_labels': ['U1', '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: 171720086
    {'ambient': '2400.bt', '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': '600.a1.a1', 'complements': ['2400.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '5.a1.a1', '5.b1.a1', '6.a1.a1', '10.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7399, 2629, 2893, 4628, 3136, 2938, 7008, 3356], 'generators': [122109387504, 130509168233, 140879192328, 1271171980, 148051235266, 122741847365], 'label': '2400.bt.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '600.146', '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': '600.146'}
  • id: 171720087
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1920.204530', 'aut_weyl_index': 10, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['20.b1.a1', '20.c1.a1', '20.d1.a1', '20.e1.a1', '20.e1.b1', '20.f1.a1', '20.f1.b1', '30.b1.a1', '50.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6860, -1, 1372, -1, 3909, -1, 6532, -1], 'generators': [122109387504, 130509168233, 140879192328, 25830469380, 1271171980, 110631910891], 'label': '2400.bt.10.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '10.b1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720088
    {'ambient': '2400.bt', 'aut_centralizer_order': 240, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2400, 'centralizer': '40.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.g1.a1', '40.b1.a1', '40.c1.a1', '40.c1.b1', '40.d1.a1', '40.d1.b1', '40.e1.a1', '40.f1.a1'], 'contains': ['160.a1.a1', '240.b1.a1', '400.b1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7143, -1, 1466, -1, 4660, -1, 6396, -1], 'generators': [140879192328, 1271171980, 90360007017], 'label': '2400.bt.80.b1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '80.b1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720089
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '120.36', 'aut_weyl_index': 160, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '40.a1.b1', '40.c1.a1'], 'contains': ['160.a1.a1', '240.g1.a1', '400.c1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3362, -1, 1033, -1, 7114, -1, 4270, -1], 'generators': [140879192328, 986356750, 105551846115], 'label': '2400.bt.80.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '80.c1.a1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720090
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '120.36', 'aut_weyl_index': 160, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a2', '40.a1.b2', '40.c1.a1'], 'contains': ['160.a1.a1', '240.g1.a1', '400.c1.a2'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3362, -1, 702, -1, 7114, -1, 4636, -1], 'generators': [11036721270, 140879192328, 105551846115], 'label': '2400.bt.80.c1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '80.c1.a2', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1.a2', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720091
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '120.36', 'aut_weyl_index': 160, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '40.a1.b2', '40.c1.b1'], 'contains': ['160.a1.a1', '240.g1.b1', '400.c1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3362, -1, 472, -1, 7114, -1, 4535, -1], 'generators': [140879192328, 25830469380, 105551846115], 'label': '2400.bt.80.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '80.c1.b1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720092
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '120.36', 'aut_weyl_index': 160, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a2', '40.a1.b1', '40.c1.b1'], 'contains': ['160.a1.a1', '240.g1.b1', '400.c1.b2'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3362, -1, 345, -1, 7114, -1, 4737, -1], 'generators': [140879192328, 283268875, 105551846115], 'label': '2400.bt.80.c1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '80.c1.b2', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1.b2', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720093
    {'ambient': '2400.bt', 'aut_centralizer_order': 200, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.2', 'aut_weyl_index': 1200, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.a1.b1', '48.b1.a1', '48.c1.a1', '48.c1.a2', '48.c1.b1', '48.c1.b2'], 'contains': ['480.a1.a1', '480.b1.a1', '480.c1.a1', '480.c1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [398, -1, 8230, -1, 8462, -1, 1655, -1], 'generators': [140879192328, 7445862067], 'label': '2400.bt.96.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720094
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '100.a1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '48.38', 'aut_weyl_index': 400, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '50.a1.a1'], 'contains': ['200.a1.a1', '200.a1.a2', '200.a1.b1', '200.a1.b2', '200.b1.a1', '200.c1.a1', '200.c1.b1', '300.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3990, -1, 990, -1, 5740, -1, 4860, -1], 'generators': [122109387504, 25830469380, 1271171980, 110631910891], 'label': '2400.bt.100.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '100.a1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720095
    {'ambient': '2400.bt', 'aut_centralizer_order': 24, 'aut_label': '100.b1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1200, 'centralizer': '100.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '25.a1.a1', '50.a1.a1'], 'contains': ['200.b1.a1', '200.d1.a1', '200.d1.b1', '300.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [8610, -1, 1503, -1, 4993, -1, 6790, -1], 'generators': [122109387504, 1271171980, 50675370281, 128717318317], 'label': '2400.bt.100.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '100.b1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720096
    {'ambient': '2400.bt', 'aut_centralizer_order': 80, 'aut_label': '100.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '24.14', 'aut_weyl_index': 800, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '20.d1.a1', '50.a1.a1'], 'contains': ['200.b1.a1', '200.e1.a1', '200.f1.a1', '300.c1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8302, -1, 730, -1, 2153, -1, 7167, -1], 'generators': [122109387504, 1271171980, 90167754342, 110631910891], 'label': '2400.bt.100.c1.a1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '100.c1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720097
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '100.d1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '24.14', 'aut_weyl_index': 800, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.e1.a1', '50.a1.a1'], 'contains': ['200.c1.a1', '200.d1.b1', '200.e1.a1', '300.d1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [7099, -1, 256, -1, 3500, -1, 6065, -1], 'generators': [11036721270, 1271171980, 140049727374, 110631910891], 'label': '2400.bt.100.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '100.d1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720098
    {'ambient': '2400.bt', 'aut_centralizer_order': 20, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 100, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.g1.a1', '30.d1.a1', '40.b1.a1', '50.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7698, -1, 2152, -1, 1535, -1, 7746, -1], 'generators': [122109387504, 140879192328, 1271171980, 98909934263, 72007755877, 45129158685], 'label': '2400.bt.10.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 171720099
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '100.d1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '24.14', 'aut_weyl_index': 800, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.e1.b1', '50.a1.a1'], 'contains': ['200.c1.b1', '200.d1.a1', '200.e1.a1', '300.d1.b1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [7099, -1, 56, -1, 3500, -1, 5757, -1], 'generators': [25830469380, 1271171980, 110631910891, 50675370281], 'label': '2400.bt.100.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '100.d1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720100
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '100.e1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '24.14', 'aut_weyl_index': 800, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.e1.a1', '20.f1.a1', '50.a1.a1'], 'contains': ['200.c1.a1', '200.d1.a1', '200.f1.a1', '300.e1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [9244, -1, 1954, -1, 2952, -1, 7522, -1], 'generators': [11036721270, 1271171980, 110631910891, 50675370281], 'label': '2400.bt.100.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '100.e1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720101
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '100.e1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '24.14', 'aut_weyl_index': 800, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.e1.b1', '20.f1.b1', '50.a1.a1'], 'contains': ['200.c1.b1', '200.d1.b1', '200.f1.a1', '300.e1.b1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [9244, -1, 1753, -1, 2952, -1, 7875, -1], 'generators': [25830469380, 1271171980, 140049727374, 110631910891], 'label': '2400.bt.100.e1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '100.e1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720102
    {'ambient': '2400.bt', 'aut_centralizer_order': 160, 'aut_label': '100.f1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '24.12', 'aut_weyl_index': 800, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '20.g1.a1', '50.b1.a1', '50.c1.a1', '50.c1.b1'], 'contains': ['300.i1.a1', '400.b1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [9902, -1, 2852, -1, 62, -1, 8473, -1], 'generators': [17605993094, 1271171980, 81506204464, 124586497402], 'label': '2400.bt.100.f1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '100.f1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 171720103
    {'ambient': '2400.bt', 'aut_centralizer_order': 2400, 'aut_label': '120.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2400, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.b1.a1', '60.a1.a1', '60.b1.a1', '60.f1.a1'], 'contains': ['240.a1.a1', '240.a1.b1', '240.b1.a1', '600.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3487, 3725, 3091, 7368, 5986, 5802, 5062, 9095], 'generators': [122109387504, 140879192328, 1271171980], 'label': '2400.bt.120.a1.a1', 'mobius_quo': -2, 'mobius_sub': 60, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['2.a1.a1', '60.a1.a1'], 'normal_contains': ['240.a1.b1', '240.a1.a1', '240.b1.a1', '600.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '600.146', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.5', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720104
    {'ambient': '2400.bt', 'aut_centralizer_order': 240, 'aut_label': '120.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '10.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '40.d1.a1', '60.a1.a1', '60.j1.b1', '60.k1.a1'], 'contains': ['240.b1.a1', '600.d1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6491, 1176, 3426, 3845, 5363, 776, 5443, 1135], 'generators': [130509168233, 140879192328, 1271171980], 'label': '2400.bt.120.b1.a1', 'mobius_quo': 0, 'mobius_sub': 60, 'normal_closure': '120.b1.a1', 'normal_contained_in': ['2.b1.a1', '60.a1.a1'], 'normal_contains': ['240.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.b1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720105
    {'ambient': '2400.bt', 'aut_centralizer_order': 240, 'aut_label': '120.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '10.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '40.d1.b1', '60.a1.a1', '60.j1.a1', '60.k1.b1'], 'contains': ['240.b1.a1', '600.d1.b1'], 'core': '120.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6491, 1176, 3249, 1302, 5363, 776, 5937, 2283], 'generators': [140879192328, 60215928797, 1271171980], 'label': '2400.bt.120.b1.b1', 'mobius_quo': 0, 'mobius_sub': 60, 'normal_closure': '120.b1.b1', 'normal_contained_in': ['2.b1.b1', '60.a1.a1'], 'normal_contains': ['240.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.b1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720106
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '300.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.a1.a2', '40.a1.a1', '40.a1.a2', '60.b1.a1'], 'contains': ['240.a1.a1', '240.g1.a1', '240.g1.b1', '600.b1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1586, -1, 4604, -1, 8319, -1, 3789, -1], 'generators': [10054287475, 140879192328, 5078828170], 'label': '2400.bt.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '120.c1.a1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720180
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '240.h1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b2', '120.d1.a2', '120.d1.b1', '120.i1.b1'], 'contains': ['480.b1.a1', '1200.c1.b1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [121, -1, 6661, -1, 8163, -1, 2591, -1], 'generators': [81420657990, 84411882688], 'label': '2400.bt.240.h1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.h1.b2', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.h1.b2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720107
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '300.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.a1.b2', '40.a1.b1', '40.a1.b2', '60.b1.a1'], 'contains': ['240.a1.b1', '240.g1.a1', '240.g1.b1', '600.b1.b1'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 30, 'diagramx': [1586, -1, 4749, -1, 8319, -1, 3688, -1], 'generators': [122109387504, 10054287475, 140879192328], 'label': '2400.bt.120.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '120.c1.b1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720108
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.c1.a1'], 'contains': ['240.c1.a1', '240.h1.a1', '240.h1.b1', '600.b1.a1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [311, -1, 7036, -1, 8937, -1, 2611, -1], 'generators': [81420657990, 64028341198, 5078828170], 'label': '2400.bt.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.d1.a1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720109
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 20, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.g1.a1', '30.f1.a1', '40.d1.a1', '50.c1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8425, -1, 3831, -1, 1885, -1, 8219, -1], 'generators': [55865201213, 4990156490, 130509168233, 140879192328, 1271171980, 45129158685], 'label': '2400.bt.10.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.d1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.a1', 'subgroup_fusion': None, 'weyl_group': '120.39'}
  • id: 171720110
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a2', '60.c1.a1'], 'contains': ['240.c1.a1', '240.h1.a2', '240.h1.b2', '600.b1.a1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [311, -1, 6843, -1, 8937, -1, 2711, -1], 'generators': [81420657990, 84411882688, 5078828170], 'label': '2400.bt.120.d1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.d1.a2', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.a2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720111
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '60.c1.a1'], 'contains': ['240.c1.b1', '240.h1.a1', '240.h1.b2', '600.b1.b1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 30, 'diagramx': [311, -1, 7831, -1, 8937, -1, 2409, -1], 'generators': [81420657990, 122109387504, 84411882688], 'label': '2400.bt.120.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.d1.b1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720112
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b2', '60.c1.a1'], 'contains': ['240.c1.b1', '240.h1.a2', '240.h1.b1', '600.b1.b1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 30, 'diagramx': [311, -1, 8063, -1, 8937, -1, 2510, -1], 'generators': [81420657990, 122109387504, 64028341198], 'label': '2400.bt.120.d1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.d1.b2', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.b2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720113
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.d1.a1'], 'contains': ['240.d1.a1', '240.i1.a1', '240.i1.c1', '600.b1.a1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [550, -1, 9553, -1, 9562, -1, 1636, -1], 'generators': [7445862067, 64028341198, 5078828170], 'label': '2400.bt.120.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '120.e1.a1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720114
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a2', '60.d1.a1'], 'contains': ['240.d1.a1', '240.i1.a2', '240.i1.c2', '600.b1.a1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [550, -1, 9066, -1, 9562, -1, 1922, -1], 'generators': [84411882688, 7445862067, 5078828170], 'label': '2400.bt.120.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '120.e1.a2', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.a2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720115
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.d1.b1'], 'contains': ['240.d1.b1', '240.i1.b1', '240.i1.d1', '600.b1.a1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [550, -1, 8351, -1, 9562, -1, 242, -1], 'generators': [64028341198, 117797313644, 5078828170], 'label': '2400.bt.120.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '120.e1.b1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720116
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a2', '60.d1.b1'], 'contains': ['240.d1.b1', '240.i1.b2', '240.i1.d2', '600.b1.a1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [550, -1, 7741, -1, 9562, -1, 343, -1], 'generators': [84411882688, 117797313644, 5078828170], 'label': '2400.bt.120.e1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '120.e1.b2', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.b2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720117
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '60.d1.a1'], 'contains': ['240.d1.c1', '240.i1.a1', '240.i1.c2', '600.b1.b1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 60, 'diagramx': [550, -1, 9727, -1, 9562, -1, 1015, -1], 'generators': [122109387504, 84411882688, 7445862067], 'label': '2400.bt.120.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '120.e1.c1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.c1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720118
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b2', '60.d1.a1'], 'contains': ['240.d1.c1', '240.i1.a2', '240.i1.c1', '600.b1.b1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 60, 'diagramx': [550, -1, 9841, -1, 9562, -1, 1430, -1], 'generators': [122109387504, 7445862067, 64028341198], 'label': '2400.bt.120.e1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '120.e1.c2', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.c2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720119
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '60.d1.b1'], 'contains': ['240.d1.d1', '240.i1.b1', '240.i1.d2', '600.b1.b1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 60, 'diagramx': [550, -1, 8789, -1, 9562, -1, 40, -1], 'generators': [122109387504, 84411882688, 117797313644], 'label': '2400.bt.120.e1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '120.e1.d1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.d1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720120
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 20, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '5.a1.a1'], 'contains': ['20.g1.a1', '30.f1.b1', '40.d1.b1', '50.c1.b1'], 'core': '120.b1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [8425, -1, 2928, -1, 1885, -1, 8352, -1], 'generators': [140879192328, 1369609910, 60215928797, 1271171980, 45129158685, 128717318317], 'label': '2400.bt.10.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.d1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.b1', 'subgroup_fusion': None, 'weyl_group': '120.39'}
  • id: 171720121
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b2', '60.d1.b1'], 'contains': ['240.d1.d1', '240.i1.b2', '240.i1.d1', '600.b1.b1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 60, 'diagramx': [550, -1, 9150, -1, 9562, -1, 141, -1], 'generators': [122109387504, 64028341198, 117797313644], 'label': '2400.bt.120.e1.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '120.e1.d2', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.d2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720122
    {'ambient': '2400.bt', 'aut_centralizer_order': 400, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2400, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '60.c1.a1', '60.e1.a1', '60.g1.a1'], 'contains': ['240.c1.a1', '240.c1.b1', '240.e1.a1', '600.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2298, -1, 6650, -1, 8091, -1, 3039, -1], 'generators': [81420657990, 122109387504, 1271171980], 'label': '2400.bt.120.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '120.f1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720123
    {'ambient': '2400.bt', 'aut_centralizer_order': 100, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2400, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '60.d1.a1'], 'contains': ['240.d1.a1', '240.d1.c1', '240.f1.a1', '600.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1056, -1, 8647, -1, 8709, -1, 2064, -1], 'generators': [122109387504, 1271171980, 7445862067], 'label': '2400.bt.120.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '120.g1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720124
    {'ambient': '2400.bt', 'aut_centralizer_order': 100, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2400, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '60.d1.b1'], 'contains': ['240.d1.b1', '240.d1.d1', '240.f1.b1', '600.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1056, -1, 7313, -1, 8709, -1, 486, -1], 'generators': [122109387504, 1271171980, 117797313644], 'label': '2400.bt.120.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '120.g1.b1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720125
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '300.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '40.c1.a1', '60.b1.a1', '60.j1.a1', '60.k1.a1', '60.l1.a1', '60.l1.a2', '60.m1.a1'], 'contains': ['240.b1.a1', '240.g1.a1', '600.c1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2534, -1, 4893, -1, 5198, -1, 6040, -1], 'generators': [10054287475, 140879192328, 1271171980], 'label': '2400.bt.120.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.h1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.h1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720126
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '300.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '40.c1.b1', '60.b1.a1', '60.j1.b1', '60.k1.b1', '60.l1.a1', '60.l1.a2', '60.m1.b1'], 'contains': ['240.b1.a1', '240.g1.b1', '600.c1.b1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2534, -1, 4496, -1, 5198, -1, 6141, -1], 'generators': [140879192328, 1271171980, 27848544525], 'label': '2400.bt.120.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.h1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.h1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720127
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '60.c1.a1', '60.h1.a1', '60.i1.a1'], 'contains': ['240.e1.a1', '240.h1.a1', '240.h1.a2', '600.c1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1752, -1, 6386, -1, 7567, -1, 3182, -1], 'generators': [81420657990, 96188940832, 1271171980], 'label': '2400.bt.120.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.i1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.i1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720128
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '60.c1.a1', '60.h1.b1', '60.i1.b1'], 'contains': ['240.e1.a1', '240.h1.b1', '240.h1.b2', '600.c1.b1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1752, -1, 6228, -1, 7567, -1, 3283, -1], 'generators': [81420657990, 1271171980, 64028341198], 'label': '2400.bt.120.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.i1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.i1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720129
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 240, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '60.d1.a1'], 'contains': ['240.f1.a1', '240.i1.a1', '240.i1.a2', '600.c1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [821, -1, 8970, -1, 8480, -1, 2207, -1], 'generators': [96188940832, 1271171980, 7445862067], 'label': '2400.bt.120.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '120.j1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720130
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 240, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '60.d1.b1'], 'contains': ['240.f1.b1', '240.i1.b1', '240.i1.b2', '600.c1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [821, -1, 7469, -1, 8480, -1, 628, -1], 'generators': [96188940832, 1271171980, 117797313644], 'label': '2400.bt.120.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '120.j1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720131
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '10.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '240.189', 'aut_weyl_index': 80, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.b1.a1'], 'contains': ['20.a1.a1', '50.c1.a1', '60.i1.a1', '100.e1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [9726, -1, 3931, -1, 3148, -1, 7177, -1], 'generators': [130509168233, 31371528410, 42634393514, 1271171980], 'label': '2400.bt.10.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.b1.a1', 'old_label': '10.e1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.e1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 171720132
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 240, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '60.d1.a1'], 'contains': ['240.f1.a1', '240.i1.c1', '240.i1.c2', '600.c1.b1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [821, -1, 8436, -1, 8480, -1, 2308, -1], 'generators': [1271171980, 7445862067, 64028341198], 'label': '2400.bt.120.j1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '120.j1.c1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.c1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720133
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 240, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '60.d1.b1'], 'contains': ['240.f1.b1', '240.i1.d1', '240.i1.d2', '600.c1.b1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [821, -1, 7194, -1, 8480, -1, 729, -1], 'generators': [1271171980, 64028341198, 117797313644], 'label': '2400.bt.120.j1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '120.j1.d1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.d1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720134
    {'ambient': '2400.bt', 'aut_centralizer_order': 40, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2400, 'centralizer': '60.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '60.e1.a1', '60.h1.b1', '60.i1.a1'], 'contains': ['240.e1.a1', '600.d1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4408, -1, 5943, -1, 6952, -1, 3384, -1], 'generators': [81420657990, 130509168233, 1271171980], 'label': '2400.bt.120.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.k1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720135
    {'ambient': '2400.bt', 'aut_centralizer_order': 40, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2400, 'centralizer': '60.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '60.e1.a1', '60.h1.a1', '60.i1.b1'], 'contains': ['240.e1.a1', '600.d1.b1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4408, -1, 6049, -1, 6952, -1, 3483, -1], 'generators': [81420657990, 60215928797, 1271171980], 'label': '2400.bt.120.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.k1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.k1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720136
    {'ambient': '2400.bt', 'aut_centralizer_order': 160, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2400, 'centralizer': '60.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '40.e1.a1', '60.f1.a1', '60.j1.a1', '60.j1.b1', '60.l1.a1', '60.l1.a2', '60.n1.a1'], 'contains': ['240.b1.a1', '600.e1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5251, -1, 3914, -1, 3773, -1, 6700, -1], 'generators': [145603735840, 140879192328, 1271171980], 'label': '2400.bt.120.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.l1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720137
    {'ambient': '2400.bt', 'aut_centralizer_order': 80, 'aut_label': '120.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '60.g1.a1', '60.h1.a1', '60.h1.b1'], 'contains': ['240.e1.a1', '600.e1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2793, -1, 5746, -1, 6789, -1, 3585, -1], 'generators': [81420657990, 1271171980, 73738889847], 'label': '2400.bt.120.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '120.m1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.m1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720138
    {'ambient': '2400.bt', 'aut_centralizer_order': 160, 'aut_label': '120.n1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2400, 'centralizer': '60.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '40.f1.a1', '60.f1.a1', '60.k1.a1', '60.k1.b1', '60.m1.a1', '60.m1.b1', '60.n1.a1', '60.o1.a1'], 'contains': ['240.b1.a1', '600.f1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7415, -1, 4064, -1, 2581, -1, 8029, -1], 'generators': [140879192328, 1271171980, 45129158685], 'label': '2400.bt.120.n1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.n1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720139
    {'ambient': '2400.bt', 'aut_centralizer_order': 160, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '24.f1.a1', '60.g1.a1', '60.i1.a1', '60.i1.b1'], 'contains': ['240.e1.a1', '600.f1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4881, -1, 5649, -1, 6218, -1, 3985, -1], 'generators': [81420657990, 1271171980, 110599489058], 'label': '2400.bt.120.o1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '120.o1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720140
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '150.a1', 'aut_quo_index': None, 'aut_stab_index': 75, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1200, 'centralizer': '150.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.b1.a1', '50.a1.a1', '75.a1.a1'], 'contains': ['300.a1.a1', '300.b1.a1', '300.c1.a1', '300.d1.a1', '300.d1.b1', '300.e1.a1', '300.e1.b1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [5877, -1, 2782, -1, 4455, -1, 6230, -1], 'generators': [122109387504, 130509168233, 1271171980, 81506204464], 'label': '2400.bt.150.a1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '150.a1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720141
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '150.b1', 'aut_quo_index': None, 'aut_stab_index': 75, 'aut_weyl_group': '32.49', 'aut_weyl_index': 600, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1', '75.a1.a1'], 'contains': ['300.a1.a1', '300.c1.a1', '300.f1.a1', '300.f1.a2', '300.g1.a1', '300.g1.b1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4712, -1, 3860, -1, 1508, -1, 9723, -1], 'generators': [122109387504, 1369609910, 1271171980, 81506204464], 'label': '2400.bt.150.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '150.b1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720142
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '10.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '240.189', 'aut_weyl_index': 80, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '5.b1.a1'], 'contains': ['20.a1.a1', '50.c1.b1', '60.i1.b1', '100.e1.b1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [9726, -1, 2719, -1, 3148, -1, 7280, -1], 'generators': [60215928797, 1271171980, 148051235266, 122741847365], 'label': '2400.bt.10.e1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.b1.a1', 'old_label': '10.e1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.e1.b1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 171720143
    {'ambient': '2400.bt', 'aut_centralizer_order': 80, 'aut_label': '150.c1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 400, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.a1', '50.b1.a1', '75.a1.a1'], 'contains': ['300.c1.a1', '300.h1.a1', '300.i1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8393, -1, 2290, -1, 513, -1, 8799, -1], 'generators': [122109387504, 1271171980, 81506204464, 34410003353], 'label': '2400.bt.150.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '150.c1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 171720181
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '120.e1.a1', '120.e1.c1', '120.j1.a1'], 'contains': ['480.c1.a1', '1200.c1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [327, -1, 9704, -1, 8602, -1, 1568, -1], 'generators': [7445862067, 105102199342], 'label': '2400.bt.240.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '240.i1.a1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720144
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '150.d1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1200, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.a1', '75.a1.a1'], 'contains': ['300.d1.b1', '300.e1.a1', '300.f1.a1', '300.f1.a2', '300.g1.b1', '300.h1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [5494, -1, 3381, -1, 1138, -1, 9854, -1], 'generators': [92911416209, 1369609910, 1271171980, 81506204464], 'label': '2400.bt.150.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '150.d1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720145
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '150.d1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1200, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.b1', '75.a1.a1'], 'contains': ['300.d1.a1', '300.e1.b1', '300.f1.a1', '300.f1.a2', '300.g1.a1', '300.h1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [5494, -1, 3486, -1, 1138, -1, 9958, -1], 'generators': [66075318946, 1369609910, 1271171980, 109226689441], 'label': '2400.bt.150.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '150.d1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720146
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '150.e1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '48.48', 'aut_weyl_index': 400, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '50.c1.a1', '75.a1.a1'], 'contains': ['300.e1.a1', '300.g1.a1', '300.i1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [8608, -1, 5004, -1, 721, -1, 9030, -1], 'generators': [92911416209, 4990156490, 1271171980, 81506204464], 'label': '2400.bt.150.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '150.e1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 171720147
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '150.e1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '48.48', 'aut_weyl_index': 400, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.b1', '50.c1.b1', '75.a1.a1'], 'contains': ['300.e1.b1', '300.g1.b1', '300.i1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [8608, -1, 2618, -1, 721, -1, 9438, -1], 'generators': [66075318946, 1369609910, 1271171980, 81506204464], 'label': '2400.bt.150.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '150.e1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 171720148
    {'ambient': '2400.bt', 'aut_centralizer_order': 240, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2400, 'centralizer': '40.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a1.a1', '80.a1.b1', '80.b1.a1', '80.c1.a1', '80.c1.a2', '80.c1.b1', '80.c1.b2'], 'contains': ['480.a1.a1', '800.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6460, -1, 622, -1, 7000, -1, 4542, -1], 'generators': [140879192328, 94329528590], 'label': '2400.bt.160.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '160.a1.a1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720149
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '200.a1', 'aut_quo_index': None, 'aut_stab_index': 200, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1600, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '100.a1.a1'], 'contains': ['400.a1.a1', '400.c1.a1', '400.c1.b1', '600.b1.a1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3676, -1, 815, -1, 7420, -1, 4443, -1], 'generators': [25830469380, 5078828170, 105551846115], 'label': '2400.bt.200.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '200.a1.a1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720150
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '200.a1', 'aut_quo_index': None, 'aut_stab_index': 200, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1600, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a2', '100.a1.a1'], 'contains': ['400.a1.a1', '400.c1.a2', '400.c1.b2', '600.b1.a1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3676, -1, 707, -1, 7420, -1, 4928, -1], 'generators': [283268875, 5078828170, 105551846115], 'label': '2400.bt.200.a1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '200.a1.a2', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.a1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720151
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '200.a1', 'aut_quo_index': None, 'aut_stab_index': 200, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1600, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.b1', '100.a1.a1'], 'contains': ['400.a1.b1', '400.c1.a1', '400.c1.b2', '600.b1.b1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 50, 'diagramx': [3676, -1, 1295, -1, 7420, -1, 4178, -1], 'generators': [122109387504, 283268875, 105551846115], 'label': '2400.bt.200.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '200.a1.b1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720152
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '200.a1', 'aut_quo_index': None, 'aut_stab_index': 200, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1600, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.b2', '100.a1.a1'], 'contains': ['400.a1.b1', '400.c1.a2', '400.c1.b1', '600.b1.b1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 50, 'diagramx': [3676, -1, 1190, -1, 7420, -1, 4362, -1], 'generators': [122109387504, 25830469380, 105551846115], 'label': '2400.bt.200.a1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '200.a1.b2', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.a1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720153
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3200.jc', 'aut_weyl_index': 6, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.a1.a1', '24.a1.a2', '24.a1.b1', '24.a1.b2', '24.b1.a1', '24.c1.a1', '24.c1.b1', '60.b1.a1', '60.c1.a1', '60.d1.a1', '60.d1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1783, -1, 7235, -1, 9084, -1, 1697, -1], 'generators': [122109387504, 140879192328, 1271171980, 7445862067, 64028341198], 'label': '2400.bt.12.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720154
    {'ambient': '2400.bt', 'aut_centralizer_order': 480, 'aut_label': '200.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4800, 'centralizer': '20.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.a1', '50.b1.a1', '100.a1.a1', '100.b1.a1', '100.c1.a1'], 'contains': ['400.a1.a1', '400.a1.b1', '400.b1.a1', '600.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7543, -1, 1024, -1, 4993, -1, 5572, -1], 'generators': [122109387504, 1271171980, 20296838936], 'label': '2400.bt.200.b1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '200.b1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720155
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '200.c1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1600, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.a1', '100.a1.a1', '100.d1.a1', '100.e1.a1'], 'contains': ['400.b1.a1', '400.c1.a1', '400.c1.a2', '600.c1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [4136, -1, 1122, -1, 4805, -1, 5350, -1], 'generators': [11036721270, 1271171980, 110631910891], 'label': '2400.bt.200.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '200.c1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720156
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '200.c1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1600, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.b1', '100.a1.a1', '100.d1.b1', '100.e1.b1'], 'contains': ['400.b1.a1', '400.c1.b1', '400.c1.b2', '600.c1.b1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [4136, -1, 490, -1, 4805, -1, 5690, -1], 'generators': [25830469380, 1271171980, 110631910891], 'label': '2400.bt.200.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '200.c1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720157
    {'ambient': '2400.bt', 'aut_centralizer_order': 48, 'aut_label': '200.d1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4800, 'centralizer': '100.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.a1', '50.c1.a1', '100.b1.a1', '100.d1.b1', '100.e1.a1'], 'contains': ['400.b1.a1', '600.d1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [9153, -1, 1959, -1, 4161, -1, 6600, -1], 'generators': [55865201213, 1271171980, 50675370281], 'label': '2400.bt.200.d1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '200.d1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720158
    {'ambient': '2400.bt', 'aut_centralizer_order': 48, 'aut_label': '200.d1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4800, 'centralizer': '100.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.b1', '50.c1.b1', '100.b1.a1', '100.d1.a1', '100.e1.b1'], 'contains': ['400.b1.a1', '600.d1.b1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [9153, -1, 1875, -1, 4161, -1, 6799, -1], 'generators': [1271171980, 140049727374, 128717318317], 'label': '2400.bt.200.d1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '200.d1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720159
    {'ambient': '2400.bt', 'aut_centralizer_order': 160, 'aut_label': '200.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1600, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.e1.a1', '100.c1.a1', '100.d1.a1', '100.d1.b1'], 'contains': ['400.b1.a1', '600.e1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7766, -1, 189, -1, 3364, -1, 6498, -1], 'generators': [1271171980, 90167754342, 110631910891], 'label': '2400.bt.200.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '200.e1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720160
    {'ambient': '2400.bt', 'aut_centralizer_order': 160, 'aut_label': '200.f1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1600, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '40.f1.a1', '100.c1.a1', '100.e1.a1', '100.e1.b1'], 'contains': ['400.b1.a1', '600.f1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [9425, -1, 2099, -1, 2418, -1, 7875, -1], 'generators': [1271171980, 100557343313, 110631910891], 'label': '2400.bt.200.f1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '200.f1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720161
    {'ambient': '2400.bt', 'aut_centralizer_order': 2400, 'aut_label': '240.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '2.a1.a1', 'complements': ['10.e1.b1', '10.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1', '120.c1.a1'], 'contains': ['480.a1.a1', '1200.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2829, 3228, 3953, 6233, 7710, 5071, 3861, 9008], 'generators': [140879192328, 5078828170], 'label': '2400.bt.240.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': ['120.a1.a1'], 'normal_contains': ['480.a1.a1', '1200.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '1200.481', 'quotient_action_image': '2.1', 'quotient_action_kernel': '120.5', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720162
    {'ambient': '2400.bt', 'aut_centralizer_order': 2400, 'aut_label': '240.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '2.a1.a1', 'complements': ['10.e1.b1', '10.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.b1', '80.a1.b1', '120.a1.a1', '120.c1.b1'], 'contains': ['480.a1.a1', '1200.a1.b1'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2829, 3228, 4036, 8698, 7710, 5071, 3598, 7910], 'generators': [122109387504, 140879192328], 'label': '2400.bt.240.a1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '240.a1.b1', 'normal_contained_in': ['120.a1.a1'], 'normal_contains': ['480.a1.a1', '1200.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '240.a1.b1', 'projective_image': '1200.481', 'quotient_action_image': '2.1', 'quotient_action_kernel': '120.5', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '240.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720163
    {'ambient': '2400.bt', 'aut_centralizer_order': 4800, 'aut_label': '240.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '80.b1.a1', '120.a1.a1', '120.b1.a1', '120.b1.b1', '120.h1.a1', '120.h1.b1', '120.l1.a1', '120.n1.a1'], 'contains': ['480.a1.a1', '1200.b1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4289, 5737, 4256, 3767, 5363, 3758, 5892, 4479], 'generators': [140879192328, 1271171980], 'label': '2400.bt.240.b1.a1', 'mobius_quo': 1, 'mobius_sub': -120, 'normal_closure': '240.b1.a1', 'normal_contained_in': ['4.a1.a1', '120.a1.a1', '120.b1.a1', '120.b1.b1'], 'normal_contains': ['480.a1.a1', '1200.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.b1.a1', 'projective_image': '1200.944', 'quotient_action_image': '2.1', 'quotient_action_kernel': '120.35', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720164
    {'ambient': '2400.bt', 'aut_centralizer_order': 5, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '640.19253', 'aut_weyl_index': 30, 'centralizer': '120.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.b1.a1', '24.d1.a1', '24.d1.b1', '60.a1.a1', '60.e1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4498, -1, 5942, -1, 8029, -1, 2715, -1], 'generators': [122109387504, 130509168233, 140879192328, 1271171980, 7445862067], 'label': '2400.bt.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720165
    {'ambient': '2400.bt', 'aut_centralizer_order': 400, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '120.d1.a1', '120.d1.a2', '120.f1.a1'], 'contains': ['480.b1.a1', '1200.a1.a1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [475, -1, 6513, -1, 8308, -1, 2857, -1], 'generators': [81420657990, 5078828170], 'label': '2400.bt.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '240.c1.a1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720166
    {'ambient': '2400.bt', 'aut_centralizer_order': 400, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.b1', '120.d1.b1', '120.d1.b2', '120.f1.a1'], 'contains': ['480.b1.a1', '1200.a1.b1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [475, -1, 8027, -1, 8308, -1, 2337, -1], 'generators': [81420657990, 122109387504], 'label': '2400.bt.240.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '240.c1.b1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720167
    {'ambient': '2400.bt', 'aut_centralizer_order': 100, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '120.e1.a1', '120.e1.a2', '120.g1.a1'], 'contains': ['480.c1.a1', '1200.a1.a1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [830, -1, 9028, -1, 8747, -1, 1996, -1], 'generators': [7445862067, 5078828170], 'label': '2400.bt.240.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '240.d1.a1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720168
    {'ambient': '2400.bt', 'aut_centralizer_order': 100, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '120.e1.b1', '120.e1.b2', '120.g1.b1'], 'contains': ['480.c1.b1', '1200.a1.a1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [830, -1, 7478, -1, 8747, -1, 902, -1], 'generators': [117797313644, 5078828170], 'label': '2400.bt.240.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '240.d1.b1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720169
    {'ambient': '2400.bt', 'aut_centralizer_order': 100, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.b1', '120.e1.c1', '120.e1.c2', '120.g1.a1'], 'contains': ['480.c1.a1', '1200.a1.b1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [830, -1, 9944, -1, 8747, -1, 1446, -1], 'generators': [122109387504, 7445862067], 'label': '2400.bt.240.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '240.d1.c1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720170
    {'ambient': '2400.bt', 'aut_centralizer_order': 100, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.b1', '120.e1.d1', '120.e1.d2', '120.g1.b1'], 'contains': ['480.c1.b1', '1200.a1.b1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [830, -1, 9185, -1, 8747, -1, 475, -1], 'generators': [122109387504, 117797313644], 'label': '2400.bt.240.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '240.d1.d1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720171
    {'ambient': '2400.bt', 'aut_centralizer_order': 800, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '120.f1.a1', '120.i1.a1', '120.i1.b1', '120.k1.a1', '120.k1.b1', '120.m1.a1', '120.o1.a1'], 'contains': ['480.b1.a1', '1200.b1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2545, -1, 5992, -1, 7420, -1, 3334, -1], 'generators': [81420657990, 1271171980], 'label': '2400.bt.240.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '240.e1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720172
    {'ambient': '2400.bt', 'aut_centralizer_order': 200, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '120.g1.a1', '120.j1.a1', '120.j1.c1'], 'contains': ['480.c1.a1', '1200.b1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1114, -1, 8514, -1, 8018, -1, 2223, -1], 'generators': [1271171980, 7445862067], 'label': '2400.bt.240.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '240.f1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720173
    {'ambient': '2400.bt', 'aut_centralizer_order': 200, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '120.g1.b1', '120.j1.b1', '120.j1.d1'], 'contains': ['480.c1.b1', '1200.b1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1114, -1, 7020, -1, 8018, -1, 1001, -1], 'generators': [1271171980, 117797313644], 'label': '2400.bt.240.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '240.f1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720174
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '300.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.c1.a2', '80.c1.a1', '80.c1.a2', '120.c1.a1', '120.c1.b1', '120.h1.a1'], 'contains': ['480.a1.a1', '1200.c1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1907, -1, 4877, -1, 7565, -1, 3688, -1], 'generators': [10054287475, 140879192328], 'label': '2400.bt.240.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '240.g1.a1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.g1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720175
    {'ambient': '2400.bt', 'aut_centralizer_order': 20, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '160.203', 'aut_weyl_index': 120, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '24.f1.a1', '60.f1.a1', '60.g1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3856, -1, 5152, -1, 6659, -1, 3623, -1], 'generators': [122109387504, 140879192328, 1271171980, 7445862067, 73738889847], 'label': '2400.bt.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '600.146', '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': '20.4'}
  • id: 171720176
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '300.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '48.c1.b2', '80.c1.b1', '80.c1.b2', '120.c1.a1', '120.c1.b1', '120.h1.b1'], 'contains': ['480.a1.a1', '1200.c1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1907, -1, 4676, -1, 7565, -1, 3770, -1], 'generators': [140879192328, 27848544525], 'label': '2400.bt.240.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '240.g1.b1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.g1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720177
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '240.h1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '120.d1.a1', '120.d1.b1', '120.i1.a1'], 'contains': ['480.b1.a1', '1200.c1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [121, -1, 7214, -1, 8163, -1, 2428, -1], 'generators': [81420657990, 105102199342], 'label': '2400.bt.240.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.h1.a1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.h1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720178
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '240.h1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a2', '120.d1.a2', '120.d1.b2', '120.i1.a1'], 'contains': ['480.b1.a1', '1200.c1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [121, -1, 6944, -1, 8163, -1, 2673, -1], 'generators': [81420657990, 96188940832], 'label': '2400.bt.240.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.h1.a2', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.h1.a2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720179
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '240.h1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '120.d1.a1', '120.d1.b2', '120.i1.b1'], 'contains': ['480.b1.a1', '1200.c1.b1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [121, -1, 7282, -1, 8163, -1, 2510, -1], 'generators': [81420657990, 64028341198], 'label': '2400.bt.240.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.h1.b1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.h1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720182
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a2', '120.e1.a2', '120.e1.c2', '120.j1.a1'], 'contains': ['480.c1.a1', '1200.c1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [327, -1, 9372, -1, 8602, -1, 1906, -1], 'generators': [96188940832, 7445862067], 'label': '2400.bt.240.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '240.i1.a2', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.a2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720183
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '120.e1.b1', '120.e1.d1', '120.j1.b1'], 'contains': ['480.c1.b1', '1200.c1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [327, -1, 8616, -1, 8602, -1, 566, -1], 'generators': [117797313644, 105102199342], 'label': '2400.bt.240.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '240.i1.b1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720184
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a2', '120.e1.b2', '120.e1.d2', '120.j1.b1'], 'contains': ['480.c1.b1', '1200.c1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [327, -1, 7892, -1, 8602, -1, 648, -1], 'generators': [96188940832, 117797313644], 'label': '2400.bt.240.i1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '240.i1.b2', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.b2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720185
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '120.e1.a1', '120.e1.c2', '120.j1.c1'], 'contains': ['480.c1.a1', '1200.c1.b1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [327, -1, 9510, -1, 8602, -1, 1824, -1], 'generators': [7445862067, 64028341198], 'label': '2400.bt.240.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '240.i1.c1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.c1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720186
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1600.10262', 'aut_weyl_index': 12, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.c1.a1', '24.d1.b1', '24.e1.a1', '60.h1.a1', '60.j1.a1'], 'core': '120.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [3540, -1, 5780, -1, 7685, -1, 3190, -1], 'generators': [140879192328, 96188940832, 60215928797, 1271171980, 7445862067], 'label': '2400.bt.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720187
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b2', '120.e1.a2', '120.e1.c1', '120.j1.c1'], 'contains': ['480.c1.a1', '1200.c1.b1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [327, -1, 8908, -1, 8602, -1, 1742, -1], 'generators': [84411882688, 7445862067], 'label': '2400.bt.240.i1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '240.i1.c2', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.c2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720188
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '120.e1.b1', '120.e1.d2', '120.j1.d1'], 'contains': ['480.c1.b1', '1200.c1.b1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [327, -1, 8321, -1, 8602, -1, 729, -1], 'generators': [64028341198, 117797313644], 'label': '2400.bt.240.i1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '240.i1.d1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.d1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720189
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 480, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b2', '120.e1.b2', '120.e1.d1', '120.j1.d1'], 'contains': ['480.c1.b1', '1200.c1.b1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [327, -1, 7685, -1, 8602, -1, 811, -1], 'generators': [84411882688, 117797313644], 'label': '2400.bt.240.i1.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '240.i1.d2', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.d2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720190
    {'ambient': '2400.bt', 'aut_centralizer_order': 32, 'aut_label': '300.a1', 'aut_quo_index': None, 'aut_stab_index': 75, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2400, 'centralizer': '150.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.c1.a1', '60.d1.a1', '60.d1.b1', '100.a1.a1', '150.a1.a1', '150.b1.a1'], 'contains': ['600.a1.a1', '600.b1.a1', '600.b1.b1', '600.c1.a1', '600.c1.b1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [2480, -1, 6007, -1, 6376, -1, 3887, -1], 'generators': [122109387504, 10054287475, 1271171980], 'label': '2400.bt.300.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '300.a1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720191
    {'ambient': '2400.bt', 'aut_centralizer_order': 480, 'aut_label': '300.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2400, 'centralizer': '5.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '60.e1.a1', '100.b1.a1', '150.a1.a1'], 'contains': ['600.a1.a1', '600.d1.a1', '600.d1.b1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5731, -1, 2344, -1, 5619, -1, 5232, -1], 'generators': [122109387504, 130509168233, 1271171980], 'label': '2400.bt.300.b1.a1', 'mobius_quo': None, 'mobius_sub': 60, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.b1.a1', 'old_label': '300.b1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 171720192
    {'ambient': '2400.bt', 'aut_centralizer_order': 320, 'aut_label': '300.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4800, 'centralizer': '30.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.a1', '60.g1.a1', '100.c1.a1', '150.a1.a1', '150.b1.a1', '150.c1.a1'], 'contains': ['600.a1.a1', '600.e1.a1', '600.f1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6086, -1, 2559, -1, 2784, -1, 7167, -1], 'generators': [122109387504, 1271171980, 81506204464], 'label': '2400.bt.300.c1.a1', 'mobius_quo': None, 'mobius_sub': 20, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '300.c1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720193
    {'ambient': '2400.bt', 'aut_centralizer_order': 32, 'aut_label': '300.d1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4800, 'centralizer': '150.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.h1.a1', '60.j1.a1', '100.d1.a1', '150.a1.a1', '150.d1.b1'], 'contains': ['600.c1.a1', '600.d1.b1', '600.e1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4644, -1, 3389, -1, 4455, -1, 6269, -1], 'generators': [60215928797, 1271171980, 109226689441], 'label': '2400.bt.300.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '300.d1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720194
    {'ambient': '2400.bt', 'aut_centralizer_order': 32, 'aut_label': '300.d1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4800, 'centralizer': '150.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.h1.b1', '60.j1.b1', '100.d1.b1', '150.a1.a1', '150.d1.a1'], 'contains': ['600.c1.b1', '600.d1.a1', '600.e1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4644, -1, 3011, -1, 4455, -1, 5808, -1], 'generators': [130509168233, 1271171980, 109226689441], 'label': '2400.bt.300.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '300.d1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720195
    {'ambient': '2400.bt', 'aut_centralizer_order': 32, 'aut_label': '300.e1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4800, 'centralizer': '150.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.i1.a1', '60.k1.a1', '100.e1.a1', '150.a1.a1', '150.d1.a1', '150.e1.a1'], 'contains': ['600.c1.a1', '600.d1.a1', '600.f1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [6845, -1, 3519, -1, 3570, -1, 7522, -1], 'generators': [130509168233, 1271171980, 81506204464], 'label': '2400.bt.300.e1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '300.e1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720196
    {'ambient': '2400.bt', 'aut_centralizer_order': 32, 'aut_label': '300.e1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4800, 'centralizer': '150.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.i1.b1', '60.k1.b1', '100.e1.b1', '150.a1.a1', '150.d1.b1', '150.e1.b1'], 'contains': ['600.c1.b1', '600.d1.b1', '600.f1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [6845, -1, 2756, -1, 3570, -1, 7746, -1], 'generators': [60215928797, 1271171980, 81506204464], 'label': '2400.bt.300.e1.b1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '300.e1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720197
    {'ambient': '2400.bt', 'aut_centralizer_order': 20, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '960.10863', 'aut_weyl_index': 20, 'centralizer': '120.a1.a1', 'complements': ['1200.c1.a1', '1200.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.a1.a1', '10.c1.a1', '12.c1.a1', '20.d1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7212, 6256, 2010, 8091, 1880, 5951, 7008, 6687], 'generators': [122109387504, 44670214561, 140879192328, 34316253738, 1271171980], 'label': '2400.bt.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', '10.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '600.146', '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': '120.35'}
  • id: 171720198
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1600.10262', 'aut_weyl_index': 12, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.c1.b1', '24.d1.a1', '24.e1.a1', '60.h1.b1', '60.j1.b1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3540, -1, 5313, -1, 7685, -1, 2986, -1], 'generators': [130509168233, 140879192328, 1271171980, 7445862067, 64028341198], 'label': '2400.bt.12.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720199
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '300.f1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2400, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.l1.a1', '150.b1.a1', '150.d1.a1', '150.d1.b1'], 'contains': ['600.c1.a1', '600.c1.b1', '600.e1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [3963, -1, 3708, -1, 2269, -1, 9234, -1], 'generators': [1369609910, 1271171980, 109226689441], 'label': '2400.bt.300.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '300.f1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720200
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '300.f1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2400, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.l1.a2', '150.b1.a1', '150.d1.a1', '150.d1.b1'], 'contains': ['600.c1.a1', '600.c1.b1', '600.e1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [3963, -1, 3816, -1, 2269, -1, 9335, -1], 'generators': [10054287475, 1369609910, 1271171980], 'label': '2400.bt.300.f1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '300.f1.a2', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.f1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720201
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '300.g1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2400, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.m1.a1', '150.b1.a1', '150.d1.b1', '150.e1.a1'], 'contains': ['600.c1.a1', '600.f1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [5106, -1, 5217, -1, 1405, -1, 8978, -1], 'generators': [4990156490, 1271171980, 81506204464], 'label': '2400.bt.300.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '300.g1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720202
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '300.g1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2400, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.m1.b1', '150.b1.a1', '150.d1.a1', '150.e1.b1'], 'contains': ['600.c1.b1', '600.f1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [5106, -1, 3255, -1, 1405, -1, 9143, -1], 'generators': [1369609910, 1271171980, 81506204464], 'label': '2400.bt.300.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '300.g1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.g1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720203
    {'ambient': '2400.bt', 'aut_centralizer_order': 160, 'aut_label': '300.h1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2400, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.n1.a1', '150.c1.a1', '150.d1.a1', '150.d1.b1'], 'contains': ['600.e1.a1', '600.f1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7181, -1, 3127, -1, 1138, -1, 9492, -1], 'generators': [1271171980, 81506204464, 34410003353], 'label': '2400.bt.300.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '300.h1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720204
    {'ambient': '2400.bt', 'aut_centralizer_order': 160, 'aut_label': '300.i1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '24.12', 'aut_weyl_index': 800, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.o1.a1', '100.f1.a1', '150.c1.a1', '150.e1.a1', '150.e1.b1'], 'contains': ['600.f1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8608, -1, 2658, -1, 513, -1, 8721, -1], 'generators': [1271171980, 81506204464, 124586497402], 'label': '2400.bt.300.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '300.i1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 171720205
    {'ambient': '2400.bt', 'aut_centralizer_order': 480, 'aut_label': '400.a1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '20.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a1.a1', '200.a1.a1', '200.a1.a2', '200.b1.a1'], 'contains': ['800.a1.a1', '1200.a1.a1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5197, -1, 787, -1, 7275, -1, 4824, -1], 'generators': [20296838936, 5078828170], 'label': '2400.bt.400.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '400.a1.a1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720206
    {'ambient': '2400.bt', 'aut_centralizer_order': 480, 'aut_label': '400.a1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '20.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a1.b1', '200.a1.b1', '200.a1.b2', '200.b1.a1'], 'contains': ['800.a1.a1', '1200.a1.b1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [5197, -1, 1660, -1, 7275, -1, 4206, -1], 'generators': [122109387504, 138641458738], 'label': '2400.bt.400.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '400.a1.b1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720207
    {'ambient': '2400.bt', 'aut_centralizer_order': 960, 'aut_label': '400.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '20.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.b1.a1', '100.f1.a1', '200.b1.a1', '200.c1.a1', '200.c1.b1', '200.d1.a1', '200.d1.b1', '200.e1.a1', '200.f1.a1'], 'contains': ['800.a1.a1', '1200.b1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [9207, -1, 1590, -1, 4660, -1, 6396, -1], 'generators': [17605993094, 1271171980], 'label': '2400.bt.400.b1.a1', 'mobius_quo': None, 'mobius_sub': -20, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '400.b1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720208
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '400.c1', 'aut_quo_index': None, 'aut_stab_index': 200, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3200, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.c1.a1', '200.a1.a1', '200.a1.b1', '200.c1.a1'], 'contains': ['800.a1.a1', '1200.c1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3786, -1, 1328, -1, 7145, -1, 4317, -1], 'generators': [986356750, 105551846115], 'label': '2400.bt.400.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '400.c1.a1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720209
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '800.1192', 'aut_weyl_index': 24, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '6.a1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.f1.a1', '60.i1.a1', '60.k1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4815, -1, 6145, -1, 6967, -1, 3815, -1], 'generators': [130509168233, 140879192328, 96188940832, 1271171980, 7445862067], 'label': '2400.bt.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720210
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '400.c1', 'aut_quo_index': None, 'aut_stab_index': 200, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3200, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.c1.a2', '200.a1.a2', '200.a1.b2', '200.c1.a1'], 'contains': ['800.a1.a1', '1200.c1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3786, -1, 1121, -1, 7145, -1, 4634, -1], 'generators': [11036721270, 105551846115], 'label': '2400.bt.400.c1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '400.c1.a2', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.c1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720211
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '400.c1', 'aut_quo_index': None, 'aut_stab_index': 200, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3200, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.c1.b1', '200.a1.a1', '200.a1.b2', '200.c1.b1'], 'contains': ['800.a1.a1', '1200.c1.b1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3786, -1, 653, -1, 7145, -1, 4445, -1], 'generators': [25830469380, 105551846115], 'label': '2400.bt.400.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '400.c1.b1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720212
    {'ambient': '2400.bt', 'aut_centralizer_order': 16, 'aut_label': '400.c1', 'aut_quo_index': None, 'aut_stab_index': 200, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3200, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.c1.b2', '200.a1.a2', '200.a1.b1', '200.c1.b1'], 'contains': ['800.a1.a1', '1200.c1.b1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3786, -1, 474, -1, 7145, -1, 4728, -1], 'generators': [283268875, 105551846115], 'label': '2400.bt.400.c1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '400.c1.b2', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.c1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720213
    {'ambient': '2400.bt', 'aut_centralizer_order': 4800, 'aut_label': '480.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '2.a1.a1', 'complements': ['5.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '160.a1.a1', '240.a1.a1', '240.a1.b1', '240.b1.a1', '240.g1.a1', '240.g1.b1'], 'contains': ['2400.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2896, 3387, 4808, 5646, 7565, 5071, 3729, 7823], 'generators': [140879192328], 'label': '2400.bt.480.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '480.a1.a1', 'normal_contained_in': ['240.a1.b1', '240.a1.a1', '240.b1.a1'], 'normal_contains': ['2400.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '480.a1.a1', 'projective_image': '2400.bt', 'quotient_action_image': '2.1', 'quotient_action_kernel': '240.94', 'quotient_action_kernel_order': 240, 'quotient_fusion': None, 'short_label': '480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720214
    {'ambient': '2400.bt', 'aut_centralizer_order': 800, 'aut_label': '480.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '240.c1.a1', '240.c1.b1', '240.e1.a1', '240.h1.a1', '240.h1.a2', '240.h1.b1', '240.h1.b2'], 'contains': ['2400.a1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [51, -1, 7177, -1, 8163, -1, 2591, -1], 'generators': [81420657990], 'label': '2400.bt.480.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '480.b1.a1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720215
    {'ambient': '2400.bt', 'aut_centralizer_order': 200, 'aut_label': '480.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '240.d1.a1', '240.d1.c1', '240.f1.a1', '240.i1.a1', '240.i1.a2', '240.i1.c1', '240.i1.c2'], 'contains': ['2400.a1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [302, -1, 9151, -1, 8462, -1, 1824, -1], 'generators': [7445862067], 'label': '2400.bt.480.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '480.c1.a1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720216
    {'ambient': '2400.bt', 'aut_centralizer_order': 200, 'aut_label': '480.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '240.d1.b1', '240.d1.d1', '240.f1.b1', '240.i1.b1', '240.i1.b2', '240.i1.d1', '240.i1.d2'], 'contains': ['2400.a1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [302, -1, 7954, -1, 8462, -1, 811, -1], 'generators': [117797313644], 'label': '2400.bt.480.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '480.c1.b1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720217
    {'ambient': '2400.bt', 'aut_centralizer_order': 9600, 'aut_label': '600.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.f1.a1', '120.g1.a1', '120.g1.b1', '200.b1.a1', '300.a1.a1', '300.b1.a1', '300.c1.a1'], 'contains': ['1200.a1.a1', '1200.a1.b1', '1200.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3289, 4581, 5860, 7896, 5986, 7621, 3957, 6850], 'generators': [122109387504, 1271171980], 'label': '2400.bt.600.a1.a1', 'mobius_quo': 2, 'mobius_sub': -300, 'normal_closure': '600.a1.a1', 'normal_contained_in': ['10.a1.a1', '120.a1.a1'], 'normal_contains': ['1200.a1.b1', '1200.a1.a1', '1200.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '600.a1.a1', 'projective_image': '600.146', 'quotient_action_image': '1.1', 'quotient_action_kernel': '600.146', 'quotient_action_kernel_order': 600, 'quotient_fusion': None, 'short_label': '600.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 171720218
    {'ambient': '2400.bt', 'aut_centralizer_order': 32, 'aut_label': '600.b1', 'aut_quo_index': None, 'aut_stab_index': 300, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '150.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '120.d1.a1', '120.d1.a2', '120.e1.a1', '120.e1.a2', '120.e1.b1', '120.e1.b2', '200.a1.a1', '200.a1.a2', '300.a1.a1'], 'contains': ['1200.a1.a1', '1200.c1.a1', '1200.c1.b1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [858, -1, 6766, -1, 7864, -1, 2953, -1], 'generators': [10054287475, 5078828170], 'label': '2400.bt.600.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '600.b1.a1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 171720219
    {'ambient': '2400.bt', 'aut_centralizer_order': 32, 'aut_label': '600.b1', 'aut_quo_index': None, 'aut_stab_index': 300, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '150.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.b1', '120.d1.b1', '120.d1.b2', '120.e1.c1', '120.e1.c2', '120.e1.d1', '120.e1.d2', '200.a1.b1', '200.a1.b2', '300.a1.a1'], 'contains': ['1200.a1.b1', '1200.c1.a1', '1200.c1.b1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 150, 'diagramx': [858, -1, 8171, -1, 7864, -1, 2760, -1], 'generators': [122109387504, 10054287475], 'label': '2400.bt.600.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '600.b1.b1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 171720220
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '800.1192', 'aut_weyl_index': 24, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '6.a1.a1'], 'contains': ['24.c1.b1', '24.d1.b1', '24.f1.a1', '60.i1.b1', '60.k1.b1'], 'core': '120.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4815, -1, 5492, -1, 6967, -1, 3981, -1], 'generators': [140879192328, 60215928797, 1271171980, 7445862067, 64028341198], 'label': '2400.bt.12.e1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.e1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720221
    {'ambient': '2400.bt', 'aut_centralizer_order': 64, 'aut_label': '600.c1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '150.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.h1.a1', '120.i1.a1', '120.j1.a1', '120.j1.b1', '200.c1.a1', '300.a1.a1', '300.d1.a1', '300.e1.a1', '300.f1.a1', '300.f1.a2', '300.g1.a1'], 'contains': ['1200.b1.a1', '1200.c1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [2468, -1, 5974, -1, 5078, -1, 5649, -1], 'generators': [10054287475, 1271171980], 'label': '2400.bt.600.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '600.c1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720222
    {'ambient': '2400.bt', 'aut_centralizer_order': 64, 'aut_label': '600.c1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '150.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.h1.b1', '120.i1.b1', '120.j1.c1', '120.j1.d1', '200.c1.b1', '300.a1.a1', '300.d1.b1', '300.e1.b1', '300.f1.a1', '300.f1.a2', '300.g1.b1'], 'contains': ['1200.b1.a1', '1200.c1.b1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [2468, -1, 4590, -1, 5078, -1, 5742, -1], 'generators': [1271171980, 27848544525], 'label': '2400.bt.600.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '600.c1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720223
    {'ambient': '2400.bt', 'aut_centralizer_order': 960, 'aut_label': '600.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '5.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.a1', '120.k1.a1', '200.d1.a1', '300.b1.a1', '300.d1.b1', '300.e1.a1'], 'contains': ['1200.b1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5731, -1, 2748, -1, 5218, -1, 5562, -1], 'generators': [130509168233, 1271171980], 'label': '2400.bt.600.d1.a1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '120.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.b1.a1', 'old_label': '600.d1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 171720224
    {'ambient': '2400.bt', 'aut_centralizer_order': 960, 'aut_label': '600.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '5.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.b1', '120.k1.b1', '200.d1.b1', '300.b1.a1', '300.d1.a1', '300.e1.b1'], 'contains': ['1200.b1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5731, -1, 2496, -1, 5218, -1, 5982, -1], 'generators': [60215928797, 1271171980], 'label': '2400.bt.600.d1.b1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '120.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.b1.a1', 'old_label': '600.d1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 171720225
    {'ambient': '2400.bt', 'aut_centralizer_order': 640, 'aut_label': '600.e1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '30.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.l1.a1', '120.m1.a1', '200.e1.a1', '300.c1.a1', '300.d1.a1', '300.d1.b1', '300.f1.a1', '300.f1.a2', '300.h1.a1'], 'contains': ['1200.b1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4773, -1, 3490, -1, 3569, -1, 6599, -1], 'generators': [1271171980, 109226689441], 'label': '2400.bt.600.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '600.e1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720226
    {'ambient': '2400.bt', 'aut_centralizer_order': 640, 'aut_label': '600.f1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '30.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.n1.a1', '120.o1.a1', '200.f1.a1', '300.c1.a1', '300.e1.a1', '300.e1.b1', '300.g1.a1', '300.g1.b1', '300.h1.a1', '300.i1.a1'], 'contains': ['1200.b1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7039, -1, 3163, -1, 2581, -1, 7875, -1], 'generators': [1271171980, 81506204464], 'label': '2400.bt.600.f1.a1', 'mobius_quo': None, 'mobius_sub': -40, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '600.f1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720227
    {'ambient': '2400.bt', 'aut_centralizer_order': 960, 'aut_label': '800.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '20.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.a1.a1', '400.a1.a1', '400.a1.b1', '400.b1.a1', '400.c1.a1', '400.c1.a2', '400.c1.b1', '400.c1.b2'], 'contains': ['2400.a1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5197, -1, 1121, -1, 7145, -1, 4542, -1], 'generators': [52093013917], 'label': '2400.bt.800.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '800.a1.a1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '800.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720228
    {'ambient': '2400.bt', 'aut_centralizer_order': 9600, 'aut_label': '1200.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 19200, 'centralizer': '1.a1.a1', 'complements': ['2.b1.b1', '2.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '240.c1.a1', '240.d1.a1', '240.d1.b1', '400.a1.a1', '600.a1.a1', '600.b1.a1'], 'contains': ['2400.a1.a1'], 'core': '1200.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1526, 2291, 6425, 6722, 7826, 7323, 2936, 8721], 'generators': [5078828170], 'label': '2400.bt.1200.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1200.a1.a1', 'normal_contained_in': ['240.a1.a1', '600.a1.a1'], 'normal_contains': ['2400.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1200.a1.a1', 'projective_image': '1200.481', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1200.481', 'quotient_action_kernel_order': 1200, 'quotient_fusion': None, 'short_label': '1200.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 171720229
    {'ambient': '2400.bt', 'aut_centralizer_order': 9600, 'aut_label': '1200.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 19200, 'centralizer': '1.a1.a1', 'complements': ['2.b1.b1', '2.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['240.a1.b1', '240.c1.b1', '240.d1.c1', '240.d1.d1', '400.a1.b1', '600.a1.a1', '600.b1.b1'], 'contains': ['2400.a1.a1'], 'core': '1200.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1526, 2291, 8115, 8130, 7826, 7323, 2675, 6924], 'generators': [122109387504], 'label': '2400.bt.1200.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1200.a1.b1', 'normal_contained_in': ['240.a1.b1', '600.a1.a1'], 'normal_contains': ['2400.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1200.a1.b1', 'projective_image': '1200.481', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1200.481', 'quotient_action_kernel_order': 1200, 'quotient_fusion': None, 'short_label': '1200.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 171720230
    {'ambient': '2400.bt', 'aut_centralizer_order': 19200, 'aut_label': '1200.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 19200, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['240.b1.a1', '240.e1.a1', '240.f1.a1', '240.f1.b1', '400.b1.a1', '600.a1.a1', '600.c1.a1', '600.c1.b1', '600.d1.a1', '600.d1.b1', '600.e1.a1', '600.f1.a1'], 'contains': ['2400.a1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4492, 5180, 4647, 4569, 5290, 6249, 5649, 5951], 'generators': [1271171980], 'label': '2400.bt.1200.b1.a1', 'mobius_quo': -1, 'mobius_sub': 600, 'normal_closure': '1200.b1.a1', 'normal_contained_in': ['20.a1.a1', '240.b1.a1', '600.a1.a1'], 'normal_contains': ['2400.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1200.b1.a1', 'projective_image': '1200.944', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1200.944', 'quotient_action_kernel_order': 1200, 'quotient_fusion': None, 'short_label': '1200.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 171720231
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '3840.fq', 'aut_weyl_index': 5, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['30.b1.a1', '30.c1.a1', '30.d1.a1', '30.e1.a1', '30.e1.b1', '30.f1.a1', '30.f1.b1', '75.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5899, -1, 3248, -1, 2621, -1, 8894, -1], 'generators': [122109387504, 130509168233, 140879192328, 1369609910, 1271171980, 45129158685], 'label': '2400.bt.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.39'}
  • id: 171720232
    {'ambient': '2400.bt', 'aut_centralizer_order': 64, 'aut_label': '1200.c1', 'aut_quo_index': None, 'aut_stab_index': 300, 'aut_weyl_group': '1.1', 'aut_weyl_index': 19200, 'centralizer': '150.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.g1.a1', '240.h1.a1', '240.h1.a2', '240.i1.a1', '240.i1.a2', '240.i1.b1', '240.i1.b2', '400.c1.a1', '400.c1.a2', '600.b1.a1', '600.b1.b1', '600.c1.a1'], 'contains': ['2400.a1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [828, -1, 7629, -1, 7695, -1, 2757, -1], 'generators': [10054287475], 'label': '2400.bt.1200.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '1200.c1.a1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 171720233
    {'ambient': '2400.bt', 'aut_centralizer_order': 64, 'aut_label': '1200.c1', 'aut_quo_index': None, 'aut_stab_index': 300, 'aut_weyl_group': '1.1', 'aut_weyl_index': 19200, 'centralizer': '150.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.g1.b1', '240.h1.b1', '240.h1.b2', '240.i1.c1', '240.i1.c2', '240.i1.d1', '240.i1.d2', '400.c1.b1', '400.c1.b2', '600.b1.a1', '600.b1.b1', '600.c1.b1'], 'contains': ['2400.a1.a1'], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [828, -1, 7233, -1, 7695, -1, 2838, -1], 'generators': [27848544525], 'label': '2400.bt.1200.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '1200.c1.b1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 171720234
    {'ambient': '2400.bt', 'aut_centralizer_order': None, 'aut_label': '2400.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': ['480.a1.a1', '480.b1.a1', '480.c1.a1', '480.c1.b1', '800.a1.a1', '1200.a1.a1', '1200.a1.b1', '1200.b1.a1', '1200.c1.a1', '1200.c1.b1'], 'contains': [], 'core': '2400.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1526, 3387, 7306, 6194, 7695, 6249, 2798, 7374], 'generators': [], 'label': '2400.bt.2400.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '2400.a1.a1', 'normal_contained_in': ['480.a1.a1', '1200.a1.b1', '1200.a1.a1', '1200.b1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '2400.a1.a1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2400.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 171720235
    {'ambient': '2400.bt', 'aut_centralizer_order': 160, 'aut_label': '20.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '120.34', 'aut_weyl_index': 160, 'centralizer': '60.a1.a1', 'complements': ['120.c1.b1', '120.c1.a1', '120.e1.d1', '120.e1.b1', '120.e1.b2', '120.e1.d2', '120.e1.c1', '120.e1.a1', '120.e1.a2', '120.e1.c2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.e1.a1', '10.e1.b1'], 'contains': ['100.f1.a1', '120.o1.a1', '200.f1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9949, 6992, 3019, 7407, 384, 6368, 7286, 5802], 'generators': [124680247042, 146062695594, 1271171980], 'label': '2400.bt.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': -10, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1'], 'normal_contains': ['1200.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '1200.944', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 171720236
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '960.11038', 'aut_weyl_index': 20, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1'], 'contains': ['40.a1.a1', '40.a1.a2', '40.a1.b1', '40.a1.b2', '40.b1.a1', '40.c1.a1', '40.c1.b1', '60.b1.a1', '100.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3437, -1, 1381, -1, 5506, -1, 4844, -1], 'generators': [122109387504, 140879192328, 25830469380, 1271171980, 110631910891], 'label': '2400.bt.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.b1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720237
    {'ambient': '2400.bt', 'aut_centralizer_order': 6, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 60, 'centralizer': '200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '10.b1.a1'], 'contains': ['40.b1.a1', '40.d1.a1', '40.d1.b1', '60.a1.a1', '100.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6834, -1, 1771, -1, 4924, -1, 6223, -1], 'generators': [122109387504, 130509168233, 140879192328, 1271171980, 128717318317], 'label': '2400.bt.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.c1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720238
    {'ambient': '2400.bt', 'aut_centralizer_order': 20, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '96.206', 'aut_weyl_index': 200, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '10.b1.a1'], 'contains': ['40.b1.a1', '40.e1.a1', '40.f1.a1', '60.f1.a1', '100.c1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7312, -1, 1103, -1, 3088, -1, 6905, -1], 'generators': [122109387504, 140879192328, 1271171980, 16193036544, 110631910891], 'label': '2400.bt.20.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.d1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 171720239
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 40, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1'], 'contains': ['40.c1.a1', '40.d1.b1', '40.e1.a1', '60.j1.a1', '100.d1.a1'], 'core': '120.b1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [6425, -1, 954, -1, 4125, -1, 6060, -1], 'generators': [11036721270, 140879192328, 60215928797, 1271171980, 110631910891], 'label': '2400.bt.20.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.e1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720240
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 40, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1'], 'contains': ['40.c1.b1', '40.d1.a1', '40.e1.a1', '60.j1.b1', '100.d1.b1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6425, -1, 805, -1, 4125, -1, 5841, -1], 'generators': [130509168233, 140879192328, 25830469380, 1271171980, 110631910891], 'label': '2400.bt.20.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.e1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720241
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4800.cf', 'aut_weyl_index': 4, 'centralizer': '600.a1.a1', 'complements': ['1200.a1.b1', '1200.a1.a1', '1200.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.d1.a1', '10.e1.a1', '12.e1.a1', '20.f1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7565, 1035, 4238, 3845, 3005, 776, 7211, 649], 'generators': [130509168233, 140879192328, 31371528410, 42634393514, 1271171980], 'label': '2400.bt.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', '120.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '1200.944', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '600.146'}
  • id: 171720242
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 40, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '10.b1.a1'], 'contains': ['40.c1.a1', '40.d1.a1', '40.f1.a1', '60.k1.a1', '100.e1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7604, -1, 2731, -1, 3458, -1, 7126, -1], 'generators': [11036721270, 130509168233, 140879192328, 1271171980, 110631910891], 'label': '2400.bt.20.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.f1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720243
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 40, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '10.b1.a1'], 'contains': ['40.c1.b1', '40.d1.b1', '40.f1.a1', '60.k1.b1', '100.e1.b1'], 'core': '120.b1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [7604, -1, 2325, -1, 3458, -1, 7532, -1], 'generators': [140879192328, 25830469380, 60215928797, 1271171980, 110631910891], 'label': '2400.bt.20.f1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.f1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720244
    {'ambient': '2400.bt', 'aut_centralizer_order': 40, 'aut_label': '20.g1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '96.186', 'aut_weyl_index': 200, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.c1.a1', '10.d1.a1', '10.d1.b1'], 'contains': ['60.o1.a1', '80.b1.a1', '100.f1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8425, -1, 3831, -1, 652, -1, 8219, -1], 'generators': [140879192328, 118727107253, 1271171980, 90360007017, 45129158685], 'label': '2400.bt.20.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.g1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 171720245
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '800.1192', 'aut_weyl_index': 24, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.a1.a1', '48.c1.a1', '48.c1.b1', '120.c1.a1', '120.d1.a1', '120.e1.a1', '120.e1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [524, -1, 8256, -1, 9865, -1, 1247, -1], 'generators': [140879192328, 7445862067, 64028341198, 5078828170], 'label': '2400.bt.24.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720246
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '800.1192', 'aut_weyl_index': 24, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.a1.a1', '48.c1.a2', '48.c1.b2', '120.c1.a1', '120.d1.a2', '120.e1.a2', '120.e1.b2'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [524, -1, 7416, -1, 9865, -1, 1436, -1], 'generators': [140879192328, 84411882688, 7445862067, 5078828170], 'label': '2400.bt.24.a1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.a1.a2', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a2', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720247
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '800.1192', 'aut_weyl_index': 24, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.a1.b1', '48.c1.a1', '48.c1.b2', '120.c1.b1', '120.d1.b1', '120.e1.c1', '120.e1.d1'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [524, -1, 8518, -1, 9865, -1, 869, -1], 'generators': [122109387504, 140879192328, 84411882688, 7445862067], 'label': '2400.bt.24.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.a1.b1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.b1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720248
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '800.1192', 'aut_weyl_index': 24, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.a1.b1', '48.c1.a2', '48.c1.b1', '120.c1.b1', '120.d1.b2', '120.e1.c2', '120.e1.d2'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [524, -1, 8792, -1, 9865, -1, 1058, -1], 'generators': [122109387504, 140879192328, 7445862067, 64028341198], 'label': '2400.bt.24.a1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.a1.b2', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.b2', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720249
    {'ambient': '2400.bt', 'aut_centralizer_order': 100, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.21', 'aut_weyl_index': 600, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.c1.a1'], 'contains': ['48.a1.a1', '48.a1.b1', '48.b1.a1', '120.a1.a1', '120.f1.a1', '120.g1.a1', '120.g1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1989, -1, 6686, -1, 9327, -1, 1773, -1], 'generators': [122109387504, 140879192328, 1271171980, 7445862067], 'label': '2400.bt.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720250
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '800.1192', 'aut_weyl_index': 24, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.d1.a1', '12.e1.a1'], 'contains': ['48.b1.a1', '48.c1.a1', '48.c1.a2', '120.h1.a1', '120.i1.a1', '120.j1.a1', '120.j1.b1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1519, -1, 7097, -1, 8788, -1, 1929, -1], 'generators': [140879192328, 96188940832, 1271171980, 7445862067], 'label': '2400.bt.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720251
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '800.1192', 'aut_weyl_index': 24, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.d1.b1', '12.e1.b1'], 'contains': ['48.b1.a1', '48.c1.b1', '48.c1.b2', '120.h1.b1', '120.i1.b1', '120.j1.c1', '120.j1.d1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1519, -1, 6438, -1, 8788, -1, 2119, -1], 'generators': [140879192328, 1271171980, 7445862067, 64028341198], 'label': '2400.bt.24.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.c1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720252
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4800.cf', 'aut_weyl_index': 4, 'centralizer': '600.a1.a1', 'complements': ['1200.a1.b1', '1200.a1.a1', '1200.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.d1.b1', '10.e1.b1', '12.e1.b1', '20.f1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7565, 1035, 3001, 1458, 3005, 776, 7383, 4267], 'generators': [140879192328, 60215928797, 1271171980, 148051235266, 122741847365], 'label': '2400.bt.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '120.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '1200.944', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '600.146'}
  • id: 171720253
    {'ambient': '2400.bt', 'aut_centralizer_order': 10, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '160.203', 'aut_weyl_index': 120, 'centralizer': '120.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.d1.b1', '12.e1.a1'], 'contains': ['48.b1.a1', '120.b1.a1', '120.k1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4352, -1, 6106, -1, 8029, -1, 2488, -1], 'generators': [130509168233, 140879192328, 1271171980, 7445862067], 'label': '2400.bt.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720254
    {'ambient': '2400.bt', 'aut_centralizer_order': 10, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '160.203', 'aut_weyl_index': 120, 'centralizer': '120.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.d1.a1', '12.e1.b1'], 'contains': ['48.b1.a1', '120.b1.b1', '120.k1.b1'], 'core': '120.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4352, -1, 5859, -1, 8029, -1, 3017, -1], 'generators': [140879192328, 60215928797, 1271171980, 7445862067], 'label': '2400.bt.24.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.d1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720255
    {'ambient': '2400.bt', 'aut_centralizer_order': 20, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '160.203', 'aut_weyl_index': 120, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.d1.a1', '12.d1.b1'], 'contains': ['48.b1.a1', '120.l1.a1', '120.m1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2541, -1, 5409, -1, 7478, -1, 3362, -1], 'generators': [140879192328, 1271171980, 7445862067, 73738889847], 'label': '2400.bt.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720256
    {'ambient': '2400.bt', 'aut_centralizer_order': 40, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '80.30', 'aut_weyl_index': 240, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '12.c1.a1', '12.e1.a1', '12.e1.b1'], 'contains': ['48.b1.a1', '120.n1.a1', '120.o1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4841, -1, 5567, -1, 6624, -1, 4051, -1], 'generators': [140879192328, 1271171980, 110599489058, 7445862067], 'label': '2400.bt.24.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720257
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '25.a1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 100, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '5.b1.a1'], 'contains': ['50.b1.a1', '50.c1.a1', '50.c1.b1', '75.a1.a1', '100.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [9266, -1, 2118, -1, 2209, -1, 8015, -1], 'generators': [122109387504, 75344408338, 1271171980, 81506204464, 50675370281, 128717318317], 'label': '2400.bt.25.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '25.a1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 171720258
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '160.207', 'aut_weyl_index': 120, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.b1.a1', '6.a1.a1'], 'contains': ['60.c1.a1', '60.e1.a1', '60.g1.a1', '60.h1.a1', '60.h1.b1', '60.i1.a1', '60.i1.b1', '150.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4302, -1, 5697, -1, 7291, -1, 3393, -1], 'generators': [81420657990, 122109387504, 130509168233, 1271171980, 64028341198], 'label': '2400.bt.30.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720259
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 60, 'centralizer': '300.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.b1.a1', '60.f1.a1', '60.j1.a1', '60.j1.b1', '60.k1.a1', '60.k1.b1', '150.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5903, -1, 3342, -1, 4564, -1, 6437, -1], 'generators': [122109387504, 130509168233, 140879192328, 1271171980, 45129158685], 'label': '2400.bt.30.b1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720260
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '640.21496', 'aut_weyl_index': 30, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1'], 'contains': ['60.b1.a1', '60.f1.a1', '60.l1.a1', '60.l1.a2', '60.m1.a1', '60.m1.b1', '150.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4937, -1, 4476, -1, 2764, -1, 9066, -1], 'generators': [122109387504, 140879192328, 1369609910, 1271171980, 45129158685], 'label': '2400.bt.30.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.c1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 171720261
    {'ambient': '2400.bt', 'aut_centralizer_order': 20, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 100, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.a1', '15.a1.a1'], 'contains': ['60.f1.a1', '60.n1.a1', '60.o1.a1', '150.c1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8272, -1, 2635, -1, 1441, -1, 8563, -1], 'generators': [122109387504, 140879192328, 1271171980, 72007755877, 45129158685], 'label': '2400.bt.30.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.d1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 171720262
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 60, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1'], 'contains': ['60.j1.b1', '60.k1.a1', '60.l1.a1', '60.l1.a2', '60.m1.b1', '60.n1.a1', '150.d1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5433, -1, 3826, -1, 2488, -1, 9239, -1], 'generators': [130509168233, 140879192328, 1369609910, 1271171980, 45129158685], 'label': '2400.bt.30.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.e1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 171720263
    {'ambient': '2400.bt', 'aut_centralizer_order': 40, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '480.943', 'aut_weyl_index': 40, 'centralizer': '120.a1.a1', 'complements': ['600.b1.b1', '600.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['20.a1.a1', '20.g1.a1', '24.f1.a1', '40.f1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7574, 6495, 3199, 1870, 703, 3028, 7450, 4167], 'generators': [140879192328, 124680247042, 146062695594, 1271171980], 'label': '2400.bt.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['20.a1.a1', '240.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '1200.944', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 171720264
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 60, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1'], 'contains': ['60.j1.a1', '60.k1.b1', '60.l1.a1', '60.l1.a2', '60.m1.a1', '60.n1.a1', '150.d1.b1'], 'core': '120.b1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [5433, -1, 4033, -1, 2488, -1, 9397, -1], 'generators': [60215928797, 1271171980, 145603735840, 1369609910, 140879192328], 'label': '2400.bt.30.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.e1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.b1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 171720265
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '30.f1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 20, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.d1.a1', '15.a1.a1'], 'contains': ['60.k1.a1', '60.m1.a1', '60.o1.a1', '150.e1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8629, -1, 4649, -1, 1930, -1, 8735, -1], 'generators': [4990156490, 130509168233, 140879192328, 1271171980, 45129158685], 'label': '2400.bt.30.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.f1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.f1.a1', 'subgroup_fusion': None, 'weyl_group': '120.39'}
  • id: 171720266
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '30.f1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 20, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.d1.b1', '15.a1.a1'], 'contains': ['60.k1.b1', '60.m1.b1', '60.o1.a1', '150.e1.b1'], 'core': '120.b1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [8629, -1, 3176, -1, 1930, -1, 8894, -1], 'generators': [140879192328, 1369609910, 60215928797, 1271171980, 45129158685], 'label': '2400.bt.30.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.f1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.f1.b1', 'subgroup_fusion': None, 'weyl_group': '120.39'}
  • id: 171720267
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '240.195', 'aut_weyl_index': 80, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1'], 'contains': ['80.a1.a1', '80.c1.a1', '80.c1.b1', '120.c1.a1', '200.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3309, -1, 1104, -1, 8556, -1, 4398, -1], 'generators': [140879192328, 25830469380, 5078828170, 105551846115], 'label': '2400.bt.40.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.a1.a1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720268
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '240.195', 'aut_weyl_index': 80, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1'], 'contains': ['80.a1.a1', '80.c1.a2', '80.c1.b2', '120.c1.a1', '200.a1.a2'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3309, -1, 516, -1, 8556, -1, 4499, -1], 'generators': [140879192328, 283268875, 5078828170, 105551846115], 'label': '2400.bt.40.a1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.a1.a2', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.a2', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720269
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '240.195', 'aut_weyl_index': 80, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1'], 'contains': ['80.a1.b1', '80.c1.a1', '80.c1.b2', '120.c1.b1', '200.a1.b1'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [3309, -1, 1569, -1, 8556, -1, 4196, -1], 'generators': [122109387504, 140879192328, 283268875, 105551846115], 'label': '2400.bt.40.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.a1.b1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720270
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '240.195', 'aut_weyl_index': 80, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1'], 'contains': ['80.a1.b1', '80.c1.a2', '80.c1.b1', '120.c1.b1', '200.a1.b2'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [3309, -1, 1443, -1, 8556, -1, 4297, -1], 'generators': [122109387504, 140879192328, 25830469380, 105551846115], 'label': '2400.bt.40.a1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.a1.b2', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.b2', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720271
    {'ambient': '2400.bt', 'aut_centralizer_order': 120, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '16.10', 'aut_weyl_index': 1200, 'centralizer': '40.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.a1', '20.b1.a1', '20.c1.a1', '20.d1.a1'], 'contains': ['80.a1.a1', '80.a1.b1', '80.b1.a1', '120.a1.a1', '200.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6401, -1, 985, -1, 5450, -1, 5332, -1], 'generators': [122109387504, 140879192328, 1271171980, 98909934263], 'label': '2400.bt.40.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.b1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720272
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '240.195', 'aut_weyl_index': 80, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '20.e1.a1', '20.f1.a1'], 'contains': ['80.b1.a1', '80.c1.a1', '80.c1.a2', '120.h1.a1', '200.c1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2906, -1, 1354, -1, 5222, -1, 5189, -1], 'generators': [11036721270, 140879192328, 1271171980, 110631910891], 'label': '2400.bt.40.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.c1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720273
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '240.195', 'aut_weyl_index': 80, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '20.e1.b1', '20.f1.b1'], 'contains': ['80.b1.a1', '80.c1.b1', '80.c1.b2', '120.h1.b1', '200.c1.b1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2906, -1, 395, -1, 5222, -1, 5475, -1], 'generators': [140879192328, 25830469380, 1271171980, 110631910891], 'label': '2400.bt.40.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.c1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 171720274
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '3840.fq', 'aut_weyl_index': 5, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.c1.a1', '10.d1.a1', '10.d1.b1', '15.a1.a1', '20.c1.a1', '25.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7720, -1, 2797, -1, 2503, -1, 8015, -1], 'generators': [122109387504, 130509168233, 140879192328, 1369609910, 1271171980, 45129158685, 128717318317], 'label': '2400.bt.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.39'}
  • id: 171720275
    {'ambient': '2400.bt', 'aut_centralizer_order': 12, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '80.50', 'aut_weyl_index': 240, 'centralizer': '200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.d1.a1', '20.c1.a1', '20.e1.b1', '20.f1.a1'], 'contains': ['80.b1.a1', '120.b1.a1', '200.d1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7373, -1, 2116, -1, 4161, -1, 6603, -1], 'generators': [55865201213, 130509168233, 140879192328, 1271171980], 'label': '2400.bt.40.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.d1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720276
    {'ambient': '2400.bt', 'aut_centralizer_order': 12, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '80.50', 'aut_weyl_index': 240, 'centralizer': '200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.d1.b1', '20.c1.a1', '20.e1.a1', '20.f1.b1'], 'contains': ['80.b1.a1', '120.b1.b1', '200.d1.b1'], 'core': '120.b1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [7373, -1, 1810, -1, 4161, -1, 6977, -1], 'generators': [140879192328, 60215928797, 1271171980, 128717318317], 'label': '2400.bt.40.d1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.d1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720277
    {'ambient': '2400.bt', 'aut_centralizer_order': 40, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '48.35', 'aut_weyl_index': 400, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.d1.a1', '20.e1.a1', '20.e1.b1'], 'contains': ['80.b1.a1', '120.l1.a1', '200.e1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6851, -1, 131, -1, 3226, -1, 6414, -1], 'generators': [140879192328, 1271171980, 16193036544, 110631910891], 'label': '2400.bt.40.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.e1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 171720278
    {'ambient': '2400.bt', 'aut_centralizer_order': 40, 'aut_label': '40.f1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '48.35', 'aut_weyl_index': 400, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '20.d1.a1', '20.f1.a1', '20.f1.b1'], 'contains': ['80.b1.a1', '120.n1.a1', '200.f1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8037, -1, 2814, -1, 1783, -1, 8202, -1], 'generators': [140879192328, 1271171980, 21943779861, 110631910891], 'label': '2400.bt.40.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.f1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 171720279
    {'ambient': '2400.bt', 'aut_centralizer_order': 100, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.2', 'aut_weyl_index': 1200, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.a1.a2', '24.b1.a1'], 'contains': ['96.a1.a1', '240.a1.a1', '240.c1.a1', '240.d1.a1', '240.d1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [606, -1, 7308, -1, 9334, -1, 1779, -1], 'generators': [140879192328, 7445862067, 5078828170], 'label': '2400.bt.48.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720280
    {'ambient': '2400.bt', 'aut_centralizer_order': 100, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.2', 'aut_weyl_index': 1200, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.a1.b2', '24.b1.a1'], 'contains': ['96.a1.a1', '240.a1.b1', '240.c1.b1', '240.d1.c1', '240.d1.d1'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [606, -1, 8713, -1, 9334, -1, 872, -1], 'generators': [122109387504, 140879192328, 7445862067], 'label': '2400.bt.48.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.a1.b1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720281
    {'ambient': '2400.bt', 'aut_centralizer_order': 200, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.2', 'aut_weyl_index': 1200, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.c1.a1', '24.c1.b1', '24.d1.a1', '24.d1.b1', '24.e1.a1', '24.f1.a1'], 'contains': ['96.a1.a1', '240.b1.a1', '240.e1.a1', '240.f1.a1', '240.f1.b1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1865, -1, 6553, -1, 7795, -1, 2854, -1], 'generators': [140879192328, 1271171980, 7445862067], 'label': '2400.bt.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720282
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '400.205', 'aut_weyl_index': 48, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.a1.b1', '24.c1.a1'], 'contains': ['96.a1.a1', '240.g1.a1', '240.h1.a1', '240.i1.a1', '240.i1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [225, -1, 8428, -1, 9102, -1, 1118, -1], 'generators': [140879192328, 7445862067, 105102199342], 'label': '2400.bt.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720283
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '400.205', 'aut_weyl_index': 48, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a2', '24.a1.b2', '24.c1.a1'], 'contains': ['96.a1.a1', '240.g1.a1', '240.h1.a2', '240.i1.a2', '240.i1.b2'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [225, -1, 8057, -1, 9102, -1, 1533, -1], 'generators': [140879192328, 96188940832, 7445862067], 'label': '2400.bt.48.c1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.c1.a2', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a2', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720284
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '400.205', 'aut_weyl_index': 48, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.a1.b2', '24.c1.b1'], 'contains': ['96.a1.a1', '240.g1.b1', '240.h1.b1', '240.i1.c1', '240.i1.d1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [225, -1, 8268, -1, 9102, -1, 1222, -1], 'generators': [140879192328, 7445862067, 64028341198], 'label': '2400.bt.48.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.c1.b1', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.b1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720285
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '5.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '960.10871', 'aut_weyl_index': 20, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.e1.a1', '10.e1.b1', '25.a1.a1', '30.a1.a1', '50.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8962, -1, 2246, -1, 3266, -1, 6780, -1], 'generators': [122109387504, 130509168233, 1271171980, 148051235266, 122741847365], 'label': '2400.bt.5.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.b1.a1', 'old_label': '5.b1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.b1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 171720286
    {'ambient': '2400.bt', 'aut_centralizer_order': 2, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '400.205', 'aut_weyl_index': 48, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a2', '24.a1.b1', '24.c1.b1'], 'contains': ['96.a1.a1', '240.g1.b1', '240.h1.b2', '240.i1.c2', '240.i1.d2'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [225, -1, 7523, -1, 9102, -1, 1327, -1], 'generators': [140879192328, 84411882688, 7445862067], 'label': '2400.bt.48.c1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.c1.b2', 'projective_image': '2400.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.b2', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720287
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '50.a1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '96.209', 'aut_weyl_index': 200, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.b1.a1', '10.b1.a1'], 'contains': ['100.a1.a1', '100.b1.a1', '100.c1.a1', '100.d1.a1', '100.d1.b1', '100.e1.a1', '100.e1.b1', '150.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [7970, -1, 867, -1, 3826, -1, 6676, -1], 'generators': [122109387504, 25830469380, 1271171980, 110631910891, 50675370281], 'label': '2400.bt.50.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '50.a1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 171720288
    {'ambient': '2400.bt', 'aut_centralizer_order': 80, 'aut_label': '50.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 400, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '10.c1.a1', '25.a1.a1'], 'contains': ['100.f1.a1', '150.c1.a1', '200.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [9451, -1, 2059, -1, 1102, -1, 7805, -1], 'generators': [122109387504, 1271171980, 81506204464, 34410003353, 20296838936], 'label': '2400.bt.50.b1.a1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '50.b1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 171720289
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '50.c1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '48.48', 'aut_weyl_index': 400, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.d1.a1', '10.e1.a1', '25.a1.a1'], 'contains': ['100.f1.a1', '150.e1.a1', '200.d1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [9828, -1, 4854, -1, 1696, -1, 7989, -1], 'generators': [55865201213, 115341611192, 1271171980, 81506204464, 50675370281], 'label': '2400.bt.50.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '50.c1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 171720290
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '50.c1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '48.48', 'aut_weyl_index': 400, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.d1.b1', '10.e1.b1', '25.a1.a1'], 'contains': ['100.f1.a1', '150.e1.b1', '200.d1.b1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [9828, -1, 2431, -1, 1696, -1, 8403, -1], 'generators': [75344408338, 1271171980, 81506204464, 140049727374, 128717318317], 'label': '2400.bt.50.c1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '50.c1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 171720291
    {'ambient': '2400.bt', 'aut_centralizer_order': 120, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '160.207', 'aut_weyl_index': 120, 'centralizer': '10.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.c1.a1', '30.b1.a1'], 'contains': ['120.a1.a1', '120.b1.a1', '120.b1.b1', '300.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5978, 1993, 3008, 5411, 6034, 2938, 5044, 2458], 'generators': [122109387504, 130509168233, 140879192328, 1271171980], 'label': '2400.bt.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': -60, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['120.a1.a1', '120.b1.a1', '120.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720292
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '160.207', 'aut_weyl_index': 120, 'centralizer': '300.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.b1.a1', '30.b1.a1', '30.c1.a1'], 'contains': ['120.a1.a1', '120.c1.a1', '120.c1.b1', '120.h1.a1', '120.h1.b1', '300.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2250, -1, 4512, -1, 6329, -1, 4639, -1], 'generators': [122109387504, 10054287475, 140879192328, 1271171980], 'label': '2400.bt.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720293
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '160.207', 'aut_weyl_index': 120, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '30.a1.a1'], 'contains': ['120.d1.a1', '120.d1.a2', '120.d1.b1', '120.d1.b2', '120.f1.a1', '120.i1.a1', '120.i1.b1', '300.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1683, -1, 6875, -1, 9084, -1, 2303, -1], 'generators': [81420657990, 122109387504, 1271171980, 64028341198], 'label': '2400.bt.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.c1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720294
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '160.207', 'aut_weyl_index': 120, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['120.e1.a1', '120.e1.a2', '120.e1.c1', '120.e1.c2', '120.g1.a1', '120.j1.a1', '120.j1.c1', '300.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [862, -1, 8944, -1, 9570, -1, 1621, -1], 'generators': [122109387504, 1271171980, 7445862067, 64028341198], 'label': '2400.bt.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '60.d1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720295
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '160.207', 'aut_weyl_index': 120, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['120.e1.b1', '120.e1.b2', '120.e1.d1', '120.e1.d2', '120.g1.b1', '120.j1.b1', '120.j1.d1', '300.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [862, -1, 7719, -1, 9570, -1, 486, -1], 'generators': [122109387504, 1271171980, 64028341198, 117797313644], 'label': '2400.bt.60.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '60.d1.b1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720296
    {'ambient': '2400.bt', 'aut_centralizer_order': 1, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3200.jc', 'aut_weyl_index': 6, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1', '12.e1.a1', '12.e1.b1', '30.a1.a1', '30.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4140, -1, 5711, -1, 7128, -1, 3412, -1], 'generators': [122109387504, 130509168233, 140879192328, 1271171980, 7445862067, 64028341198], 'label': '2400.bt.6.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 171720297
    {'ambient': '2400.bt', 'aut_centralizer_order': 20, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '32.25', 'aut_weyl_index': 600, 'centralizer': '60.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '30.a1.a1'], 'contains': ['120.f1.a1', '120.k1.a1', '120.k1.b1', '300.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4233, -1, 6298, -1, 8328, -1, 2675, -1], 'generators': [81420657990, 122109387504, 130509168233, 1271171980], 'label': '2400.bt.60.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.e1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 171720298
    {'ambient': '2400.bt', 'aut_centralizer_order': 80, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.10', 'aut_weyl_index': 1200, 'centralizer': '60.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.d1.a1', '30.b1.a1', '30.c1.a1', '30.d1.a1'], 'contains': ['120.a1.a1', '120.l1.a1', '120.n1.a1', '300.c1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6722, -1, 3237, -1, 2682, -1, 7354, -1], 'generators': [122109387504, 140879192328, 1271171980, 45129158685], 'label': '2400.bt.60.f1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.f1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720299
    {'ambient': '2400.bt', 'aut_centralizer_order': 80, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '12.c1.a1', '30.a1.a1'], 'contains': ['120.f1.a1', '120.m1.a1', '120.o1.a1', '300.c1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3854, -1, 5495, -1, 6927, -1, 3551, -1], 'generators': [81420657990, 122109387504, 1271171980, 73738889847], 'label': '2400.bt.60.g1.a1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '60.g1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720300
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '80.50', 'aut_weyl_index': 240, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '30.a1.a1'], 'contains': ['120.i1.a1', '120.k1.b1', '120.m1.a1', '300.d1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3500, -1, 6156, -1, 7754, -1, 3190, -1], 'generators': [81420657990, 96188940832, 60215928797, 1271171980], 'label': '2400.bt.60.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.h1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720301
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '80.50', 'aut_weyl_index': 240, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '30.a1.a1'], 'contains': ['120.i1.b1', '120.k1.a1', '120.m1.a1', '300.d1.b1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3500, -1, 5805, -1, 7754, -1, 2845, -1], 'generators': [81420657990, 130509168233, 1271171980, 64028341198], 'label': '2400.bt.60.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.h1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720302
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.e1.a1', '12.e1.a1', '30.a1.a1'], 'contains': ['120.i1.a1', '120.k1.a1', '120.o1.a1', '300.e1.a1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4656, -1, 5935, -1, 7202, -1, 3724, -1], 'generators': [81420657990, 130509168233, 96188940832, 1271171980], 'label': '2400.bt.60.i1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.i1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720303
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.e1.b1', '12.e1.b1', '30.a1.a1'], 'contains': ['120.i1.b1', '120.k1.b1', '120.o1.a1', '300.e1.b1'], 'core': '1200.b1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4656, -1, 5638, -1, 7202, -1, 3879, -1], 'generators': [81420657990, 60215928797, 1271171980, 64028341198], 'label': '2400.bt.60.i1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.i1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 171720304
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '80.50', 'aut_weyl_index': 240, 'centralizer': '300.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '20.e1.a1', '30.b1.a1', '30.e1.b1'], 'contains': ['120.b1.b1', '120.h1.a1', '120.l1.a1', '300.d1.a1'], 'core': '120.b1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [5127, -1, 4013, -1, 4721, -1, 5911, -1], 'generators': [145603735840, 140879192328, 60215928797, 1271171980], 'label': '2400.bt.60.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.j1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.j1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720305
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '80.50', 'aut_weyl_index': 240, 'centralizer': '300.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '20.e1.b1', '30.b1.a1', '30.e1.a1'], 'contains': ['120.b1.a1', '120.h1.b1', '120.l1.a1', '300.d1.b1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5127, -1, 3508, -1, 4721, -1, 5603, -1], 'generators': [145603735840, 130509168233, 140879192328, 1271171980], 'label': '2400.bt.60.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.j1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.j1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720306
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '80.50', 'aut_weyl_index': 240, 'centralizer': '300.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '20.f1.a1', '30.b1.a1', '30.e1.a1', '30.f1.a1'], 'contains': ['120.b1.a1', '120.h1.a1', '120.n1.a1', '300.e1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7146, -1, 3846, -1, 3886, -1, 7721, -1], 'generators': [130509168233, 140879192328, 1271171980, 45129158685], 'label': '2400.bt.60.k1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.k1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.k1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720307
    {'ambient': '2400.bt', 'aut_centralizer_order': 80, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '240.189', 'aut_weyl_index': 80, 'centralizer': '60.a1.a1', 'complements': ['240.g1.a1', '240.g1.b1', '240.i1.b1', '240.i1.d2', '240.i1.d1', '240.i1.b2', '240.i1.a1', '240.i1.c2', '240.i1.c1', '240.i1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.b1.a1'], 'contains': ['20.a1.a1', '50.b1.a1', '60.g1.a1', '100.c1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9100, 8965, 1869, 8091, 1116, 8576, 6963, 6775], 'generators': [122109387504, 44670214561, 34316253738, 1271171980], 'label': '2400.bt.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['20.a1.a1', '600.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '600.146', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 171720308
    {'ambient': '2400.bt', 'aut_centralizer_order': 8, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '80.50', 'aut_weyl_index': 240, 'centralizer': '300.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '20.f1.b1', '30.b1.a1', '30.e1.b1', '30.f1.b1'], 'contains': ['120.b1.b1', '120.h1.b1', '120.n1.a1', '300.e1.b1'], 'core': '120.b1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [7146, -1, 3378, -1, 3886, -1, 8029, -1], 'generators': [140879192328, 60215928797, 1271171980, 45129158685], 'label': '2400.bt.60.k1.b1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.k1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.k1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 171720309
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '160.207', 'aut_weyl_index': 120, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1', '30.e1.a1', '30.e1.b1'], 'contains': ['120.h1.a1', '120.h1.b1', '120.l1.a1', '300.f1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3075, -1, 4665, -1, 2454, -1, 9234, -1], 'generators': [145603735840, 140879192328, 1369609910, 1271171980], 'label': '2400.bt.60.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.l1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.l1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 171720310
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '160.207', 'aut_weyl_index': 120, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1', '30.e1.a1', '30.e1.b1'], 'contains': ['120.h1.a1', '120.h1.b1', '120.l1.a1', '300.f1.a2'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3075, -1, 4750, -1, 2454, -1, 9335, -1], 'generators': [10054287475, 140879192328, 1369609910, 1271171980], 'label': '2400.bt.60.l1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.l1.a2', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.l1.a2', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 171720311
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '60.m1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '160.207', 'aut_weyl_index': 120, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1', '30.e1.b1', '30.f1.a1'], 'contains': ['120.h1.a1', '120.n1.a1', '300.g1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5552, -1, 4845, -1, 1303, -1, 8927, -1], 'generators': [4990156490, 140879192328, 1271171980, 45129158685], 'label': '2400.bt.60.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.m1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.m1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 171720312
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '60.m1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '160.207', 'aut_weyl_index': 120, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1', '30.e1.a1', '30.f1.b1'], 'contains': ['120.h1.b1', '120.n1.a1', '300.g1.b1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5552, -1, 4250, -1, 1303, -1, 9133, -1], 'generators': [140879192328, 1369609910, 1271171980, 45129158685], 'label': '2400.bt.60.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.m1.b1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.m1.b1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 171720313
    {'ambient': '2400.bt', 'aut_centralizer_order': 40, 'aut_label': '60.n1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.25', 'aut_weyl_index': 600, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.a1', '30.e1.a1', '30.e1.b1'], 'contains': ['120.l1.a1', '120.n1.a1', '300.h1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7970, -1, 3716, -1, 930, -1, 9568, -1], 'generators': [140879192328, 1271171980, 72007755877, 45129158685], 'label': '2400.bt.60.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.n1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 171720314
    {'ambient': '2400.bt', 'aut_centralizer_order': 40, 'aut_label': '60.o1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '96.186', 'aut_weyl_index': 200, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.g1.a1', '30.d1.a1', '30.f1.a1', '30.f1.b1'], 'contains': ['120.n1.a1', '300.i1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8865, -1, 4143, -1, 265, -1, 8643, -1], 'generators': [140879192328, 118727107253, 1271171980, 45129158685], 'label': '2400.bt.60.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.o1.a1', 'projective_image': '1200.944', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.o1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 171720315
    {'ambient': '2400.bt', 'aut_centralizer_order': 4, 'aut_label': '75.a1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 100, 'centralizer': '300.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '25.a1.a1'], 'contains': ['150.a1.a1', '150.b1.a1', '150.c1.a1', '150.d1.a1', '150.d1.b1', '150.e1.a1', '150.e1.b1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6268, -1, 2432, -1, 2209, -1, 9572, -1], 'generators': [122109387504, 92911416209, 1369609910, 1271171980, 81506204464], 'label': '2400.bt.75.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '75.a1.a1', 'projective_image': '600.146', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 171720316
    {'ambient': '2400.bt', 'aut_centralizer_order': 120, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2400, 'centralizer': '40.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '40.a1.a2', '40.b1.a1'], 'contains': ['160.a1.a1', '240.a1.a1', '400.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6299, -1, 232, -1, 7275, -1, 4838, -1], 'generators': [140879192328, 98909934263, 5078828170], 'label': '2400.bt.80.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '80.a1.a1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 171720317
    {'ambient': '2400.bt', 'aut_centralizer_order': 120, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2400, 'centralizer': '40.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.b1', '40.a1.b2', '40.b1.a1'], 'contains': ['160.a1.a1', '240.a1.b1', '400.a1.b1'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [6299, -1, 1550, -1, 7275, -1, 4087, -1], 'generators': [122109387504, 140879192328, 65887753435], 'label': '2400.bt.80.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '80.a1.b1', 'projective_image': '1200.481', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}