Formats: - HTML - YAML - JSON - 2026-07-25T13:06:16.858698
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 24, 'aut_gen_orders': [4, 3, 2, 2, 8, 2, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 8], [145, 98, 136], [1, 66, 8], [1, 2, 88], [5, 2, 136], [29, 146, 40], [1, 6, 40], [97, 2, 136], [1, 2, 40], [1, 2, 136], [97, 98, 136], [1, 2, 140]], 'aut_group': '3072.bjt', 'aut_hash': 910391297008766483, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3072, 'aut_permdeg': 40, 'aut_perms': [88868316494242690473837498480469962818815777929, 3677547347235672804574884287021565917908987913, 7006555675661923894521914233490017488195575509, 265146235720895070280262646268481932804304467671, 57094613329566139174697828753252859847415096380, 2950316865485882357966416960561225612459901149, 489371426319356466770003474997325019962715586231, 20219725117467930174794781358827148850612743671, 19889005908539465566540502826563629787233113305, 476812941792740836527951352489533678997868060671, 20371123449143426525363869918629082820290257351], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 4, 4, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 6, 4, 1], [4, 12, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 8, 4, 1], [8, 4, 2, 1], [8, 12, 2, 1], [12, 4, 1, 2], [24, 4, 4, 1]], 'aut_supersolvable': True, 'aut_tex': '(D_4\\times C_2^5).D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '48.38', 'autcentquo_hash': 38, 'autcentquo_nilpotent': False, 'autcentquo_order': 48, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times D_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 4], [3, 2, 1], [4, 2, 2], [4, 6, 4], [4, 12, 4], [6, 2, 3], [6, 8, 4], [8, 4, 2], [8, 12, 2], [12, 4, 2], [24, 4, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '48.38', 'commutator_count': 1, 'commutator_label': '12.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 711, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 4], [3, 2, 1, 1], [4, 2, 1, 2], [4, 6, 2, 2], [4, 12, 2, 2], [6, 2, 1, 3], [6, 8, 1, 4], [8, 4, 1, 2], [8, 12, 2, 1], [12, 4, 1, 2], [24, 4, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 672, 'exponent': 24, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '24.14', 'hash': 711, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 12], 'inner_gens': [[1, 98, 56], [97, 2, 40], [145, 162, 8]], 'inner_hash': 38, 'inner_nilpotent': False, 'inner_order': 48, 'inner_split': True, 'inner_tex': 'S_3\\times D_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 12], [4, 8]], 'label': '192.711', 'linC_count': 32, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 8, 'linQ_dim': 8, 'linQ_dim_count': 40, 'linR_count': 40, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C24:(C2*C4)', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 17, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 36, 'number_divisions': 29, 'number_normal_subgroups': 57, 'number_subgroup_autclasses': 70, 'number_subgroup_classes': 132, 'number_subgroups': 360, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 19], [3, 2], [4, 76], [6, 38], [8, 32], [12, 8], [24, 16]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 48, 0, 0, 48], 'outer_gens': [[5, 102, 8], [149, 6, 108], [1, 2, 104], [1, 98, 8], [25, 54, 12]], 'outer_group': '64.202', 'outer_hash': 202, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [126, 806407, 127, 7, 811456], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 14], [4, 5], [8, 2]], 'representations': {'PC': {'code': 1181801355240221365128047732309249, 'gens': [1, 2, 4], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 1373, 36, 1571, 570, 80, 3924, 1411, 102, 3372, 124, 3149]}, 'GLZN': {'d': 2, 'p': 40, 'gens': [1216239, 1857019, 576009, 77793, 64801, 602751, 64401]}, 'Perm': {'d': 15, 'gens': [100677467649, 193158120960, 26428590736, 288369849616, 102150720000, 288369849600, 840]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{24}:(C_2\\times C_4)', 'transitive_degree': 96, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    • id: 96390125
      {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 711, 'group_order': 192, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 96390136
      {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 711, 'group_order': 192, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 4, 'size': 1}
    • id: 96390147
      {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 711, 'group_order': 192, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 100, 'size': 1}
    • id: 96390155
      {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 711, 'group_order': 192, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 96, 'size': 1}
    • id: 96390156
      {'aut_label': '2D', 'centralizer': '4.g2.a1', 'counter': 5, 'group_counter': 711, 'group_order': 192, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 1, 'size': 4}
    • id: 96390157
      {'aut_label': '2D', 'centralizer': '4.g2.b1', 'counter': 6, 'group_counter': 711, 'group_order': 192, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 73, 'size': 4}
    • id: 96390158
      {'aut_label': '2D', 'centralizer': '4.g2.a1', 'counter': 7, 'group_counter': 711, 'group_order': 192, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 5, 'size': 4}
    • id: 96390159
      {'aut_label': '2D', 'centralizer': '4.g2.b1', 'counter': 8, 'group_counter': 711, 'group_order': 192, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 77, 'size': 4}
    • id: 96390160
      {'aut_label': '3A', 'centralizer': '2.c1.a1', 'counter': 9, 'group_counter': 711, 'group_order': 192, 'label': '3A', 'order': 3, 'powers': [9, 1], 'representative': 128, 'size': 2}
    • id: 96390126
      {'aut_label': '4A', 'centralizer': '2.d1.a1', 'counter': 10, 'group_counter': 711, 'group_order': 192, 'label': '4A', 'order': 4, 'powers': [4, 10], 'representative': 52, 'size': 2}
    • id: 96390127
      {'aut_label': '4B', 'centralizer': '2.d1.a1', 'counter': 11, 'group_counter': 711, 'group_order': 192, 'label': '4B', 'order': 4, 'powers': [4, 11], 'representative': 48, 'size': 2}
    • id: 96390128
      {'aut_label': '4C1', 'centralizer': '6.b1.b1', 'counter': 12, 'group_counter': 711, 'group_order': 192, 'label': '4C1', 'order': 4, 'powers': [2, 13], 'representative': 2, 'size': 6}
    • id: 96390129
      {'aut_label': '4C1', 'centralizer': '6.b1.b1', 'counter': 13, 'group_counter': 711, 'group_order': 192, 'label': '4C-1', 'order': 4, 'powers': [2, 12], 'representative': 6, 'size': 6}
    • id: 96390130
      {'aut_label': '4C1', 'centralizer': '6.b1.a1', 'counter': 14, 'group_counter': 711, 'group_order': 192, 'label': '4D1', 'order': 4, 'powers': [3, 15], 'representative': 18, 'size': 6}
    • id: 96390131
      {'aut_label': '4C1', 'centralizer': '6.b1.a1', 'counter': 15, 'group_counter': 711, 'group_order': 192, 'label': '4D-1', 'order': 4, 'powers': [3, 14], 'representative': 22, 'size': 6}
    • id: 96390132
      {'aut_label': '4E1', 'centralizer': '12.d2.a1', 'counter': 16, 'group_counter': 711, 'group_order': 192, 'label': '4E1', 'order': 4, 'powers': [3, 17], 'representative': 3, 'size': 12}
    • id: 96390133
      {'aut_label': '4E1', 'centralizer': '12.d2.a1', 'counter': 17, 'group_counter': 711, 'group_order': 192, 'label': '4E-1', 'order': 4, 'powers': [3, 16], 'representative': 7, 'size': 12}
    • id: 96390134
      {'aut_label': '4E1', 'centralizer': '12.d2.b1', 'counter': 18, 'group_counter': 711, 'group_order': 192, 'label': '4F1', 'order': 4, 'powers': [2, 19], 'representative': 11, 'size': 12}
    • id: 96390135
      {'aut_label': '4E1', 'centralizer': '12.d2.b1', 'counter': 19, 'group_counter': 711, 'group_order': 192, 'label': '4F-1', 'order': 4, 'powers': [2, 18], 'representative': 15, 'size': 12}
    • id: 96390137
      {'aut_label': '6A', 'centralizer': '2.c1.a1', 'counter': 20, 'group_counter': 711, 'group_order': 192, 'label': '6A', 'order': 6, 'powers': [9, 2], 'representative': 68, 'size': 2}
    • id: 96390138
      {'aut_label': '6A', 'centralizer': '2.c1.a1', 'counter': 21, 'group_counter': 711, 'group_order': 192, 'label': '6B', 'order': 6, 'powers': [9, 3], 'representative': 36, 'size': 2}
    • id: 96390139
      {'aut_label': '6C', 'centralizer': '2.c1.a1', 'counter': 22, 'group_counter': 711, 'group_order': 192, 'label': '6C', 'order': 6, 'powers': [9, 4], 'representative': 32, 'size': 2}
    • id: 96390140
      {'aut_label': '6D', 'centralizer': '8.f1.a1', 'counter': 23, 'group_counter': 711, 'group_order': 192, 'label': '6D', 'order': 6, 'powers': [9, 5], 'representative': 65, 'size': 8}
    • id: 96390141
      {'aut_label': '6D', 'centralizer': '8.f1.b1', 'counter': 24, 'group_counter': 711, 'group_order': 192, 'label': '6E', 'order': 6, 'powers': [9, 6], 'representative': 9, 'size': 8}
    • id: 96390142
      {'aut_label': '6D', 'centralizer': '8.f1.a1', 'counter': 25, 'group_counter': 711, 'group_order': 192, 'label': '6F', 'order': 6, 'powers': [9, 7], 'representative': 69, 'size': 8}
    • id: 96390143
      {'aut_label': '6D', 'centralizer': '8.f1.b1', 'counter': 26, 'group_counter': 711, 'group_order': 192, 'label': '6G', 'order': 6, 'powers': [9, 8], 'representative': 13, 'size': 8}
    • id: 96390144
      {'aut_label': '8A', 'centralizer': '4.d1.a1', 'counter': 27, 'group_counter': 711, 'group_order': 192, 'label': '8A', 'order': 8, 'powers': [11, 27], 'representative': 24, 'size': 4}
    • id: 96390145
      {'aut_label': '8A', 'centralizer': '4.d1.a1', 'counter': 28, 'group_counter': 711, 'group_order': 192, 'label': '8B', 'order': 8, 'powers': [11, 28], 'representative': 28, 'size': 4}
    • id: 96390146
      {'aut_label': '8C1', 'centralizer': '12.g1.a1', 'counter': 29, 'group_counter': 711, 'group_order': 192, 'label': '8C1', 'order': 8, 'powers': [10, 30], 'representative': 10, 'size': 12}
    • id: 96390148
      {'aut_label': '8C1', 'centralizer': '12.g1.a1', 'counter': 30, 'group_counter': 711, 'group_order': 192, 'label': '8C-1', 'order': 8, 'powers': [10, 29], 'representative': 14, 'size': 12}
    • id: 96390149
      {'aut_label': '12A', 'centralizer': '4.d1.a1', 'counter': 31, 'group_counter': 711, 'group_order': 192, 'label': '12A', 'order': 12, 'powers': [22, 10], 'representative': 20, 'size': 4}
    • id: 96390150
      {'aut_label': '12B', 'centralizer': '4.d1.a1', 'counter': 32, 'group_counter': 711, 'group_order': 192, 'label': '12B', 'order': 12, 'powers': [22, 11], 'representative': 16, 'size': 4}
    • id: 96390151
      {'aut_label': '24A1', 'centralizer': '4.d1.a1', 'counter': 33, 'group_counter': 711, 'group_order': 192, 'label': '24A1', 'order': 24, 'powers': [32, 27], 'representative': 8, 'size': 4}
    • id: 96390152
      {'aut_label': '24A1', 'centralizer': '4.d1.a1', 'counter': 34, 'group_counter': 711, 'group_order': 192, 'label': '24A-1', 'order': 24, 'powers': [32, 27], 'representative': 136, 'size': 4}
    • id: 96390153
      {'aut_label': '24A1', 'centralizer': '4.d1.a1', 'counter': 35, 'group_counter': 711, 'group_order': 192, 'label': '24B1', 'order': 24, 'powers': [32, 28], 'representative': 12, 'size': 4}
    • id: 96390154
      {'aut_label': '24A1', 'centralizer': '4.d1.a1', 'counter': 36, 'group_counter': 711, 'group_order': 192, 'label': '24B-1', 'order': 24, 'powers': [32, 28], 'representative': 140, 'size': 4}
  • gps_qchar • Show schema
    • id: 240151
      {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.1a', '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], 'schur_index': 1}
    • id: 240162
      {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.1b', '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], 'schur_index': 1}
    • id: 240173
      {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.1c', '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], 'schur_index': 1}
    • id: 240174
      {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.1d', '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], 'schur_index': 1}
    • id: 240175
      {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 240176
      {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 240177
      {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 240178
      {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 240179
      {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, -2, 2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -2, 2, -2, 2, -2, 0, 0, -2, 2, -2, -2, 2, 2], 'schur_index': 1}
    • id: 240152
      {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, -2, -2, 2, 0, 0, -2, 2, 2, 2, -2, -2], 'schur_index': 1}
    • id: 240153
      {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.1k', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, -2, 2, 2, -2, 2, 0, 0, -2, 2, 2, 2, -2, -2], 'schur_index': 1}
    • id: 240154
      {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.1l', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, 2, -2, 2, 2, -2, 0, 0, -2, 2, -2, -2, 2, 2], 'schur_index': 1}
    • id: 240155
      {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 240156
      {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
    • id: 240157
      {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
    • id: 240158
      {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 240159
      {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, -2, 2, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, -1, -1, 1, -2, -2, 0, 0, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 240160
      {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, 2, -2, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, -1, -2, -2, 0, 0, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 240161
      {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.2g', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, -2, 2, 2, -1, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, -1, 1, 2, -2, 0, 0, 1, -1, 1, 1, -1, -1], 'schur_index': 2}
    • id: 240163
      {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.2h', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 2, -2, -1, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, 1, 1, -2, 2, 0, 0, 1, -1, -1, -1, 1, 1], 'schur_index': 2}
    • id: 240164
      {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.2i', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, -2, 2, -1, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, 1, -1, -1, -2, 2, 0, 0, 1, -1, -1, -1, 1, 1], 'schur_index': 2}
    • id: 240165
      {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.2j', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, -2, -2, -1, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, -1, 1, -1, 2, -2, 0, 0, 1, -1, 1, 1, -1, -1], 'schur_index': 2}
    • id: 240166
      {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.2k', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0], 'schur_index': 1}
    • id: 240167
      {'cdim': 4, 'counter': 24, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.4a', 'multiplicity': 1, 'nt': [8, 15], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 240168
      {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.4b', 'multiplicity': 1, 'nt': [8, 15], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 240169
      {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.4c', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, -2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0], 'schur_index': 1}
    • id: 240170
      {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.4d', 'multiplicity': 1, 'nt': [24, 18], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, -2, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0], 'schur_index': 2}
    • id: 240171
      {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.4e', 'multiplicity': 2, 'nt': [24, 141], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 240172
      {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '192.711', 'group_order': 192, 'image': None, 'label': '192.711.4f', 'multiplicity': 2, 'nt': [24, 141], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • gps_char • Show schema
    • id: 323039
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    • id: 323050
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 96, 'label': '192.711.1b', '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]]]}
    • id: 323061
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 96, 'label': '192.711.1c', '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]]]}
    • id: 323069
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 96, 'label': '192.711.1d', '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]]]}
    • id: 323070
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 96, 'label': '192.711.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 323071
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 96, 'label': '192.711.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 323072
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 96, 'label': '192.711.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 323073
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 96, 'label': '192.711.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 323074
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.a1', 'kernel_order': 48, 'label': '192.711.1i1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 323040
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.a1', 'kernel_order': 48, 'label': '192.711.1i2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 323041
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.b1', 'kernel_order': 48, 'label': '192.711.1j1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 323042
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.b1', 'kernel_order': 48, 'label': '192.711.1j2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 323043
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.c1', 'kernel_order': 48, 'label': '192.711.1k1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 323044
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 14, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.c1', 'kernel_order': 48, 'label': '192.711.1k2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 323045
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 15, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.d1', 'kernel_order': 48, 'label': '192.711.1l1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 323046
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 16, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.f1.d1', 'kernel_order': 48, 'label': '192.711.1l2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 323047
      {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 32, 'label': '192.711.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 323048
      {'center': '4.b1.a1', 'center_index': 4, 'center_order': 48, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 24, 'label': '192.711.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 323049
      {'center': '4.b1.a1', 'center_index': 4, 'center_order': 48, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 24, 'label': '192.711.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 323051
      {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 16, 'label': '192.711.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 323052
      {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.b1', 'kernel_order': 16, 'label': '192.711.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 323053
      {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 16, 'label': '192.711.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 323054
      {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.c1.a1', 'kernel_order': 16, 'label': '192.711.2g', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 323055
      {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.c1.b1', 'kernel_order': 16, 'label': '192.711.2h', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 323056
      {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.c1.c1', 'kernel_order': 16, 'label': '192.711.2i', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 323057
      {'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.c1.d1', 'kernel_order': 16, 'label': '192.711.2j', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 323058
      {'center': '4.b1.a1', 'center_index': 4, 'center_order': 48, 'counter': 27, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 12, 'label': '192.711.2k1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 323059
      {'center': '4.b1.a1', 'center_index': 4, 'center_order': 48, 'counter': 28, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 12, 'label': '192.711.2k2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 323060
      {'center': '16.a1.a1', 'center_index': 16, 'center_order': 12, 'counter': 29, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '32.43', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 6, 'label': '192.711.4a', 'nt': [8, 15], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 323062
      {'center': '16.a1.a1', 'center_index': 16, 'center_order': 12, 'counter': 30, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '32.43', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.b1', 'kernel_order': 6, 'label': '192.711.4b', 'nt': [8, 15], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 323063
      {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 31, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 4, 'label': '192.711.4c', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 323064
      {'center': '24.a1.a1', 'center_index': 24, 'center_order': 8, 'counter': 32, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '48.39', 'image_order': 48, 'indicator': -1, 'kernel': '48.b1.a1', 'kernel_order': 4, 'label': '192.711.4d', 'nt': [24, 18], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 323065
      {'center': '48.a1.a1', 'center_index': 48, 'center_order': 4, 'counter': 33, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [6, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '96.118', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.a1', 'kernel_order': 2, 'label': '192.711.4e1', 'nt': [24, 141], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]]]}
    • id: 323066
      {'center': '48.a1.a1', 'center_index': 48, 'center_order': 4, 'counter': 34, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [6, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '96.118', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.a1', 'kernel_order': 2, 'label': '192.711.4e2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]]]}
    • id: 323067
      {'center': '48.a1.a1', 'center_index': 48, 'center_order': 4, 'counter': 35, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [6, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '96.118', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.b1', 'kernel_order': 2, 'label': '192.711.4f1', 'nt': [24, 141], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]]]}
    • id: 323068
      {'center': '48.a1.a1', 'center_index': 48, 'center_order': 4, 'counter': 36, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [6, 0, 1], 'group': '192.711', 'group_counter': 711, 'group_order': 192, 'image': None, 'image_isoclass': '96.118', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.b1', 'kernel_order': 2, 'label': '192.711.4f2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]]]}
  • gps_subgroup_search • Show schema
    Showing the first 100 of 132 matching records in this table.
    • id: 20363270
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '192.711.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.711', 'subgroup_hash': 711, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:(C_2\\times C_4)', 'supersolvable': True, 'sylow': 0}
    • id: 20363314
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 20363325
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 20363336
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, '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': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.39', 'subgroup_hash': 39, 'subgroup_order': 96, 'subgroup_tex': 'C_6.D_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363347
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, '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': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.39', 'subgroup_hash': 39, 'subgroup_order': 96, 'subgroup_tex': 'C_6.D_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363358
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 96, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.179', 'subgroup_hash': 179, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times D_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363369
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.22', 'subgroup_hash': 22, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363380
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.24', 'subgroup_hash': 24, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363391
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '192.711.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.123', 'subgroup_hash': 123, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_4', 'supersolvable': True, 'sylow': 2}
    • id: 20363271
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363282
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.4.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.b1', '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': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363293
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 48, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.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': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363304
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.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': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363308
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.b1', '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': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363309
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 48, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.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': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
    • id: 20363310
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 48, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.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': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363311
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363312
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363313
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.4.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363315
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.4.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363316
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363317
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.4.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363318
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.4.g2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.g2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 20363319
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.4.g2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.g2.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 20363320
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 32, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363321
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363322
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363323
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363324
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.6.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363326
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363327
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363328
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 24, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
    • id: 20363329
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 20363330
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 20363331
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363332
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363333
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.8.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363334
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.8.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363335
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 39, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.711.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
    • id: 20363337
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 40, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.711.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
    • id: 20363338
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363339
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.8.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363340
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363341
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.8.e1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363342
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 20363343
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.8.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 20363344
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363345
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.8.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363346
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363348
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363349
      {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363350
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 20363351
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 20363352
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 16, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363353
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363354
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.12.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363355
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.12.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363356
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.12.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363357
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363359
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363360
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.12.d2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d2.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363361
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.12.d2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d2.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363362
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
    • id: 20363363
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363364
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363365
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363366
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 12, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 20363367
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 12, 'counter': 68, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.711.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
    • id: 20363368
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 12, 'counter': 69, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.711.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
    • id: 20363370
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 20363371
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.16.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 20363372
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.16.d2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.d2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 20363373
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.16.d2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.d2.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 20363374
      {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363375
      {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.16.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363376
      {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363377
      {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.16.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363378
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 20363379
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.16.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 20363381
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.16.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 20363382
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.16.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g1.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 20363383
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 8, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'U1'], 'split': False, '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: 20363384
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363385
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.24.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363386
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.24.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363387
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.711.24.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363388
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 87, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.711.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363389
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 88, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.711.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
    • id: 20363390
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363392
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.24.d1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363393
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363394
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.24.d1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363395
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 20363396
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 20363397
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363398
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363399
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363400
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.24.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363401
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
    • id: 20363272
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.711', 'ambient_counter': 711, 'ambient_order': 192, 'ambient_tex': 'C_{24}:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.711.24.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 132 matching records in this table.
    • id: 20363270
      {'ambient': '192.711', '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': '48.a1.a1', 'complements': ['192.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.b1.b1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6647, 5923, 5429, 7209, 6916, 3870, 5829, 2954], 'generators': [1, 96, 144, 2, 64, 24, 4], 'label': '192.711.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.b1', '2.a1.a1', '2.b1.b1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '48.38', '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': '48.38'}
    • id: 20363271
      {'ambient': '192.711', 'aut_centralizer_order': 48, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.46', 'aut_weyl_index': 96, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.c1.c1', '8.f1.a1', '8.h1.a1', '12.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5513, 4599, 7007, 4172, 5501, 6695, 5935, 5610], 'generators': [1, 96, 4, 48, 64], 'label': '192.711.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.c1', '8.c1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363272
      {'ambient': '192.711', 'aut_centralizer_order': 96, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 384, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '12.a1.b1'], 'contains': ['48.b1.a1', '48.g1.b1', '48.g1.d1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5535, -1, 3117, -1, 5939, -1, 7332, -1], 'generators': [73, 52], 'label': '192.711.24.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '24.h1.b1', 'projective_image': '96.141', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 20363273
      {'ambient': '192.711', 'aut_centralizer_order': 128, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 768, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.g1.a1'], 'contains': ['48.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8184, -1, 6648, -1, 7550, -1, 6573, -1], 'generators': [10], 'label': '192.711.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.i1.a1', 'projective_image': '96.141', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363274
      {'ambient': '192.711', 'aut_centralizer_order': 768, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.a1', '16.d2.a1', '16.e1.a1', '16.f1.a1'], 'contains': ['64.a1.a1', '96.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3603, 8561, 800, 8180, 3032, 3087, 3322, 2891], 'generators': [4, 64], 'label': '192.711.32.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '96.118', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.7', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363275
      {'ambient': '192.711', 'aut_centralizer_order': 768, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.b1', '16.d2.b1', '16.e1.b1', '16.f1.b1'], 'contains': ['64.a1.a1', '96.a1.b1'], 'core': '32.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3603, 8561, 9268, 8591, 3032, 3087, 2484, 2512], 'generators': [100, 64], 'label': '192.711.32.a1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1.b1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '96.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.b1', 'projective_image': '96.118', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.7', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363276
      {'ambient': '192.711', 'aut_centralizer_order': 1536, 'aut_label': '32.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.g1.a1', '16.g1.b1', '16.g1.c1', '16.g1.d1'], 'contains': ['64.a1.a1', '96.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5226, 7367, 6286, 7431, 4867, 3801, 6096, 3269], 'generators': [96, 64], 'label': '192.711.32.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'normal_contains': ['64.a1.a1', '96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '96.141', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363277
      {'ambient': '192.711', 'aut_centralizer_order': 96, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '16.d2.a1', '16.g1.a1'], 'contains': ['64.a1.a1', '96.c1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4482, -1, 8437, -1, 3706, -1, 2982, -1], 'generators': [1, 64], 'label': '192.711.32.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.a1', 'old_label': '32.c1.a1', 'projective_image': '192.711', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363278
      {'ambient': '192.711', 'aut_centralizer_order': 96, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '8.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.d2.b1', '16.g1.b1'], 'contains': ['64.a1.a1', '96.c1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4482, -1, 1905, -1, 3706, -1, 4589, -1], 'generators': [73, 64], 'label': '192.711.32.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.b1', 'old_label': '32.c1.b1', 'projective_image': '192.711', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363279
      {'ambient': '192.711', 'aut_centralizer_order': 96, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '16.d2.a1', '16.g1.c1'], 'contains': ['64.a1.a1', '96.c1.c1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4482, -1, 8056, -1, 3706, -1, 2643, -1], 'generators': [5, 64], 'label': '192.711.32.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.a1', 'old_label': '32.c1.c1', 'projective_image': '192.711', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363280
      {'ambient': '192.711', 'aut_centralizer_order': 96, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '8.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.d2.b1', '16.g1.d1'], 'contains': ['64.a1.a1', '96.c1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4482, -1, 1618, -1, 3706, -1, 4929, -1], 'generators': [77, 64], 'label': '192.711.32.c1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.b1', 'old_label': '32.c1.d1', 'projective_image': '192.711', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363281
      {'ambient': '192.711', 'aut_centralizer_order': 1536, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.e1.a1', '24.e1.b1', '24.f1.a1', '24.f1.b1', '24.g1.a1', '24.g1.b1'], 'contains': ['96.a1.a1', '96.a1.b1', '96.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3859, 6900, 5988, 7329, 4043, 4564, 3152, 3673], 'generators': [4, 96], 'label': '192.711.48.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['96.b1.a1', '96.a1.a1', '96.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '48.38', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.38', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363282
      {'ambient': '192.711', 'aut_centralizer_order': 48, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.46', 'aut_weyl_index': 96, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.b1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.c1.b1', '8.c1.d1', '8.f1.b1', '8.h1.b1', '12.a1.b1'], 'core': '4.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5513, 4599, 2567, 5736, 5501, 6695, 7206, 3316], 'generators': [73, 96, 4, 48, 64], 'label': '192.711.4.a1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.b1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.b1', '8.c1.d1', '12.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.b1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363283
      {'ambient': '192.711', 'aut_centralizer_order': 1536, 'aut_label': '48.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.h1.a1', '24.h1.b1', '24.i1.a1'], 'contains': ['96.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6207, 5652, 6501, 6673, 5939, 5327, 6326, 4077], 'generators': [52], 'label': '192.711.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.b1.a1', '24.a1.a1'], 'normal_contains': ['96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '96.141', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363284
      {'ambient': '192.711', 'aut_centralizer_order': 1536, 'aut_label': '48.c1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.a1', '24.b1.a1', '24.b1.b1', '24.b1.c1', '24.b1.d1', '24.c1.a1', '24.c1.b1'], 'contains': ['96.b1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7109, 4631, 4343, 4115, 6885, 6041, 8290, 7244], 'generators': [48], 'label': '192.711.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.c1.a1', '24.a1.a1', '24.b1.b1', '24.b1.d1', '24.b1.c1', '24.b1.a1', '24.c1.b1', '24.c1.a1'], 'normal_contains': ['96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '96.141', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.7', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363285
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '4.g2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.d1.a1', '24.d1.a2', '24.e1.b1'], 'contains': ['96.a1.a1', '96.c1.b1', '96.c1.d1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2846, -1, 1066, -1, 3369, -1, 4419, -1], 'generators': [73, 4], 'label': '192.711.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.b1', 'old_label': '48.d1.a1', 'projective_image': '96.118', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363286
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '4.g2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.d1.b1', '24.d1.b2', '24.e1.a1'], 'contains': ['96.a1.b1', '96.c1.a1', '96.c1.c1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2846, -1, 9064, -1, 3369, -1, 2314, -1], 'generators': [1, 100], 'label': '192.711.48.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.a1', 'old_label': '48.d1.b1', 'projective_image': '96.118', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363287
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '48.d2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '4.g2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d2.a1', '24.e1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '96.c1.c1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3491, -1, 7852, -1, 4402, -1, 2812, -1], 'generators': [1, 4], 'label': '192.711.48.d2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.a1', 'old_label': '48.d2.a1', 'projective_image': '96.118', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363288
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '48.d2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '4.g2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d2.b1', '24.e1.b1'], 'contains': ['96.a1.b1', '96.c1.b1', '96.c1.d1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3491, -1, 2191, -1, 4402, -1, 4759, -1], 'generators': [73, 100], 'label': '192.711.48.d2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.b1', 'old_label': '48.d2.b1', 'projective_image': '96.118', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d2.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363289
      {'ambient': '192.711', 'aut_centralizer_order': 128, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '6.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.d1.a1', '24.d1.a2', '24.f1.a1'], 'contains': ['96.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [606, -1, 1477, -1, 2647, -1, 3481, -1], 'generators': [2], 'label': '192.711.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '48.e1.a1', 'projective_image': '96.118', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363290
      {'ambient': '192.711', 'aut_centralizer_order': 128, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '24.d1.b1', '24.d1.b2', '24.f1.b1'], 'contains': ['96.a1.b1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [606, -1, 8812, -1, 2647, -1, 1069, -1], 'generators': [50], 'label': '192.711.48.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.e1.b1', 'projective_image': '96.118', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363291
      {'ambient': '192.711', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '12.d2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.d1.a1', '24.d1.a2', '24.g1.b1'], 'contains': ['96.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1506, -1, 1319, -1, 1561, -1, 3708, -1], 'generators': [11], 'label': '192.711.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d2.b1', 'old_label': '48.f1.a1', 'projective_image': '96.118', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363292
      {'ambient': '192.711', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '12.d2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.b1', '24.d1.b1', '24.d1.b2', '24.g1.a1'], 'contains': ['96.a1.b1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1506, -1, 8648, -1, 1561, -1, 866, -1], 'generators': [3], 'label': '192.711.48.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d2.a1', 'old_label': '48.f1.b1', 'projective_image': '96.118', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363293
      {'ambient': '192.711', 'aut_centralizer_order': 32, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '96.209', 'aut_weyl_index': 32, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.e1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4123, 9354, 6060, 9845, 4836, 738, 3896, 391], 'generators': [2, 64, 48, 4, 96], 'label': '192.711.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.b1', '2.a1.a1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 20363294
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '4.g2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.b1.a1', '24.e1.a1', '24.h1.a1'], 'contains': ['96.b1.a1', '96.c1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4791, -1, 7185, -1, 5204, -1, 5648, -1], 'generators': [1, 96], 'label': '192.711.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.g1.a1', 'projective_image': '96.141', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363295
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '4.g2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.b1', '24.b1.b1', '24.e1.b1', '24.h1.b1'], 'contains': ['96.b1.a1', '96.c1.b1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4791, -1, 2957, -1, 5204, -1, 6685, -1], 'generators': [73, 96], 'label': '192.711.48.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '48.g1.b1', 'projective_image': '96.141', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363296
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '4.g2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.c1', '24.b1.c1', '24.e1.a1', '24.h1.a1'], 'contains': ['96.b1.a1', '96.c1.c1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4791, -1, 7457, -1, 5204, -1, 5408, -1], 'generators': [5, 96], 'label': '192.711.48.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.g1.c1', 'projective_image': '96.141', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363297
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '4.g2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.d1', '24.b1.d1', '24.e1.b1', '24.h1.b1'], 'contains': ['96.b1.a1', '96.c1.d1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4791, -1, 2775, -1, 5204, -1, 6985, -1], 'generators': [77, 96], 'label': '192.711.48.g1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '48.g1.d1', 'projective_image': '96.141', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363298
      {'ambient': '192.711', 'aut_centralizer_order': 1536, 'aut_label': '64.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1536, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.a1.b1', '32.b1.a1', '32.c1.a1', '32.c1.b1', '32.c1.c1', '32.c1.d1'], 'contains': ['192.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4438, 8561, 6358, 8299, 3706, 3464, 3481, 2891], 'generators': [64], 'label': '192.711.64.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.b1.a1', '32.a1.a1', '32.a1.b1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '192.711', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.39', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363299
      {'ambient': '192.711', 'aut_centralizer_order': 1536, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3072, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.d1.a1', '48.d2.a1', '48.e1.a1', '48.f1.a1'], 'contains': ['192.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3222, 7520, 1477, 7575, 3369, 4177, 3322, 3647], 'generators': [4], 'label': '192.711.96.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '96.118', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.118', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363300
      {'ambient': '192.711', 'aut_centralizer_order': 1536, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3072, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.b1', '48.a1.a1', '48.d1.b1', '48.d2.b1', '48.e1.b1', '48.f1.b1'], 'contains': ['192.a1.a1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3222, 7520, 8562, 7986, 3369, 4177, 2484, 3269], 'generators': [100], 'label': '192.711.96.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1.b1', 'normal_contained_in': ['32.a1.b1', '48.a1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.b1', 'projective_image': '96.118', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.118', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363301
      {'ambient': '192.711', 'aut_centralizer_order': 3072, 'aut_label': '96.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3072, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.g1.a1', '48.g1.b1', '48.g1.c1', '48.g1.d1'], 'contains': ['192.a1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5091, 6249, 6154, 6986, 5033, 4891, 6096, 4025], 'generators': [96], 'label': '192.711.96.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.b1.a1', 'normal_contained_in': ['32.b1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.b1.a1', 'projective_image': '96.141', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.141', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363302
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3072, 'centralizer': '4.g2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.d1.b1', '48.d2.a1', '48.g1.a1'], 'contains': ['192.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4141, -1, 7727, -1, 4021, -1, 2982, -1], 'generators': [1], 'label': '192.711.96.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.a1', 'old_label': '96.c1.a1', 'projective_image': '192.711', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363303
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3072, 'centralizer': '4.g2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.b1', '48.d1.a1', '48.d2.b1', '48.g1.b1'], 'contains': ['192.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4141, -1, 2268, -1, 4021, -1, 4589, -1], 'generators': [73], 'label': '192.711.96.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.b1', 'old_label': '96.c1.b1', 'projective_image': '192.711', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363304
      {'ambient': '192.711', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.209', 'aut_weyl_index': 32, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.b1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.g1.a1', '12.f1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4764, 5988, 7288, 9030, 3610, 3811, 4679, 2644], 'generators': [3, 64, 48, 100, 96], 'label': '192.711.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
    • id: 20363305
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3072, 'centralizer': '4.g2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.c1', '48.d1.b1', '48.d2.a1', '48.g1.c1'], 'contains': ['192.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4141, -1, 7894, -1, 4021, -1, 2812, -1], 'generators': [5], 'label': '192.711.96.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.a1', 'old_label': '96.c1.c1', 'projective_image': '192.711', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363306
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3072, 'centralizer': '4.g2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.d1', '48.d1.a1', '48.d2.b1', '48.g1.d1'], 'contains': ['192.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4141, -1, 2110, -1, 4021, -1, 4759, -1], 'generators': [77], 'label': '192.711.96.c1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.b1', 'old_label': '96.c1.d1', 'projective_image': '192.711', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363307
      {'ambient': '192.711', 'aut_centralizer_order': None, 'aut_label': '192.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': ['64.a1.a1', '96.a1.a1', '96.a1.b1', '96.b1.a1', '96.c1.a1', '96.c1.b1', '96.c1.c1', '96.c1.d1'], 'contains': [], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4289, 7520, 6216, 7780, 3864, 4177, 3402, 3458], 'generators': [], 'label': '192.711.192.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['64.a1.a1', '96.b1.a1', '96.a1.a1', '96.a1.b1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '192.711', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 20363308
      {'ambient': '192.711', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.209', 'aut_weyl_index': 32, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.g1.b1', '12.f1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4764, 5988, 4503, 8351, 3610, 3811, 4942, 2019], 'generators': [11, 64, 48, 4, 96], 'label': '192.711.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
    • id: 20363309
      {'ambient': '192.711', 'aut_centralizer_order': 96, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 96, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.d1.b1', '12.b1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8534, 2970, 4813, 6593, 8483, 5208, 7875, 4103], 'generators': [4, 96, 24, 64, 48], 'label': '192.711.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.d1.b1', '8.d1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '48.38', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 20363310
      {'ambient': '192.711', 'aut_centralizer_order': 32, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '96.209', 'aut_weyl_index': 32, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.b1.b1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.i1.a1', '12.g1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7454, 7542, 6675, 7534, 6574, 2393, 6476, 1268], 'generators': [10, 64, 48, 52, 96], 'label': '192.711.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.b1', '2.b1.a1', '2.d1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 20363311
      {'ambient': '192.711', 'aut_centralizer_order': 12, 'aut_label': '4.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '64.254', 'aut_weyl_index': 48, 'centralizer': '16.a1.a1', 'complements': ['48.e1.a1', '48.e1.b1', '48.f1.b1', '48.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.c1.a1', '8.c1.b1', '8.d1.a1', '12.c1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9834, 1341, 2868, 3391, 9740, 8053, 8206, 7049], 'generators': [1, 96, 24, 64, 144], 'label': '192.711.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.c1.b1', '8.c1.a1', '8.d1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '96.141', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363312
      {'ambient': '192.711', 'aut_centralizer_order': 12, 'aut_label': '4.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '64.254', 'aut_weyl_index': 48, 'centralizer': '16.a1.a1', 'complements': ['48.e1.a1', '48.e1.b1', '48.f1.b1', '48.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.c1.a1', '8.c1.d1', '8.d1.b1', '12.c1.b1'], 'core': '4.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9834, 1341, 4137, 1827, 9740, 8053, 9514, 4891], 'generators': [1, 96, 28, 64, 144], 'label': '192.711.4.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.f1.b1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.c1.d1', '8.c1.a1', '8.d1.b1', '12.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.b1', 'projective_image': '96.141', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363313
      {'ambient': '192.711', 'aut_centralizer_order': 12, 'aut_label': '4.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '64.254', 'aut_weyl_index': 48, 'centralizer': '16.a1.a1', 'complements': ['48.e1.a1', '48.e1.b1', '48.f1.a1', '48.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.c1.b1', '8.c1.c1', '8.d1.b1', '12.c1.c1'], 'core': '4.f1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9834, 1341, 3837, 4955, 9740, 8053, 8698, 6330], 'generators': [73, 96, 28, 64, 144], 'label': '192.711.4.f1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.f1.c1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.c1.b1', '8.c1.c1', '8.d1.b1', '12.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.c1', 'projective_image': '96.141', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363314
      {'ambient': '192.711', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 8, 'centralizer': '48.a1.a1', 'complements': ['96.c1.b1', '96.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.g1.a1', '4.g2.a1', '6.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4123, 9094, 7288, 9845, 4170, 2156, 3896, 2954], 'generators': [1, 64, 96, 2, 48, 4], 'label': '192.711.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '48.38', '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': '48.38'}
    • id: 20363315
      {'ambient': '192.711', 'aut_centralizer_order': 12, 'aut_label': '4.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '64.254', 'aut_weyl_index': 48, 'centralizer': '16.a1.a1', 'complements': ['48.e1.a1', '48.e1.b1', '48.f1.b1', '48.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.c1.c1', '8.c1.d1', '8.d1.a1', '12.c1.d1'], 'core': '4.f1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9834, 1341, 3167, 2608, 9740, 8053, 9088, 7769], 'generators': [5, 96, 24, 64, 144], 'label': '192.711.4.f1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.f1.d1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.c1.d1', '8.c1.c1', '8.d1.a1', '12.c1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.d1', 'projective_image': '96.141', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363316
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.230', 'aut_weyl_index': 32, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '8.g1.a1', '12.d1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2671, -1, 7865, -1, 3089, -1, 2223, -1], 'generators': [1, 64, 2, 4, 96], 'label': '192.711.4.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 20363317
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.230', 'aut_weyl_index': 32, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.b1.b1', '8.f1.b1', '8.g1.b1', '12.d1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2671, -1, 1850, -1, 3089, -1, 3258, -1], 'generators': [73, 64, 50, 100, 96], 'label': '192.711.4.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.g1.b1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 20363318
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '4.g2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.230', 'aut_weyl_index': 32, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.b1', '8.e1.b1', '8.e1.b2', '8.f1.a1', '8.g1.a1', '12.d2.a1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1564, -1, 9031, -1, 2121, -1, 1248, -1], 'generators': [1, 64, 50, 96, 100], 'label': '192.711.4.g2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.g2.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g2.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 20363319
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '4.g2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.230', 'aut_weyl_index': 32, 'centralizer': '24.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.e1.a2', '8.f1.b1', '8.g1.b1', '12.d2.b1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1564, -1, 933, -1, 2121, -1, 4289, -1], 'generators': [73, 64, 2, 96, 4], 'label': '192.711.4.g2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.g2.b1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g2.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 20363320
      {'ambient': '192.711', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.1735', 'aut_weyl_index': 24, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.a1.b1', '12.b1.a1', '12.c1.a1', '12.c1.b1', '12.c1.c1', '12.c1.d1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8987, 646, 4574, 1238, 9140, 9411, 7544, 8520], 'generators': [1, 4, 24], 'label': '192.711.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['12.a1.b1', '12.a1.a1', '12.b1.a1', '12.c1.c1', '12.c1.a1', '12.c1.d1', '12.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '48.38', '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': '16.11'}
    • id: 20363321
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.261', 'aut_weyl_index': 48, 'centralizer': '24.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.d2.a1', '12.e1.a1', '12.f1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3666, -1, 7462, -1, 4170, -1, 3561, -1], 'generators': [1, 2, 48], 'label': '192.711.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
    • id: 20363322
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.261', 'aut_weyl_index': 48, 'centralizer': '24.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.d1.b1', '12.d2.b1', '12.e1.a1', '12.f1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3666, -1, 3477, -1, 4170, -1, 5225, -1], 'generators': [73, 2, 48], 'label': '192.711.6.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
    • id: 20363323
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.261', 'aut_weyl_index': 48, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.f1.b1', '12.g1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6450, -1, 6702, -1, 6005, -1, 5681, -1], 'generators': [1, 10], 'label': '192.711.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363324
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.261', 'aut_weyl_index': 48, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.f1.a1', '12.g1.a1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6450, -1, 5668, -1, 6005, -1, 6189, -1], 'generators': [73, 10], 'label': '192.711.6.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.b1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363325
      {'ambient': '192.711', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 8, 'centralizer': '48.a1.a1', 'complements': ['96.c1.a1', '96.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.b1.a1', '4.c1.b1', '4.g1.b1', '4.g2.b1', '6.b1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4123, 9094, 3477, 7209, 4170, 2156, 4913, 1137], 'generators': [73, 64, 96, 2, 48, 4], 'label': '192.711.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.b1.a1', '4.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '48.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
    • id: 20363326
      {'ambient': '192.711', 'aut_centralizer_order': 16, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.202', 'aut_weyl_index': 48, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '12.g1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7937, -1, 5372, -1, 7734, -1, 6858, -1], 'generators': [2, 24], 'label': '192.711.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
    • id: 20363327
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1735', 'aut_weyl_index': 24, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.f1.a1', '12.f1.b1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6862, -1, 5075, -1, 7143, -1, 5478, -1], 'generators': [3, 24], 'label': '192.711.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363328
      {'ambient': '192.711', 'aut_centralizer_order': 384, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 384, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.a1.b1', '4.b1.a1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '24.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6495, 6347, 6530, 7682, 5746, 3553, 6189, 2134], 'generators': [4, 48, 64, 96], 'label': '192.711.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.b1', '4.a1.a1', '4.b1.a1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.e1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '48.38', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 20363329
      {'ambient': '192.711', 'aut_centralizer_order': 64, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.g1.a1', '4.g2.b1'], 'contains': ['16.a1.a1', '16.e1.a1', '24.f1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1466, 8561, 5668, 9778, 2476, 1462, 2581, 391], 'generators': [2, 96, 4, 64], 'label': '192.711.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 20363330
      {'ambient': '192.711', 'aut_centralizer_order': 64, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.g1.b1', '4.g2.a1'], 'contains': ['16.a1.a1', '16.e1.b1', '24.f1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1466, 8561, 7308, 8694, 2476, 1462, 1617, 1268], 'generators': [50, 96, 100, 64], 'label': '192.711.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 20363331
      {'ambient': '192.711', 'aut_centralizer_order': 48, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 192, 'centralizer': '16.a1.a1', 'complements': ['24.d1.a1', '24.d1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.f1.b1'], 'contains': ['16.c1.a1', '16.g1.a1', '24.b1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7341, 4718, 4418, 3368, 7003, 7270, 7932, 5548], 'generators': [1, 48, 64, 96], 'label': '192.711.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1', '4.f1.a1', '4.f1.b1'], 'normal_contains': ['16.c1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '96.141', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363332
      {'ambient': '192.711', 'aut_centralizer_order': 48, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 192, 'centralizer': '16.a1.a1', 'complements': ['24.d1.b1', '24.d1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.f1.a1', '4.f1.c1'], 'contains': ['16.c1.a1', '16.g1.b1', '24.b1.b1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7341, 4718, 2042, 6096, 7003, 7270, 8396, 4109], 'generators': [73, 48, 64, 96], 'label': '192.711.8.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': ['4.a1.b1', '4.f1.c1', '4.f1.a1'], 'normal_contains': ['16.c1.a1', '24.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.b1', 'projective_image': '96.141', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363333
      {'ambient': '192.711', 'aut_centralizer_order': 48, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 192, 'centralizer': '16.a1.a1', 'complements': ['24.d1.a1', '24.d1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.c1', '4.f1.d1'], 'contains': ['16.c1.a1', '16.g1.c1', '24.b1.c1'], 'core': '8.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7341, 4718, 3588, 4590, 7003, 7270, 8698, 6734], 'generators': [5, 48, 64, 96], 'label': '192.711.8.c1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.c1', 'normal_contained_in': ['4.a1.a1', '4.f1.c1', '4.f1.d1'], 'normal_contains': ['16.c1.a1', '24.b1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.c1', 'projective_image': '96.141', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363334
      {'ambient': '192.711', 'aut_centralizer_order': 48, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 192, 'centralizer': '16.a1.a1', 'complements': ['24.d1.b1', '24.d1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.f1.b1', '4.f1.d1'], 'contains': ['16.c1.a1', '16.g1.d1', '24.b1.d1'], 'core': '8.c1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7341, 4718, 2343, 2363, 7003, 7270, 9514, 2922], 'generators': [77, 48, 64, 96], 'label': '192.711.8.c1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.d1', 'normal_contained_in': ['4.a1.b1', '4.f1.d1', '4.f1.b1'], 'normal_contains': ['16.c1.a1', '24.b1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.d1', 'projective_image': '96.141', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363335
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '8.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 384, 'centralizer': '4.d1.a1', 'complements': ['24.d1.b1', '24.d1.b2', '24.d1.a1', '24.d1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.f1.a1', '4.f1.d1'], 'contains': ['16.c1.a1', '24.c1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9668, 3079, 3007, 5451, 9091, 4802, 9265, 6141], 'generators': [24, 64, 48, 96], 'label': '192.711.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.d1.a1', '4.f1.a1', '4.f1.d1'], 'normal_contains': ['16.c1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '96.141', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 20363336
      {'ambient': '192.711', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 8, 'centralizer': '48.a1.a1', 'complements': ['96.c1.b1', '96.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.b1', '4.e1.a1', '6.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5791, 5923, 6370, 5205, 5847, 3870, 5681, 3862], 'generators': [1, 64, 96, 10, 52, 144], 'label': '192.711.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.b1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '48.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
    • id: 20363337
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '8.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 384, 'centralizer': '4.d1.a1', 'complements': ['24.d1.b1', '24.d1.b2', '24.d1.a1', '24.d1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.f1.b1', '4.f1.c1'], 'contains': ['16.c1.a1', '24.c1.b1'], 'core': '8.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9668, 3079, 4086, 6958, 9091, 4802, 9923, 3515], 'generators': [28, 64, 48, 96], 'label': '192.711.8.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': ['4.d1.a1', '4.f1.c1', '4.f1.b1'], 'normal_contains': ['16.c1.a1', '24.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.b1', 'projective_image': '96.141', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 20363338
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 128, 'centralizer': '24.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g2.b1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.f1.a1', '24.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [529, -1, 163, -1, 326, -1, 3748, -1], 'generators': [73, 2, 4, 64], 'label': '192.711.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.b1', 'old_label': '8.e1.a1', 'projective_image': '96.118', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 20363339
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 128, 'centralizer': '24.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g2.b1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.f1.a1', '24.d1.a2'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [529, -1, 530, -1, 326, -1, 4117, -1], 'generators': [73, 98, 4, 64], 'label': '192.711.8.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.b1', 'old_label': '8.e1.a2', 'projective_image': '96.118', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 20363340
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 128, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g2.a1'], 'contains': ['16.d1.b1', '16.e1.b1', '16.f1.b1', '24.d1.b1'], 'core': '32.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [529, -1, 9470, -1, 326, -1, 533, -1], 'generators': [1, 146, 100, 64], 'label': '192.711.8.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.a1', 'old_label': '8.e1.b1', 'projective_image': '96.118', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 20363341
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 128, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g2.a1'], 'contains': ['16.d1.b1', '16.e1.b1', '16.f1.b1', '24.d1.b2'], 'core': '32.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [529, -1, 9837, -1, 326, -1, 164, -1], 'generators': [1, 50, 100, 64], 'label': '192.711.8.e1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g2.a1', 'old_label': '8.e1.b2', 'projective_image': '96.118', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 20363342
      {'ambient': '192.711', 'aut_centralizer_order': 96, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 384, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.g1.a1', '4.g2.a1'], 'contains': ['16.a1.a1', '16.d1.b1', '16.d2.a1', '16.g1.a1', '16.g1.c1', '24.e1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3451, -1, 9031, -1, 3680, -1, 2223, -1], 'generators': [1, 4, 96, 64], 'label': '192.711.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 20363343
      {'ambient': '192.711', 'aut_centralizer_order': 96, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 384, 'centralizer': '8.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.g1.b1', '4.g2.b1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.d2.b1', '16.g1.b1', '16.g1.d1', '24.e1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3451, -1, 885, -1, 3680, -1, 5026, -1], 'generators': [73, 4, 96, 64], 'label': '192.711.8.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.f1.b1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 20363344
      {'ambient': '192.711', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 128, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.g1.a1', '4.g2.a1'], 'contains': ['16.a1.a1', '16.f1.b1', '24.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2215, -1, 8676, -1, 1057, -1, 1248, -1], 'generators': [3, 96, 100, 64], 'label': '192.711.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 20363345
      {'ambient': '192.711', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 128, 'centralizer': '24.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '4.g1.b1', '4.g2.b1'], 'contains': ['16.a1.a1', '16.f1.a1', '24.g1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2215, -1, 1323, -1, 1057, -1, 2949, -1], 'generators': [11, 96, 4, 64], 'label': '192.711.8.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.g1.b1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 20363346
      {'ambient': '192.711', 'aut_centralizer_order': 48, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 192, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.b1.a1', '16.g1.a1', '16.g1.c1', '24.h1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5307, -1, 8259, -1, 5090, -1, 5555, -1], 'generators': [1, 52, 64, 96], 'label': '192.711.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '96.141', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
    • id: 20363347
      {'ambient': '192.711', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 8, 'centralizer': '48.a1.a1', 'complements': ['96.c1.a1', '96.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.c1.a1', '4.e1.a1', '6.c1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5791, 5923, 5979, 6221, 5847, 3870, 6277, 2045], 'generators': [73, 64, 96, 10, 52, 48], 'label': '192.711.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.c1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '48.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
    • id: 20363348
      {'ambient': '192.711', 'aut_centralizer_order': 48, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 192, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1'], 'contains': ['16.b1.a1', '16.g1.b1', '16.g1.d1', '24.h1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5307, -1, 1657, -1, 5090, -1, 7025, -1], 'generators': [73, 52, 64, 96], 'label': '192.711.8.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.h1.b1', 'projective_image': '96.141', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
    • id: 20363349
      {'ambient': '192.711', 'aut_centralizer_order': 64, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 128, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.b1.a1', '24.i1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8027, -1, 8008, -1, 7506, -1, 6771, -1], 'generators': [10, 52, 96, 64], 'label': '192.711.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.i1.a1', 'projective_image': '96.141', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 20363350
      {'ambient': '192.711', 'aut_centralizer_order': 96, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 192, 'centralizer': '8.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.b1.c1', '24.e1.a1', '24.h1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6042, 3676, 7040, 2203, 6403, 8627, 5858, 8551], 'generators': [1, 4, 48], 'label': '192.711.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.c1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '48.38', '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': '8.3'}
    • id: 20363351
      {'ambient': '192.711', 'aut_centralizer_order': 96, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 192, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '6.a1.a1', '6.b1.b1', '6.c1.b1'], 'contains': ['24.a1.a1', '24.b1.b1', '24.b1.d1', '24.e1.b1', '24.h1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6042, 3676, 3492, 4087, 6403, 8627, 7328, 4828], 'generators': [73, 4, 48], 'label': '192.711.12.a1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.b1', 'normal_contained_in': ['4.a1.b1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.b1', '24.b1.d1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.b1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
    • id: 20363352
      {'ambient': '192.711', 'aut_centralizer_order': 192, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 192, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.a1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.c1.b1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8789, 1776, 5310, 5303, 8601, 5912, 7630, 7453], 'generators': [4, 24], 'label': '192.711.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.d1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.c1.b1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '48.38', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 20363353
      {'ambient': '192.711', 'aut_centralizer_order': 24, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 96, 'centralizer': '16.a1.a1', 'complements': ['16.e1.a1', '16.e1.b1', '16.f1.b1', '16.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '24.b1.b1', '24.c1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9425, 646, 2937, 2859, 9442, 9668, 8164, 9480], 'generators': [1, 24], 'label': '192.711.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.f1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.b1', '24.b1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '96.141', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363354
      {'ambient': '192.711', 'aut_centralizer_order': 24, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 96, 'centralizer': '16.a1.a1', 'complements': ['16.e1.a1', '16.e1.b1', '16.f1.b1', '16.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.a1.a1'], 'contains': ['24.b1.a1', '24.b1.d1', '24.c1.b1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9425, 646, 4464, 155, 9442, 9668, 9746, 8000], 'generators': [1, 28], 'label': '192.711.12.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.c1.b1', 'normal_contained_in': ['4.f1.b1', '6.a1.a1'], 'normal_contains': ['24.b1.d1', '24.b1.a1', '24.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.b1', 'projective_image': '96.141', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.c1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363355
      {'ambient': '192.711', 'aut_centralizer_order': 24, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 96, 'centralizer': '16.a1.a1', 'complements': ['16.e1.a1', '16.e1.b1', '16.f1.a1', '16.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.c1', '6.a1.a1'], 'contains': ['24.b1.b1', '24.b1.c1', '24.c1.b1'], 'core': '12.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9425, 646, 4139, 3270, 9442, 9668, 8930, 9102], 'generators': [73, 28], 'label': '192.711.12.c1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.c1.c1', 'normal_contained_in': ['4.f1.c1', '6.a1.a1'], 'normal_contains': ['24.b1.b1', '24.b1.c1', '24.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.c1', 'projective_image': '96.141', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.c1.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363356
      {'ambient': '192.711', 'aut_centralizer_order': 24, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 96, 'centralizer': '16.a1.a1', 'complements': ['16.e1.a1', '16.e1.b1', '16.f1.b1', '16.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.d1', '6.a1.a1'], 'contains': ['24.b1.c1', '24.b1.d1', '24.c1.a1'], 'core': '12.c1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9425, 646, 3096, 782, 9442, 9668, 9088, 9858], 'generators': [5, 24], 'label': '192.711.12.c1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.c1.d1', 'normal_contained_in': ['4.f1.d1', '6.a1.a1'], 'normal_contains': ['24.b1.d1', '24.b1.c1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.d1', 'projective_image': '96.141', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.c1.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363357
      {'ambient': '192.711', 'aut_centralizer_order': 16, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 192, 'centralizer': '24.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.b1.a1'], 'contains': ['24.e1.a1', '24.f1.a1', '24.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2403, -1, 7314, -1, 3089, -1, 1925, -1], 'generators': [1, 2], 'label': '192.711.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.d1.a1', 'projective_image': '48.38', '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': '4.2'}
    • id: 20363358
      {'ambient': '192.711', 'aut_centralizer_order': 12, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.53342', 'aut_weyl_index': 12, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.a1.b1', '4.d1.a1', '4.f1.a1', '4.f1.b1', '4.f1.c1', '4.f1.d1', '6.a1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8534, 2297, 4137, 4172, 8483, 7180, 7875, 5616], 'generators': [1, 96, 144, 4, 24, 64], 'label': '192.711.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.a1.a1', '4.d1.a1', '4.f1.c1', '4.f1.a1', '4.f1.d1', '4.f1.b1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 20363359
      {'ambient': '192.711', 'aut_centralizer_order': 16, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 192, 'centralizer': '24.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '6.b1.b1'], 'contains': ['24.e1.b1', '24.f1.b1', '24.g1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2403, -1, 2484, -1, 3089, -1, 3258, -1], 'generators': [73, 50], 'label': '192.711.12.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '12.d1.b1', 'projective_image': '48.38', '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': '4.2'}
    • id: 20363360
      {'ambient': '192.711', 'aut_centralizer_order': 16, 'aut_label': '12.d2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 192, 'centralizer': '12.d2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g2.a1', '6.b1.a1'], 'contains': ['24.d1.b1', '24.d1.b2', '24.e1.a1', '24.f1.b1', '24.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1480, -1, 8529, -1, 1767, -1, 890, -1], 'generators': [1, 50, 96], 'label': '192.711.12.d2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.d2.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363361
      {'ambient': '192.711', 'aut_centralizer_order': 16, 'aut_label': '12.d2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 192, 'centralizer': '12.d2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g2.b1', '6.b1.b1'], 'contains': ['24.d1.a1', '24.d1.a2', '24.e1.b1', '24.f1.a1', '24.g1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1480, -1, 2102, -1, 1767, -1, 4474, -1], 'generators': [73, 2, 96], 'label': '192.711.12.d2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '12.d2.b1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363362
      {'ambient': '192.711', 'aut_centralizer_order': 64, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 192, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1', '6.b1.b1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.f1.a1', '24.f1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4231, -1, 5799, -1, 4608, -1, 3475, -1], 'generators': [2, 48], 'label': '192.711.12.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '48.38', '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': '4.2'}
    • id: 20363363
      {'ambient': '192.711', 'aut_centralizer_order': 32, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 192, 'centralizer': '24.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.c1.b1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.g1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4621, -1, 6621, -1, 4227, -1, 4750, -1], 'generators': [3, 48], 'label': '192.711.12.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
    • id: 20363364
      {'ambient': '192.711', 'aut_centralizer_order': 32, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 192, 'centralizer': '24.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.b1.b1', '6.c1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.g1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4621, -1, 5060, -1, 4227, -1, 5302, -1], 'generators': [11, 48], 'label': '192.711.12.f1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.b1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
    • id: 20363365
      {'ambient': '192.711', 'aut_centralizer_order': 64, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 192, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.c1.a1', '6.c1.b1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.i1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8009, -1, 6289, -1, 8006, -1, 6520, -1], 'generators': [10, 48], 'label': '192.711.12.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '48.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 20363366
      {'ambient': '192.711', 'aut_centralizer_order': 768, 'aut_label': '16.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 768, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.f1.a1', '8.f1.b1', '8.g1.a1', '8.g1.b1'], 'contains': ['32.a1.a1', '32.a1.b1', '32.b1.a1', '48.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4352, 8084, 6439, 8391, 4144, 2820, 2702, 2512], 'generators': [4, 96, 64], 'label': '192.711.16.a1.a1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normal_contains': ['32.b1.a1', '32.a1.a1', '32.a1.b1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '48.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 20363367
      {'ambient': '192.711', 'aut_centralizer_order': 768, 'aut_label': '16.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 768, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.h1.a1', '8.h1.b1', '8.i1.a1'], 'contains': ['32.b1.a1', '48.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6315, 6868, 6935, 7751, 5589, 3930, 6396, 3269], 'generators': [52, 64, 96], 'label': '192.711.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.b1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '96.141', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 20363368
      {'ambient': '192.711', 'aut_centralizer_order': 768, 'aut_label': '16.c1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 768, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '8.c1.c1', '8.c1.d1', '8.d1.a1', '8.d1.b1'], 'contains': ['32.b1.a1', '48.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7391, 5913, 3871, 6449, 6885, 4802, 8625, 4109], 'generators': [48, 64, 96], 'label': '192.711.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.c1.b1', '8.c1.d1', '8.c1.c1', '8.c1.a1', '8.d1.b1', '8.d1.a1'], 'normal_contains': ['32.b1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '96.141', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 20363369
      {'ambient': '192.711', 'aut_centralizer_order': 8, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.18491', 'aut_weyl_index': 8, 'centralizer': '24.a1.a1', 'complements': ['96.c1.a1', '96.c1.b1', '96.c1.c1', '96.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.e1.a1', '6.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7548, 7542, 5514, 9030, 7673, 738, 6606, 386], 'generators': [2, 64, 96, 24, 4, 48], 'label': '192.711.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '48.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}