Formats: - HTML - YAML - JSON - 2026-07-24T19:24:52.191727
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 168, 'aut_gen_orders': [6, 8, 4, 6, 6, 24], 'aut_gens': [[127370880, 87178291200, 174403768543, 93532721625, 174356582400, 40279680], [127370880, 87178291200, 93452525342, 174483987106, 93405312000, 87091200], [127370880, 87305662080, 174403780020, 93532688335, 174356582400, 87091200], [127370880, 6354391680, 93452487821, 174483973091, 93405312000, 87091200], [127370880, 6354391680, 174436817822, 93532709730, 174356582400, 40279680], [127370880, 87305662080, 93485513437, 174483959039, 93405312000, 40279680], [127370880, 180583603200, 174403759079, 93532688335, 174356582400, 87091200]], 'aut_group': None, 'aut_hash': 6220676842330196211, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 16128, 'aut_permdeg': 64, 'aut_perms': [39856665492537203659291685482026655970956316337824259638639291061163030229749547824433762, 56584121952136965796466200128185226907480523325432514690406585592530894316592553842106724, 37788484462878540447079462301302500078029286514698128035527153921741262080095648161550260, 66912879348074926445594415905114019605059751381443180509948353043019411057388496062795055, 63270650255060800573893643216374462378373436183147155266467420451502559611099945457819425, 31818558100670896300174934589950334359915188264004688230780559188775054063588020561231798], 'aut_phi_ratio': 7.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 3, 2, 1], [2, 6, 1, 1], [2, 21, 1, 2], [2, 42, 1, 1], [2, 56, 1, 1], [2, 63, 2, 1], [2, 126, 1, 1], [2, 168, 1, 1], [3, 2, 1, 1], [3, 56, 1, 1], [3, 112, 1, 1], [4, 42, 1, 2], [4, 56, 1, 1], [4, 84, 1, 1], [4, 126, 2, 1], [4, 168, 1, 1], [4, 252, 1, 1], [6, 2, 1, 1], [6, 4, 1, 1], [6, 42, 1, 2], [6, 56, 1, 1], [6, 84, 1, 1], [6, 112, 1, 4], [6, 168, 2, 1], [6, 224, 1, 2], [6, 336, 1, 2], [7, 48, 1, 1], [8, 84, 1, 4], [8, 252, 1, 4], [12, 84, 1, 2], [12, 112, 1, 2], [12, 168, 1, 1], [12, 224, 1, 1], [12, 336, 1, 1], [14, 48, 1, 1], [14, 48, 2, 1], [14, 144, 2, 2], [21, 96, 1, 1], [24, 168, 1, 4], [42, 96, 1, 1], [42, 96, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^3\\times \\SO(3,7)\\times S_3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 168, 'autcentquo_group': '2016.cw', 'autcentquo_hash': 117371359274444897, 'autcentquo_nilpotent': False, 'autcentquo_order': 2016, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times \\PGL(2,7)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 3, 2], [2, 6, 1], [2, 21, 2], [2, 42, 1], [2, 56, 1], [2, 63, 2], [2, 126, 1], [2, 168, 1], [3, 2, 1], [3, 56, 1], [3, 112, 1], [4, 42, 2], [4, 56, 1], [4, 84, 1], [4, 126, 2], [4, 168, 1], [4, 252, 1], [6, 2, 1], [6, 4, 1], [6, 42, 2], [6, 56, 1], [6, 84, 1], [6, 112, 4], [6, 168, 2], [6, 224, 2], [6, 336, 2], [7, 48, 1], [8, 84, 4], [8, 252, 4], [12, 84, 2], [12, 112, 2], [12, 168, 1], [12, 224, 1], [12, 336, 1], [14, 48, 3], [14, 144, 4], [21, 96, 1], [24, 168, 4], [42, 96, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '4032.ds', 'commutator_count': 1, 'commutator_label': '1008.884', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '168.42'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 75, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['1344.11295', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 3, 1, 2], [2, 6, 1, 1], [2, 21, 1, 2], [2, 42, 1, 1], [2, 56, 1, 1], [2, 63, 1, 2], [2, 126, 1, 1], [2, 168, 1, 1], [3, 2, 1, 1], [3, 56, 1, 1], [3, 112, 1, 1], [4, 42, 1, 2], [4, 56, 1, 1], [4, 84, 1, 1], [4, 126, 1, 2], [4, 168, 1, 1], [4, 252, 1, 1], [6, 2, 1, 1], [6, 4, 1, 1], [6, 42, 1, 2], [6, 56, 1, 1], [6, 84, 1, 1], [6, 112, 1, 4], [6, 168, 1, 2], [6, 224, 1, 2], [6, 336, 1, 2], [7, 48, 1, 1], [8, 84, 2, 2], [8, 252, 2, 2], [12, 84, 1, 2], [12, 112, 1, 2], [12, 168, 1, 1], [12, 224, 1, 1], [12, 336, 1, 1], [14, 48, 1, 1], [14, 48, 2, 1], [14, 144, 1, 2], [14, 144, 2, 1], [21, 96, 1, 1], [24, 168, 2, 2], [42, 96, 1, 1], [42, 96, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 9305856, 'exponent': 168, 'exponents_of_order': [7, 2, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[12, 0, 2], [24, 1, 1], [28, 1, 1], [32, 1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '4032.ds', 'hash': 4734243620999118076, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 168, 'inner_gen_orders': [1, 2, 6, 6, 3, 2], 'inner_gens': [[127370880, 87178291200, 174403768543, 93532721625, 174356582400, 40279680], [127370880, 87178291200, 93452498143, 174483992025, 93405312000, 40279680], [127370880, 180583603200, 174403768543, 93532688335, 174356582400, 87091200], [127370880, 6227020800, 174403768244, 93532721625, 174356582400, 40279680], [127370880, 180583603200, 174403768543, 93532721625, 174356582400, 40279680], [127370880, 87178291200, 174436790623, 93532721625, 174356582400, 40279680]], 'inner_hash': 5672968783997510635, 'inner_nilpotent': False, 'inner_order': 4032, 'inner_split': True, 'inner_tex': 'D_6\\times \\PGL(2,7)', 'inner_used': [2, 3, 4, 6], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 6], [4, 1], [6, 16], [7, 8], [8, 8], [12, 10], [14, 6], [16, 6], [24, 1], [28, 1], [32, 1]], 'label': '8064.cw', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'S3*GL(3,2):D4', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 64, 'number_characteristic_subgroups': 32, 'number_conjugacy_classes': 72, 'number_divisions': 63, 'number_normal_subgroups': 36, 'number_subgroup_autclasses': 1040, 'number_subgroup_classes': 1403, 'number_subgroups': 83398, 'old_label': None, 'order': 8064, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 575], [3, 170], [4, 896], [6, 2134], [7, 48], [8, 1344], [12, 1120], [14, 720], [21, 96], [24, 672], [42, 288]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[127370880, 87178291200, 174403768543, 93532721625, 174356582400, 87091200], [127370880, 87305662080, 174403768543, 93532721625, 174356582400, 40279680]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 1], [6, 4], [7, 8], [8, 8], [12, 10], [14, 6], [16, 6], [24, 4], [28, 1], [32, 1]], 'representations': {'Perm': {'d': 15, 'gens': [127370880, 87178291200, 174403768543, 93532721625, 174356582400, 40279680]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'S_3\\times \\GL(3,2):D_4', 'transitive_degree': 84, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    • id: 168401242
      {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 75, 'group_order': 8064, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
    • id: 168401253
      {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 75, 'group_order': 8064, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 127370880, 'size': 1}
    • id: 168401264
      {'aut_label': '2B', 'centralizer': '2.a1', 'counter': 3, 'group_counter': 75, 'group_order': 8064, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 40279680, 'size': 2}
    • id: 168401275
      {'aut_label': '2C', 'centralizer': '3.a1', 'counter': 4, 'group_counter': 75, 'group_order': 8064, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 6354391680, 'size': 3}
    • id: 168401286
      {'aut_label': '2C', 'centralizer': '3.a1', 'counter': 5, 'group_counter': 75, 'group_order': 8064, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 87178291200, 'size': 3}
    • id: 168401297
      {'aut_label': '2E', 'centralizer': '6.b1', 'counter': 6, 'group_counter': 75, 'group_order': 8064, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 180670694400, 'size': 6}
    • id: 168401308
      {'aut_label': '2F', 'centralizer': '21.a1', 'counter': 7, 'group_counter': 75, 'group_order': 8064, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 127376063, 'size': 21}
    • id: 168401312
      {'aut_label': '2G', 'centralizer': '21.a1', 'counter': 8, 'group_counter': 75, 'group_order': 8064, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 23449, 'size': 21}
    • id: 168401313
      {'aut_label': '2H', 'centralizer': '42.d1', 'counter': 9, 'group_counter': 75, 'group_order': 8064, 'label': '2H', 'order': 2, 'powers': [1, 9, 9], 'representative': 40284863, 'size': 42}
    • id: 168401243
      {'aut_label': '2I', 'centralizer': '56.i1', 'counter': 10, 'group_counter': 75, 'group_order': 8064, 'label': '2I', 'order': 2, 'powers': [1, 10, 10], 'representative': 123760693, 'size': 56}
    • id: 168401244
      {'aut_label': '2J', 'centralizer': '63.a1', 'counter': 11, 'group_counter': 75, 'group_order': 8064, 'label': '2J', 'order': 2, 'powers': [1, 11, 11], 'representative': 6227025983, 'size': 63}
    • id: 168401245
      {'aut_label': '2J', 'centralizer': '63.a1', 'counter': 12, 'group_counter': 75, 'group_order': 8064, 'label': '2K', 'order': 2, 'powers': [1, 12, 12], 'representative': 6354396863, 'size': 63}
    • id: 168401246
      {'aut_label': '2L', 'centralizer': '126.c1', 'counter': 13, 'group_counter': 75, 'group_order': 8064, 'label': '2L', 'order': 2, 'powers': [1, 13, 13], 'representative': 6267339225, 'size': 126}
    • id: 168401247
      {'aut_label': '2M', 'centralizer': '168.t1', 'counter': 14, 'group_counter': 75, 'group_order': 8064, 'label': '2M', 'order': 2, 'powers': [1, 14, 14], 'representative': 6230654700, 'size': 168}
    • id: 168401248
      {'aut_label': '3A', 'centralizer': '2.b1', 'counter': 15, 'group_counter': 75, 'group_order': 8064, 'label': '3A', 'order': 3, 'powers': [15, 1, 15], 'representative': 174356582400, 'size': 2}
    • id: 168401249
      {'aut_label': '3B', 'centralizer': '56.b1', 'counter': 16, 'group_counter': 75, 'group_order': 8064, 'label': '3B', 'order': 3, 'powers': [16, 1, 16], 'representative': 35799, 'size': 56}
    • id: 168401250
      {'aut_label': '3C', 'centralizer': '112.c1', 'counter': 17, 'group_counter': 75, 'group_order': 8064, 'label': '3C', 'order': 3, 'powers': [17, 1, 17], 'representative': 93405347799, 'size': 112}
    • id: 168401251
      {'aut_label': '4A', 'centralizer': '42.c1', 'counter': 18, 'group_counter': 75, 'group_order': 8064, 'label': '4A', 'order': 4, 'powers': [8, 18, 18], 'representative': 127403085, 'size': 42}
    • id: 168401252
      {'aut_label': '4B', 'centralizer': '42.c1', 'counter': 19, 'group_counter': 75, 'group_order': 8064, 'label': '4B', 'order': 4, 'powers': [8, 19, 19], 'representative': 12738, 'size': 42}
    • id: 168401254
      {'aut_label': '4C', 'centralizer': '56.j1', 'counter': 20, 'group_counter': 75, 'group_order': 8064, 'label': '4C', 'order': 4, 'powers': [2, 20, 20], 'representative': 80215093, 'size': 56}
    • id: 168401255
      {'aut_label': '4D', 'centralizer': '84.d1', 'counter': 21, 'group_counter': 75, 'group_order': 8064, 'label': '4D', 'order': 4, 'powers': [8, 21, 21], 'representative': 87123405, 'size': 84}
    • id: 168401256
      {'aut_label': '4E', 'centralizer': '126.b1', 'counter': 22, 'group_counter': 75, 'group_order': 8064, 'label': '4E', 'order': 4, 'powers': [8, 22, 22], 'representative': 6354426114, 'size': 126}
    • id: 168401257
      {'aut_label': '4E', 'centralizer': '126.b1', 'counter': 23, 'group_counter': 75, 'group_order': 8064, 'label': '4F', 'order': 4, 'powers': [8, 23, 23], 'representative': 180583610159, 'size': 126}
    • id: 168401258
      {'aut_label': '4G', 'centralizer': '168.u1', 'counter': 24, 'group_counter': 75, 'group_order': 8064, 'label': '4G', 'order': 4, 'powers': [2, 24, 24], 'representative': 87225484213, 'size': 168}
    • id: 168401259
      {'aut_label': '4H', 'centralizer': '252.b1', 'counter': 25, 'group_counter': 75, 'group_order': 8064, 'label': '4H', 'order': 4, 'powers': [8, 25, 25], 'representative': 87218596403, 'size': 252}
    • id: 168401260
      {'aut_label': '6A', 'centralizer': '2.b1', 'counter': 26, 'group_counter': 75, 'group_order': 8064, 'label': '6A', 'order': 6, 'powers': [15, 2, 26], 'representative': 93532682880, 'size': 2}
    • id: 168401261
      {'aut_label': '6B', 'centralizer': '4.a1', 'counter': 27, 'group_counter': 75, 'group_order': 8064, 'label': '6B', 'order': 6, 'powers': [15, 3, 27], 'representative': 93492403200, 'size': 4}
    • id: 168401262
      {'aut_label': '6C', 'centralizer': '42.g1', 'counter': 28, 'group_counter': 75, 'group_order': 8064, 'label': '6C', 'order': 6, 'powers': [15, 7, 28], 'representative': 93532688063, 'size': 42}
    • id: 168401263
      {'aut_label': '6D', 'centralizer': '42.g1', 'counter': 29, 'group_counter': 75, 'group_order': 8064, 'label': '6D', 'order': 6, 'powers': [15, 8, 29], 'representative': 174356605849, 'size': 42}
    • id: 168401265
      {'aut_label': '6E', 'centralizer': '56.b1', 'counter': 30, 'group_counter': 75, 'group_order': 8064, 'label': '6E', 'order': 6, 'powers': [16, 2, 30], 'representative': 127380567, 'size': 56}
    • id: 168401266
      {'aut_label': '6F', 'centralizer': '84.o1', 'counter': 31, 'group_counter': 75, 'group_order': 8064, 'label': '6F', 'order': 6, 'powers': [15, 9, 31], 'representative': 93445596863, 'size': 84}
    • id: 168401267
      {'aut_label': '6G', 'centralizer': '112.c1', 'counter': 32, 'group_counter': 75, 'group_order': 8064, 'label': '6G', 'order': 6, 'powers': [17, 2, 32], 'representative': 174483962967, 'size': 112}
    • id: 168401268
      {'aut_label': '6H', 'centralizer': '112.a1', 'counter': 33, 'group_counter': 75, 'group_order': 8064, 'label': '6H', 'order': 6, 'powers': [16, 3, 33], 'representative': 87095816, 'size': 112}
    • id: 168401269
      {'aut_label': '6I', 'centralizer': '112.t1', 'counter': 34, 'group_counter': 75, 'group_order': 8064, 'label': '6I', 'order': 6, 'powers': [15, 10, 34], 'representative': 174360211859, 'size': 112}
    • id: 168401270
      {'aut_label': '6J', 'centralizer': '112.j1', 'counter': 35, 'group_counter': 75, 'group_order': 8064, 'label': '6J', 'order': 6, 'powers': [16, 10, 35], 'representative': 3637631, 'size': 112}
    • id: 168401271
      {'aut_label': '6K', 'centralizer': '168.b1', 'counter': 36, 'group_counter': 75, 'group_order': 8064, 'label': '6K', 'order': 6, 'powers': [16, 4, 36], 'representative': 180711006821, 'size': 168}
    • id: 168401272
      {'aut_label': '6K', 'centralizer': '168.b1', 'counter': 37, 'group_counter': 75, 'group_order': 8064, 'label': '6L', 'order': 6, 'powers': [16, 5, 37], 'representative': 180583627966, 'size': 168}
    • id: 168401273
      {'aut_label': '6M', 'centralizer': '224.f1', 'counter': 38, 'group_counter': 75, 'group_order': 8064, 'label': '6M', 'order': 6, 'powers': [17, 10, 38], 'representative': 174480351131, 'size': 224}
    • id: 168401274
      {'aut_label': '6N', 'centralizer': '224.a1', 'counter': 39, 'group_counter': 75, 'group_order': 8064, 'label': '6N', 'order': 6, 'powers': [17, 3, 39], 'representative': 93445624164, 'size': 224}
    • id: 168401276
      {'aut_label': '6O', 'centralizer': '336.b1', 'counter': 40, 'group_counter': 75, 'group_order': 8064, 'label': '6O', 'order': 6, 'powers': [16, 6, 40], 'representative': 180670704087, 'size': 336}
    • id: 168401277
      {'aut_label': '6P', 'centralizer': '336.r1', 'counter': 41, 'group_counter': 75, 'group_order': 8064, 'label': '6P', 'order': 6, 'powers': [16, 14, 41], 'representative': 6230682996, 'size': 336}
    • id: 168401278
      {'aut_label': '7A', 'centralizer': '48.c1', 'counter': 42, 'group_counter': 75, 'group_order': 8064, 'label': '7A', 'order': 7, 'powers': [42, 42, 1], 'representative': 22521, 'size': 48}
    • id: 168401279
      {'aut_label': '8A1', 'centralizer': '84.w1', 'counter': 43, 'group_counter': 75, 'group_order': 8064, 'label': '8A1', 'order': 8, 'powers': [19, 44, 43], 'representative': 3657831, 'size': 84}
    • id: 168401280
      {'aut_label': '8A3', 'centralizer': '84.w1', 'counter': 44, 'group_counter': 75, 'group_order': 8064, 'label': '8A3', 'order': 8, 'powers': [19, 43, 44], 'representative': 3635571, 'size': 84}
    • id: 168401281
      {'aut_label': '8B1', 'centralizer': '84.x1', 'counter': 45, 'group_counter': 75, 'group_order': 8064, 'label': '8B1', 'order': 8, 'powers': [18, 46, 45], 'representative': 80204976, 'size': 84}
    • id: 168401282
      {'aut_label': '8B3', 'centralizer': '84.x1', 'counter': 46, 'group_counter': 75, 'group_order': 8064, 'label': '8B3', 'order': 8, 'powers': [18, 45, 46], 'representative': 47188701, 'size': 84}
    • id: 168401283
      {'aut_label': '8C1', 'centralizer': '252.q1', 'counter': 47, 'group_counter': 75, 'group_order': 8064, 'label': '8C1', 'order': 8, 'powers': [18, 48, 47], 'representative': 87258498345, 'size': 252}
    • id: 168401284
      {'aut_label': '8C3', 'centralizer': '252.q1', 'counter': 48, 'group_counter': 75, 'group_order': 8064, 'label': '8C3', 'order': 8, 'powers': [18, 47, 48], 'representative': 87225494885, 'size': 252}
    • id: 168401285
      {'aut_label': '8D1', 'centralizer': '252.p1', 'counter': 49, 'group_counter': 75, 'group_order': 8064, 'label': '8D1', 'order': 8, 'powers': [19, 50, 49], 'representative': 180587249988, 'size': 252}
    • id: 168401287
      {'aut_label': '8D3', 'centralizer': '252.p1', 'counter': 50, 'group_counter': 75, 'group_order': 8064, 'label': '8D3', 'order': 8, 'powers': [19, 49, 50], 'representative': 180587241424, 'size': 252}
    • id: 168401288
      {'aut_label': '12A', 'centralizer': '84.j1', 'counter': 51, 'group_counter': 75, 'group_order': 8064, 'label': '12A', 'order': 12, 'powers': [29, 19, 51], 'representative': 93405330076, 'size': 84}
    • id: 168401289
      {'aut_label': '12B', 'centralizer': '84.j1', 'counter': 52, 'group_counter': 75, 'group_order': 8064, 'label': '12B', 'order': 12, 'powers': [29, 18, 52], 'representative': 174483991590, 'size': 84}
    • id: 168401290
      {'aut_label': '12C', 'centralizer': '112.v1', 'counter': 53, 'group_counter': 75, 'group_order': 8064, 'label': '12C', 'order': 12, 'powers': [26, 20, 53], 'representative': 174403775413, 'size': 112}
    • id: 168401291
      {'aut_label': '12D', 'centralizer': '112.l1', 'counter': 54, 'group_counter': 75, 'group_order': 8064, 'label': '12D', 'order': 12, 'powers': [30, 20, 54], 'representative': 47174780, 'size': 112}
    • id: 168401292
      {'aut_label': '12E', 'centralizer': '168.i1', 'counter': 55, 'group_counter': 75, 'group_order': 8064, 'label': '12E', 'order': 12, 'powers': [29, 21, 55], 'representative': 93492440852, 'size': 168}
    • id: 168401293
      {'aut_label': '12F', 'centralizer': '224.l1', 'counter': 56, 'group_counter': 75, 'group_order': 8064, 'label': '12F', 'order': 12, 'powers': [32, 20, 56], 'representative': 93452498143, 'size': 224}
    • id: 168401294
      {'aut_label': '12G', 'centralizer': '336.t1', 'counter': 57, 'group_counter': 75, 'group_order': 8064, 'label': '12G', 'order': 12, 'powers': [30, 24, 57], 'representative': 87258499423, 'size': 336}
    • id: 168401295
      {'aut_label': '14A', 'centralizer': '48.c1', 'counter': 58, 'group_counter': 75, 'group_order': 8064, 'label': '14A', 'order': 14, 'powers': [42, 58, 2], 'representative': 127388582, 'size': 48}
    • id: 168401296
      {'aut_label': '14B1', 'centralizer': '48.c1', 'counter': 59, 'group_counter': 75, 'group_order': 8064, 'label': '14B1', 'order': 14, 'powers': [42, 60, 3], 'representative': 87113218, 'size': 48}
    • id: 168401298
      {'aut_label': '14B1', 'centralizer': '48.c1', 'counter': 60, 'group_counter': 75, 'group_order': 8064, 'label': '14B-1', 'order': 14, 'powers': [42, 59, 3], 'representative': 87124489, 'size': 48}
    • id: 168401299
      {'aut_label': '14C', 'centralizer': '144.a1', 'counter': 61, 'group_counter': 75, 'group_order': 8064, 'label': '14C', 'order': 14, 'powers': [42, 61, 4], 'representative': 6354407471, 'size': 144}
    • id: 168401300
      {'aut_label': '14C', 'centralizer': '144.a1', 'counter': 62, 'group_counter': 75, 'group_order': 8064, 'label': '14D', 'order': 14, 'powers': [42, 62, 5], 'representative': 87178325201, 'size': 144}
    • id: 168401301
      {'aut_label': '14E1', 'centralizer': '144.a1', 'counter': 63, 'group_counter': 75, 'group_order': 8064, 'label': '14E1', 'order': 14, 'powers': [42, 64, 6], 'representative': 180623900582, 'size': 144}
    • id: 168401302
      {'aut_label': '14E1', 'centralizer': '144.a1', 'counter': 64, 'group_counter': 75, 'group_order': 8064, 'label': '14E-1', 'order': 14, 'powers': [42, 63, 6], 'representative': 180623917080, 'size': 144}
    • id: 168401303
      {'aut_label': '21A', 'centralizer': '96.a1', 'counter': 65, 'group_counter': 75, 'group_order': 8064, 'label': '21A', 'order': 21, 'powers': [65, 42, 15], 'representative': 174356597466, 'size': 96}
    • id: 168401304
      {'aut_label': '24A1', 'centralizer': '168.cg1', 'counter': 66, 'group_counter': 75, 'group_order': 8064, 'label': '24A1', 'order': 24, 'powers': [51, 43, 66], 'representative': 174360217971, 'size': 168}
    • id: 168401305
      {'aut_label': '24A5', 'centralizer': '168.cg1', 'counter': 67, 'group_counter': 75, 'group_order': 8064, 'label': '24A5', 'order': 24, 'powers': [51, 44, 67], 'representative': 93408978090, 'size': 168}
    • id: 168401306
      {'aut_label': '24B1', 'centralizer': '168.ch1', 'counter': 68, 'group_counter': 75, 'group_order': 8064, 'label': '24B1', 'order': 24, 'powers': [52, 45, 68], 'representative': 93452500701, 'size': 168}
    • id: 168401307
      {'aut_label': '24B5', 'centralizer': '168.ch1', 'counter': 69, 'group_counter': 75, 'group_order': 8064, 'label': '24B5', 'order': 24, 'powers': [52, 46, 69], 'representative': 174403777410, 'size': 168}
    • id: 168401309
      {'aut_label': '42A', 'centralizer': '96.a1', 'counter': 70, 'group_counter': 75, 'group_order': 8064, 'label': '42A', 'order': 42, 'powers': [65, 58, 26], 'representative': 174483974966, 'size': 96}
    • id: 168401310
      {'aut_label': '42B1', 'centralizer': '96.a1', 'counter': 71, 'group_counter': 75, 'group_order': 8064, 'label': '42B1', 'order': 42, 'powers': [65, 59, 27], 'representative': 93492438907, 'size': 96}
    • id: 168401311
      {'aut_label': '42B1', 'centralizer': '96.a1', 'counter': 72, 'group_counter': 75, 'group_order': 8064, 'label': '42B-1', 'order': 42, 'powers': [65, 60, 27], 'representative': 174443682179, 'size': 96}
  • gps_qchar • Show schema
    • id: 16906564
      {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 16906575
      {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1], 'schur_index': 1}
    • id: 16906586
      {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1], 'schur_index': 1}
    • id: 16906597
      {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1], 'schur_index': 1}
    • id: 16906608
      {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1], 'schur_index': 1}
    • id: 16906619
      {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
    • id: 16906624
      {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 16906625
      {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
    • id: 16906626
      {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, -1, 2, -1, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, -1, 2, -1, 2, 0, 0, -1, -1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, 2, -1, -1, 0, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 16906565
      {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, -2, 2, 0, -2, 2, 0, 0, 2, -2, 0, 0, 2, 2, 2, -2, 2, 0, 0, -2, 2, 0, 0, -2, 0, -2, 2, -2, 0, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
    • id: 16906566
      {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 2, -2, 0, -2, 2, 0, 0, -2, 2, 0, 0, 2, 2, 2, -2, 2, 0, 0, 2, -2, 0, 0, -2, 0, -2, 2, -2, 0, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
    • id: 16906567
      {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, -1, 2, -1, 2, 2, 2, -2, 0, 0, 0, 0, -1, 1, -1, -1, 2, 1, -1, -2, 1, -2, 0, 0, 1, 1, 0, 0, 2, -2, -2, 2, 2, 0, 0, 0, 0, -1, -1, -1, 2, 1, -1, 0, 2, -2, -2, 0, 0, 0, 0, -1, 1, 1, -1, -1, -1, 1, 1], 'schur_index': 1}
    • id: 16906568
      {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 0, 2, 2, -2, 2, 0, 0, 0, 0, -1, 2, -1, 2, 2, -2, -2, 0, 0, 0, 0, -1, 1, -1, -1, 2, 1, -1, -2, -1, 2, 0, 0, -1, 1, 0, 0, 2, 2, 2, -2, -2, 0, 0, 0, 0, -1, -1, 1, -2, 1, 1, 0, 2, -2, -2, 0, 0, 0, 0, -1, -1, -1, 1, 1, -1, 1, 1], 'schur_index': 1}
    • id: 16906569
      {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 0, 2, 2, 2, -2, 0, 0, 0, 0, -1, 2, -1, 2, 2, -2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, -1, 2, 1, -2, 0, 0, 1, -1, 0, 0, 2, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, 1, -2, -1, 1, 0, 2, 2, 2, 0, 0, 0, 0, -1, 1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
    • id: 16906570
      {'cdim': 4, 'counter': 15, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.4a', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, -2, 4, -2, -4, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, -2, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
    • id: 16906571
      {'cdim': 6, 'counter': 16, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.6a', 'multiplicity': 1, 'nt': [42, 82], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, -2, -2, -2, 0, -2, -2, -2, 0, 6, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 6, 6, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
    • id: 16906572
      {'cdim': 6, 'counter': 17, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.6b', 'multiplicity': 1, 'nt': [42, 131], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -6, 6, -2, -2, 2, 0, 2, 2, -2, 0, 6, 0, 0, 2, 2, 0, -2, -2, -2, 0, 2, 6, -6, -2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -1, 1, 1, 1, 1, -1, -1, -1, 0, 0, 0, 0, -1, 1, 1], 'schur_index': 1}
    • id: 16906573
      {'cdim': 6, 'counter': 18, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.6c', 'multiplicity': 1, 'nt': [42, 131], 'qdim': 6, 'qvalues': [6, 6, -6, 6, 6, -6, -2, -2, 2, 0, -2, -2, 2, 0, 6, 0, 0, 2, 2, 0, -2, 2, 2, 0, -2, 6, -6, -2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -1, 1, 1, -1, -1, 1, 1, -1, 0, 0, 0, 0, -1, 1, 1], 'schur_index': 1}
    • id: 16906574
      {'cdim': 6, 'counter': 19, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.6d', 'multiplicity': 1, 'nt': [42, 131], 'qdim': 6, 'qvalues': [6, 6, 6, -6, -6, -6, -2, -2, -2, 0, 2, 2, 2, 0, 6, 0, 0, 2, 2, 0, 2, -2, -2, 0, -2, 6, 6, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, -1, -1, -1, 1, 1, 1, 1, -1, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
    • id: 16906582
      {'cdim': 7, 'counter': 26, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.7a', 'multiplicity': 1, 'nt': [8, 43], 'qdim': 7, 'qvalues': [7, 7, 7, 7, 7, 7, -1, -1, -1, 1, -1, -1, -1, 1, 7, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 7, 7, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
    • id: 16906583
      {'cdim': 7, 'counter': 27, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.7b', 'multiplicity': 1, 'nt': [16, 713], 'qdim': 7, 'qvalues': [7, 7, 7, 7, 7, 7, -1, -1, -1, -1, -1, -1, -1, -1, 7, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 7, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 0, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
    • id: 16906584
      {'cdim': 7, 'counter': 28, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.7c', 'multiplicity': 1, 'nt': [16, 1035], 'qdim': 7, 'qvalues': [7, 7, -7, -7, -7, 7, -1, -1, 1, -1, 1, 1, -1, 1, 7, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 7, -7, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 0, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0], 'schur_index': 1}
    • id: 16906585
      {'cdim': 7, 'counter': 29, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.7d', 'multiplicity': 1, 'nt': [16, 1035], 'qdim': 7, 'qvalues': [7, 7, -7, -7, -7, 7, -1, -1, 1, 1, 1, 1, -1, -1, 7, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 7, -7, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 0, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0], 'schur_index': 1}
    • id: 16906587
      {'cdim': 7, 'counter': 30, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.7e', 'multiplicity': 1, 'nt': [16, 1035], 'qdim': 7, 'qvalues': [7, 7, -7, 7, 7, -7, -1, -1, 1, -1, -1, -1, 1, -1, 7, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 7, -7, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 0, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0], 'schur_index': 1}
    • id: 16906588
      {'cdim': 7, 'counter': 31, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.7f', 'multiplicity': 1, 'nt': [16, 1035], 'qdim': 7, 'qvalues': [7, 7, -7, 7, 7, -7, -1, -1, 1, 1, -1, -1, 1, 1, 7, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 7, -7, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 0, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0], 'schur_index': 1}
    • id: 16906589
      {'cdim': 7, 'counter': 32, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.7g', 'multiplicity': 1, 'nt': [16, 1035], 'qdim': 7, 'qvalues': [7, 7, 7, -7, -7, -7, -1, -1, -1, -1, 1, 1, 1, 1, 7, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 7, 7, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 0, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
    • id: 16906590
      {'cdim': 7, 'counter': 33, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.7h', 'multiplicity': 1, 'nt': [16, 1035], 'qdim': 7, 'qvalues': [7, 7, 7, -7, -7, -7, -1, -1, -1, 1, 1, 1, 1, -1, 7, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 7, 7, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 0, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
    • id: 16906591
      {'cdim': 8, 'counter': 34, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.8a', 'multiplicity': 1, 'nt': [21, 20], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 8, 8, 0, 0, 0, 2, 0, 0, 0, 2, 8, -1, -1, 0, 0, 2, 0, 0, 0, 2, 0, 8, 8, 0, 0, -1, 0, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1], 'schur_index': 1}
    • id: 16906592
      {'cdim': 8, 'counter': 35, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.8b', 'multiplicity': 1, 'nt': [42, 81], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 8, 8, 0, 0, 0, -2, 0, 0, 0, -2, 8, -1, -1, 0, 0, -2, 0, 0, 0, -2, 0, 8, 8, 0, 0, -1, 0, -1, -1, -2, 1, -1, -1, 1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1], 'schur_index': 1}
    • id: 16906593
      {'cdim': 8, 'counter': 36, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.8c', 'multiplicity': 1, 'nt': [42, 130], 'qdim': 8, 'qvalues': [8, 8, -8, -8, -8, 8, 0, 0, 0, -2, 0, 0, 0, 2, 8, -1, -1, 0, 0, 2, 0, 0, 0, -2, 0, 8, -8, 0, 0, -1, 0, -1, 1, -2, 1, 1, 1, 1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 1, -1, -1], 'schur_index': 1}
    • id: 16906594
      {'cdim': 8, 'counter': 37, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.8d', 'multiplicity': 1, 'nt': [42, 130], 'qdim': 8, 'qvalues': [8, 8, -8, -8, -8, 8, 0, 0, 0, 2, 0, 0, 0, -2, 8, -1, -1, 0, 0, -2, 0, 0, 0, 2, 0, 8, -8, 0, 0, -1, 0, -1, 1, 2, -1, 1, 1, -1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 1, -1, -1], 'schur_index': 1}
    • id: 16906595
      {'cdim': 8, 'counter': 38, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.8e', 'multiplicity': 1, 'nt': [42, 130], 'qdim': 8, 'qvalues': [8, 8, -8, 8, 8, -8, 0, 0, 0, -2, 0, 0, 0, -2, 8, -1, -1, 0, 0, 2, 0, 0, 0, 2, 0, 8, -8, 0, 0, -1, 0, -1, 1, -2, 1, -1, -1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 0, 0, 0, 0, 1, -1, -1], 'schur_index': 1}
    • id: 16906596
      {'cdim': 8, 'counter': 39, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.8f', 'multiplicity': 1, 'nt': [42, 130], 'qdim': 8, 'qvalues': [8, 8, -8, 8, 8, -8, 0, 0, 0, 2, 0, 0, 0, 2, 8, -1, -1, 0, 0, -2, 0, 0, 0, -2, 0, 8, -8, 0, 0, -1, 0, -1, 1, 2, -1, -1, -1, -1, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 0, 0, 0, 0, 1, -1, -1], 'schur_index': 1}
    • id: 16906598
      {'cdim': 8, 'counter': 40, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.8g', 'multiplicity': 1, 'nt': [42, 130], 'qdim': 8, 'qvalues': [8, 8, 8, -8, -8, -8, 0, 0, 0, -2, 0, 0, 0, 2, 8, -1, -1, 0, 0, -2, 0, 0, 0, 2, 0, 8, 8, 0, 0, -1, 0, -1, -1, -2, 1, 1, 1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 0, 0, 0, 0, 1, 1, 1], 'schur_index': 1}
    • id: 16906599
      {'cdim': 8, 'counter': 41, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.8h', 'multiplicity': 1, 'nt': [42, 130], 'qdim': 8, 'qvalues': [8, 8, 8, -8, -8, -8, 0, 0, 0, 2, 0, 0, 0, -2, 8, -1, -1, 0, 0, 2, 0, 0, 0, -2, 0, 8, 8, 0, 0, -1, 0, -1, -1, 2, -1, 1, 1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 0, 0, 0, 0, 1, 1, 1], 'schur_index': 1}
    • id: 16906576
      {'cdim': 6, 'counter': 20, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.6e', 'multiplicity': 2, 'nt': [14, 16], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 12, 12, 4, 4, 4, 0, 4, 4, 4, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, 4, 4, 0, 4, 0, 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, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2], 'schur_index': 1}
    • id: 16906577
      {'cdim': 6, 'counter': 21, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.6f', 'multiplicity': 2, 'nt': [28, 81], 'qdim': 12, 'qvalues': [12, 12, -12, -12, -12, 12, 4, 4, -4, 0, -4, -4, 4, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -12, 4, 4, 0, -4, 0, 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, -2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, -2, 2, 2], 'schur_index': 1}
    • id: 16906578
      {'cdim': 6, 'counter': 22, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.6g', 'multiplicity': 2, 'nt': [28, 81], 'qdim': 12, 'qvalues': [12, 12, -12, 12, 12, -12, 4, 4, -4, 0, 4, 4, -4, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -12, 4, 4, 0, -4, 0, 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, -2, 2, 2, -2, -2, 2, 2, -2, 0, 0, 0, 0, -2, 2, 2], 'schur_index': 1}
    • id: 16906579
      {'cdim': 6, 'counter': 23, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.6h', 'multiplicity': 2, 'nt': [28, 81], 'qdim': 12, 'qvalues': [12, 12, 12, -12, -12, -12, 4, 4, 4, 0, -4, -4, -4, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, 4, 4, 0, 4, 0, 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, -2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, -2, -2, -2], 'schur_index': 1}
    • id: 16906580
      {'cdim': 6, 'counter': 24, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.6i', 'multiplicity': 2, 'nt': [84, 0], 'qdim': 12, 'qvalues': [12, -12, 0, -12, 12, 0, 4, -4, 0, 0, -4, 4, 0, 0, 12, 0, 0, -4, 4, 0, 0, -4, 4, 0, 0, -12, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2, 0, 0, 2, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
    • id: 16906581
      {'cdim': 6, 'counter': 25, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.6j', 'multiplicity': 2, 'nt': [84, 0], 'qdim': 12, 'qvalues': [12, -12, 0, 12, -12, 0, 4, -4, 0, 0, 4, -4, 0, 0, 12, 0, 0, -4, 4, 0, 0, 4, -4, 0, 0, -12, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2, 0, 0, -2, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
    • id: 16906600
      {'cdim': 12, 'counter': 42, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.12a', 'multiplicity': 1, 'nt': [28, 147], 'qdim': 12, 'qvalues': [12, -12, 0, -12, 12, 0, -4, 4, 0, 0, 4, -4, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, -4, 4, 0, 0, 0, 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, 2, 0, 0, 2, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
    • id: 16906601
      {'cdim': 12, 'counter': 43, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.12b', 'multiplicity': 1, 'nt': [28, 147], 'qdim': 12, 'qvalues': [12, -12, 0, 12, -12, 0, -4, 4, 0, 0, -4, 4, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, -4, 4, 0, 0, 0, 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, 2, 0, 0, -2, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
    • id: 16906602
      {'cdim': 12, 'counter': 44, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.12c', 'multiplicity': 1, 'nt': [126, 0], 'qdim': 12, 'qvalues': [12, 12, -12, 0, 0, 0, -4, -4, 4, 0, 0, 0, 0, 0, -6, 0, 0, 4, 4, 0, -4, 0, 0, 0, 0, -6, 6, 2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, -2, 2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, -1, -1], 'schur_index': 1}
    • id: 16906603
      {'cdim': 12, 'counter': 45, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.12d', 'multiplicity': 1, 'nt': [126, 0], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, -6, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, -6, -6, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, -2, -2, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1], 'schur_index': 1}
    • id: 16906607
      {'cdim': 14, 'counter': 49, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.14a', 'multiplicity': 1, 'nt': [24, 4986], 'qdim': 14, 'qvalues': [14, 14, 14, 0, 0, 0, -2, -2, -2, 2, 0, 0, 0, 0, -7, 2, -1, -2, -2, 2, -2, 0, 0, 0, 0, -7, -7, 1, 1, 2, 1, -1, 2, -1, 2, 0, 0, -1, -1, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, -1, 2, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
    • id: 16906609
      {'cdim': 14, 'counter': 50, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.14b', 'multiplicity': 1, 'nt': [28, 146], 'qdim': 14, 'qvalues': [14, -14, 0, -14, 14, 0, 2, -2, 0, 0, -2, 2, 0, 0, 14, 2, 2, 2, -2, 0, 0, 2, -2, 0, 0, -14, 0, 2, -2, -2, 0, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16906610
      {'cdim': 14, 'counter': 51, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.14c', 'multiplicity': 1, 'nt': [28, 146], 'qdim': 14, 'qvalues': [14, -14, 0, 14, -14, 0, 2, -2, 0, 0, 2, -2, 0, 0, 14, 2, 2, 2, -2, 0, 0, -2, 2, 0, 0, -14, 0, 2, -2, -2, 0, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16906611
      {'cdim': 14, 'counter': 52, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.14d', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 14, 'qvalues': [14, 14, -14, 0, 0, 0, -2, -2, 2, -2, 0, 0, 0, 0, -7, 2, -1, -2, -2, 2, 2, 0, 0, 0, 0, -7, 7, 1, 1, 2, -1, -1, -2, 1, -2, 0, 0, 1, 1, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 1, 1, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0], 'schur_index': 1}
    • id: 16906612
      {'cdim': 14, 'counter': 53, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.14e', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 14, 'qvalues': [14, 14, -14, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, -7, 2, -1, -2, -2, -2, 2, 0, 0, 0, 0, -7, 7, 1, 1, 2, -1, -1, -2, -1, 2, 0, 0, -1, 1, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 1, 1, 1, -2, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0], 'schur_index': 1}
    • id: 16906613
      {'cdim': 14, 'counter': 54, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.14f', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 14, 'qvalues': [14, 14, 14, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, -7, 2, -1, -2, -2, -2, -2, 0, 0, 0, 0, -7, -7, 1, 1, 2, 1, -1, 2, 1, -2, 0, 0, 1, -1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
    • id: 16906614
      {'cdim': 16, 'counter': 55, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.16a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 16, 16, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -8, -2, 1, 0, 0, 4, 0, 0, 0, 0, 0, -8, -8, 0, 0, -2, 0, 1, -2, -2, -2, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
    • id: 16906615
      {'cdim': 16, 'counter': 56, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.16b', 'multiplicity': 1, 'nt': [84, 0], 'qdim': 16, 'qvalues': [16, -16, 0, -16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
    • id: 16906616
      {'cdim': 16, 'counter': 57, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.16c', 'multiplicity': 1, 'nt': [84, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 2, 0, 2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
    • id: 16906617
      {'cdim': 16, 'counter': 58, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.16d', 'multiplicity': 1, 'nt': [84, 0], 'qdim': 16, 'qvalues': [16, 16, 16, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -8, -2, 1, 0, 0, -4, 0, 0, 0, 0, 0, -8, -8, 0, 0, -2, 0, 1, -2, 2, 2, 0, 0, -1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -1, 0, 2, 2, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
    • id: 16906618
      {'cdim': 16, 'counter': 59, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.16e', 'multiplicity': 1, 'nt': [96, 0], 'qdim': 16, 'qvalues': [16, 16, -16, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -8, -2, 1, 0, 0, 4, 0, 0, 0, 0, 0, -8, 8, 0, 0, -2, 0, 1, 2, 2, 2, 0, 0, -1, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 1, 0, 2, -2, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1, 1], 'schur_index': 1}
    • id: 16906620
      {'cdim': 16, 'counter': 60, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.16f', 'multiplicity': 1, 'nt': [96, 0], 'qdim': 16, 'qvalues': [16, 16, -16, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -8, -2, 1, 0, 0, -4, 0, 0, 0, 0, 0, -8, 8, 0, 0, -2, 0, 1, 2, -2, -2, 0, 0, 1, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -1, 0, 2, -2, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1, 1], 'schur_index': 1}
    • id: 16906604
      {'cdim': 12, 'counter': 46, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.12e', 'multiplicity': 2, 'nt': [42, 265], 'qdim': 24, 'qvalues': [24, 24, 24, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, -4, -4, 0, -4, 0, 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, -4, -4, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2], 'schur_index': 1}
    • id: 16906605
      {'cdim': 12, 'counter': 47, 'faithful': False, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.12f', 'multiplicity': 2, 'nt': [84, 0], 'qdim': 24, 'qvalues': [24, 24, -24, 0, 0, 0, 8, 8, -8, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 12, -4, -4, 0, 4, 0, 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, -4, 4, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -2, -2], 'schur_index': 1}
    • id: 16906606
      {'cdim': 12, 'counter': 48, 'faithful': True, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.12g', 'multiplicity': 2, 'nt': [252, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, -12, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 12, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
    • id: 16906621
      {'cdim': 24, 'counter': 61, 'faithful': True, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.24a', 'multiplicity': 1, 'nt': [84, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 4, -4, 0, 0, 0, 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, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
    • id: 16906622
      {'cdim': 28, 'counter': 62, 'faithful': True, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.28a', 'multiplicity': 1, 'nt': [84, 0], 'qdim': 28, 'qvalues': [28, -28, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, -14, 4, -2, 4, -4, 0, 0, 0, 0, 0, 0, 14, 0, -2, 2, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16906623
      {'cdim': 32, 'counter': 63, 'faithful': True, 'group': '8064.cw', 'group_order': 8064, 'image': None, 'label': '8064.cw.32a', 'multiplicity': 1, 'nt': [168, 0], 'qdim': 32, 'qvalues': [32, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 4, 0, -2, 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, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
  • gps_char • Show schema
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    • id: 37220797
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    • id: 37220808
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    • id: 37220819
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    • id: 37220830
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    • id: 37220834
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    • id: 37220835
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    • id: 37220765
      {'center': '4.b1', 'center_index': 4, 'center_order': 2016, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1', 'kernel_order': 1008, 'label': '8064.cw.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 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]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220766
      {'center': '4.b1', 'center_index': 4, 'center_order': 2016, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1', 'kernel_order': 1008, 'label': '8064.cw.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 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]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220767
      {'center': '6.a1', 'center_index': 6, 'center_order': 1344, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 672, 'label': '8064.cw.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220768
      {'center': '6.a1', 'center_index': 6, 'center_order': 1344, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 672, 'label': '8064.cw.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220769
      {'center': '6.a1', 'center_index': 6, 'center_order': 1344, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 672, 'label': '8064.cw.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220770
      {'center': '24.a1', 'center_index': 24, 'center_order': 336, 'counter': 15, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 168, 'label': '8064.cw.4a', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220771
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 16, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '336.208', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1', 'kernel_order': 24, 'label': '8064.cw.6a', 'nt': [42, 82], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 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]], [[-1, 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]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220772
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 17, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.c1', 'kernel_order': 12, 'label': '8064.cw.6b', 'nt': [42, 131], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 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]], [[-1, 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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220773
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 18, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.b1', 'kernel_order': 12, 'label': '8064.cw.6c', 'nt': [42, 131], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 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]], [[-1, 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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220774
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 19, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.a1', 'kernel_order': 12, 'label': '8064.cw.6d', 'nt': [42, 131], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 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]], [[-1, 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]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220776
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 20, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [-2, 0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '336.208', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1', 'kernel_order': 24, 'label': '8064.cw.6e1', 'nt': [14, 16], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220777
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 21, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [-2, 0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '336.208', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1', 'kernel_order': 24, 'label': '8064.cw.6e2', 'nt': [14, 16], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220778
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 22, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [-2, 0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.c1', 'kernel_order': 12, 'label': '8064.cw.6f1', 'nt': [28, 81], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220779
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 23, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [-2, 0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.c1', 'kernel_order': 12, 'label': '8064.cw.6f2', 'nt': [28, 81], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220780
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 24, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [-2, 0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.b1', 'kernel_order': 12, 'label': '8064.cw.6g1', 'nt': [28, 81], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220781
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 25, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [-2, 0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.b1', 'kernel_order': 12, 'label': '8064.cw.6g2', 'nt': [28, 81], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220782
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 26, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [-2, 0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.a1', 'kernel_order': 12, 'label': '8064.cw.6h1', 'nt': [28, 81], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220783
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 27, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [-2, 0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.a1', 'kernel_order': 12, 'label': '8064.cw.6h2', 'nt': [28, 81], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220784
      {'center': '672.b1', 'center_index': 672, 'center_order': 12, 'counter': 28, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '1344.11295', 'image_order': 1344, 'indicator': 0, 'kernel': '1344.b1', 'kernel_order': 6, 'label': '8064.cw.6i1', 'nt': [84, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 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]], [[0, 0]], [[1, 0]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]], [[1, 0], [2, 1], [2, 2], [2, -3]], [[1, 0]], [[-1, 0]], [[1, 0], [2, 1], [2, 2], [2, -3]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0], [2, 1], [2, 2], [2, -3]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]]]}
    • id: 37220785
      {'center': '672.b1', 'center_index': 672, 'center_order': 12, 'counter': 29, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '1344.11295', 'image_order': 1344, 'indicator': 0, 'kernel': '1344.b1', 'kernel_order': 6, 'label': '8064.cw.6i2', 'nt': [84, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 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]], [[0, 0]], [[1, 0]], [[1, 0], [2, 1], [2, 2], [2, -3]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]], [[1, 0]], [[-1, 0]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]], [[1, 0], [2, 1], [2, 2], [2, -3]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]], [[1, 0], [2, 1], [2, 2], [2, -3]]]}
    • id: 37220787
      {'center': '672.b1', 'center_index': 672, 'center_order': 12, 'counter': 30, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '1344.11295', 'image_order': 1344, 'indicator': 0, 'kernel': '1344.b1', 'kernel_order': 6, 'label': '8064.cw.6j1', 'nt': [84, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 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]], [[0, 0]], [[1, 0]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]], [[1, 0], [2, 1], [2, 2], [2, -3]], [[-1, 0]], [[1, 0]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]], [[1, 0], [2, 1], [2, 2], [2, -3]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0], [2, 1], [2, 2], [2, -3]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]]]}
    • id: 37220788
      {'center': '672.b1', 'center_index': 672, 'center_order': 12, 'counter': 31, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '1344.11295', 'image_order': 1344, 'indicator': 0, 'kernel': '1344.b1', 'kernel_order': 6, 'label': '8064.cw.6j2', 'nt': [84, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 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]], [[0, 0]], [[1, 0]], [[1, 0], [2, 1], [2, 2], [2, -3]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]], [[-1, 0]], [[1, 0]], [[1, 0], [2, 1], [2, 2], [2, -3]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]], [[1, 0], [2, 1], [2, 2], [2, -3]]]}
    • id: 37220789
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 32, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '336.208', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1', 'kernel_order': 24, 'label': '8064.cw.7a', 'nt': [8, 43], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220790
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 33, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '336.208', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1', 'kernel_order': 24, 'label': '8064.cw.7b', 'nt': [16, 713], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220791
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 34, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.c1', 'kernel_order': 12, 'label': '8064.cw.7c', 'nt': [16, 1035], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220792
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 35, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.c1', 'kernel_order': 12, 'label': '8064.cw.7d', 'nt': [16, 1035], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220793
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 36, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.b1', 'kernel_order': 12, 'label': '8064.cw.7e', 'nt': [16, 1035], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220794
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 37, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.b1', 'kernel_order': 12, 'label': '8064.cw.7f', 'nt': [16, 1035], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220795
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 38, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.a1', 'kernel_order': 12, 'label': '8064.cw.7g', 'nt': [16, 1035], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220796
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 39, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.a1', 'kernel_order': 12, 'label': '8064.cw.7h', 'nt': [16, 1035], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220798
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 40, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '336.208', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1', 'kernel_order': 24, 'label': '8064.cw.8a', 'nt': [21, 20], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220799
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 41, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '336.208', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1', 'kernel_order': 24, 'label': '8064.cw.8b', 'nt': [42, 81], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220800
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 42, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.c1', 'kernel_order': 12, 'label': '8064.cw.8c', 'nt': [42, 130], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220801
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 43, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.c1', 'kernel_order': 12, 'label': '8064.cw.8d', 'nt': [42, 130], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220802
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 44, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.b1', 'kernel_order': 12, 'label': '8064.cw.8e', 'nt': [42, 130], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220803
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 45, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.b1', 'kernel_order': 12, 'label': '8064.cw.8f', 'nt': [42, 130], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220804
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 46, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.a1', 'kernel_order': 12, 'label': '8064.cw.8g', 'nt': [42, 130], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220805
      {'center': '336.a1', 'center_index': 336, 'center_order': 24, 'counter': 47, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '672.1254', 'image_order': 672, 'indicator': 1, 'kernel': '672.a1', 'kernel_order': 12, 'label': '8064.cw.8h', 'nt': [42, 130], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220806
      {'center': '672.b1', 'center_index': 672, 'center_order': 12, 'counter': 48, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '1344.11295', 'image_order': 1344, 'indicator': 1, 'kernel': '1344.b1', 'kernel_order': 6, 'label': '8064.cw.12a', 'nt': [28, 147], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[0, 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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220807
      {'center': '672.b1', 'center_index': 672, 'center_order': 12, 'counter': 49, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '1344.11295', 'image_order': 1344, 'indicator': 1, 'kernel': '1344.b1', 'kernel_order': 6, 'label': '8064.cw.12b', 'nt': [28, 147], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[0, 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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220809
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 50, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '4032.ds', 'image_order': 4032, 'indicator': 1, 'kernel': '4032.a1', 'kernel_order': 2, 'label': '8064.cw.12c', 'nt': [126, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220810
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 51, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '2016.cw', 'image_order': 2016, 'indicator': 1, 'kernel': '2016.a1', 'kernel_order': 4, 'label': '8064.cw.12d', 'nt': [126, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220811
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 52, 'cyclotomic_n': 8, 'dim': 12, 'faithful': False, 'field': [-2, 0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '2016.cw', 'image_order': 2016, 'indicator': 1, 'kernel': '2016.a1', 'kernel_order': 4, 'label': '8064.cw.12e1', 'nt': [42, 265], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 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, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]]]}
    • id: 37220812
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 53, 'cyclotomic_n': 8, 'dim': 12, 'faithful': False, 'field': [-2, 0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '2016.cw', 'image_order': 2016, 'indicator': 1, 'kernel': '2016.a1', 'kernel_order': 4, 'label': '8064.cw.12e2', 'nt': [42, 265], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 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, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]]]}
    • id: 37220813
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 54, 'cyclotomic_n': 8, 'dim': 12, 'faithful': False, 'field': [-2, 0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '4032.ds', 'image_order': 4032, 'indicator': 1, 'kernel': '4032.a1', 'kernel_order': 2, 'label': '8064.cw.12f1', 'nt': [84, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[-2, 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, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]]]}
    • id: 37220814
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 55, 'cyclotomic_n': 8, 'dim': 12, 'faithful': False, 'field': [-2, 0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '4032.ds', 'image_order': 4032, 'indicator': 1, 'kernel': '4032.a1', 'kernel_order': 2, 'label': '8064.cw.12f2', 'nt': [84, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[-2, 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, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]]]}
    • id: 37220815
      {'center': '4032.a1', 'center_index': 4032, 'center_order': 2, 'counter': 56, 'cyclotomic_n': 7, 'dim': 12, 'faithful': True, 'field': [2, -1, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '8064.cw', 'image_order': 8064, 'indicator': 0, 'kernel': '8064.a1', 'kernel_order': 1, 'label': '8064.cw.12g1', 'nt': [252, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[0, 0]], [[2, 0]], [[-2, 0], [-4, 1], [-4, 2], [-4, -3]], [[2, 0], [4, 1], [4, 2], [4, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]], [[1, 0], [2, 1], [2, 2], [2, -3]]]}
    • id: 37220816
      {'center': '4032.a1', 'center_index': 4032, 'center_order': 2, 'counter': 57, 'cyclotomic_n': 7, 'dim': 12, 'faithful': True, 'field': [2, -1, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '8064.cw', 'image_order': 8064, 'indicator': 0, 'kernel': '8064.a1', 'kernel_order': 1, 'label': '8064.cw.12g2', 'nt': [252, 2], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[0, 0]], [[2, 0]], [[2, 0], [4, 1], [4, 2], [4, -3]], [[-2, 0], [-4, 1], [-4, 2], [-4, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0], [2, 1], [2, 2], [2, -3]], [[-1, 0], [-2, 1], [-2, 2], [-2, -3]]]}
    • id: 37220817
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 58, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '2016.cw', 'image_order': 2016, 'indicator': 1, 'kernel': '2016.a1', 'kernel_order': 4, 'label': '8064.cw.14a', 'nt': [24, 4986], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[14, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-7, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-7, 0]], [[-7, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220818
      {'center': '672.b1', 'center_index': 672, 'center_order': 12, 'counter': 59, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '1344.11295', 'image_order': 1344, 'indicator': 1, 'kernel': '1344.b1', 'kernel_order': 6, 'label': '8064.cw.14b', 'nt': [28, 146], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[0, 0]], [[-14, 0]], [[14, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[14, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-14, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220820
      {'center': '672.b1', 'center_index': 672, 'center_order': 12, 'counter': 60, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '1344.11295', 'image_order': 1344, 'indicator': 1, 'kernel': '1344.b1', 'kernel_order': 6, 'label': '8064.cw.14c', 'nt': [28, 146], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[0, 0]], [[14, 0]], [[-14, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[14, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-14, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220821
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 61, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '4032.ds', 'image_order': 4032, 'indicator': 1, 'kernel': '4032.a1', 'kernel_order': 2, 'label': '8064.cw.14d', 'nt': [48, 0], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[-14, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-7, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-7, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220822
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 62, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '4032.ds', 'image_order': 4032, 'indicator': 1, 'kernel': '4032.a1', 'kernel_order': 2, 'label': '8064.cw.14e', 'nt': [48, 0], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[-14, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-7, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-7, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220823
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 63, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '2016.cw', 'image_order': 2016, 'indicator': 1, 'kernel': '2016.a1', 'kernel_order': 4, 'label': '8064.cw.14f', 'nt': [48, 0], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[14, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-7, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-7, 0]], [[-7, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220824
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 64, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '2016.cw', 'image_order': 2016, 'indicator': 1, 'kernel': '2016.a1', 'kernel_order': 4, 'label': '8064.cw.16a', 'nt': [48, 0], 'q_character': None, 'values': [[[16, 0]], [[16, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 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]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220825
      {'center': '672.b1', 'center_index': 672, 'center_order': 12, 'counter': 65, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '1344.11295', 'image_order': 1344, 'indicator': 1, 'kernel': '1344.b1', 'kernel_order': 6, 'label': '8064.cw.16b', 'nt': [84, 0], 'q_character': None, 'values': [[[16, 0]], [[-16, 0]], [[0, 0]], [[-16, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220826
      {'center': '672.b1', 'center_index': 672, 'center_order': 12, 'counter': 66, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '1344.11295', 'image_order': 1344, 'indicator': 1, 'kernel': '1344.b1', 'kernel_order': 6, 'label': '8064.cw.16c', 'nt': [84, 0], 'q_character': None, 'values': [[[16, 0]], [[-16, 0]], [[0, 0]], [[16, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220827
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 67, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '2016.cw', 'image_order': 2016, 'indicator': 1, 'kernel': '2016.a1', 'kernel_order': 4, 'label': '8064.cw.16d', 'nt': [84, 0], 'q_character': None, 'values': [[[16, 0]], [[16, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 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]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 37220828
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 68, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '4032.ds', 'image_order': 4032, 'indicator': 1, 'kernel': '4032.a1', 'kernel_order': 2, 'label': '8064.cw.16e', 'nt': [96, 0], 'q_character': None, 'values': [[[16, 0]], [[16, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 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]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220829
      {'center': '2016.a1', 'center_index': 2016, 'center_order': 4, 'counter': 69, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '4032.ds', 'image_order': 4032, 'indicator': 1, 'kernel': '4032.a1', 'kernel_order': 2, 'label': '8064.cw.16f', 'nt': [96, 0], 'q_character': None, 'values': [[[16, 0]], [[16, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 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]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 37220831
      {'center': '4032.a1', 'center_index': 4032, 'center_order': 2, 'counter': 70, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '8064.cw', 'image_order': 8064, 'indicator': 1, 'kernel': '8064.a1', 'kernel_order': 1, 'label': '8064.cw.24a', 'nt': [84, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 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]], [[-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]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
    • id: 37220832
      {'center': '4032.a1', 'center_index': 4032, 'center_order': 2, 'counter': 71, 'cyclotomic_n': 1, 'dim': 28, 'faithful': True, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '8064.cw', 'image_order': 8064, 'indicator': 1, 'kernel': '8064.a1', 'kernel_order': 1, 'label': '8064.cw.28a', 'nt': [84, 0], 'q_character': None, 'values': [[[28, 0]], [[-28, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-14, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[14, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-4, 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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 37220833
      {'center': '4032.a1', 'center_index': 4032, 'center_order': 2, 'counter': 72, 'cyclotomic_n': 1, 'dim': 32, 'faithful': True, 'field': [0, 1], 'group': '8064.cw', 'group_counter': 75, 'group_order': 8064, 'image': None, 'image_isoclass': '8064.cw', 'image_order': 8064, 'indicator': 1, 'kernel': '8064.a1', 'kernel_order': 1, 'label': '8064.cw.32a', 'nt': [168, 0], 'q_character': None, 'values': [[[32, 0]], [[-32, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-16, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
  • gps_subgroup_search • Show schema
    Showing the first 100 of 1040 matching records in this table.
    • id: 253961738
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 8064, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '8064.cw.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': False, 'special_labels': ['L0', 'D0', 'C0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8064.cw', 'subgroup_hash': 4734243620999118076, 'subgroup_order': 8064, 'subgroup_tex': 'S_3\\times \\GL(3,2):D_4', 'supersolvable': False, 'sylow': 0}
    • id: 253961890
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 4032, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': ['C1', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4032.cs', 'subgroup_hash': 801603273932280202, 'subgroup_order': 4032, 'subgroup_tex': 'C_2\\times D_6\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253962001
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 4032, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4032.es', 'subgroup_hash': 1025961881311188616, 'subgroup_order': 4032, 'subgroup_tex': 'C_3\\times \\GL(3,2):D_4', 'supersolvable': False, 'sylow': 0}
    • id: 253962112
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 4032, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4032.ev', 'subgroup_hash': 665563335129422252, 'subgroup_order': 4032, 'subgroup_tex': '(C_2\\times C_6):\\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253962223
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 4032, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4032.ds', 'subgroup_hash': 5672968783997510635, 'subgroup_order': 4032, 'subgroup_tex': 'D_6\\times \\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253962334
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 4032, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4032.ep', 'subgroup_hash': 698061400812981998, 'subgroup_order': 4032, 'subgroup_tex': 'D_6.\\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253962445
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 4032, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.2.f1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4032.em', 'subgroup_hash': 6423428947524754670, 'subgroup_order': 4032, 'subgroup_tex': 'D_6:\\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253962556
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 4032, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.2.g1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4032.eq', 'subgroup_hash': 2179492404176655572, 'subgroup_order': 4032, 'subgroup_tex': 'D_6:\\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253962667
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1344, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2688.eb', 'subgroup_hash': 5732375002125462488, 'subgroup_order': 2688, 'subgroup_tex': 'C_2^3:\\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253961739
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 2016, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2016.de', 'subgroup_hash': 8243817548473506686, 'subgroup_order': 2016, 'subgroup_tex': 'C_2\\times C_6\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253961791
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 2016, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2016.dd', 'subgroup_hash': 8333125712768441886, 'subgroup_order': 2016, 'subgroup_tex': 'D_6\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253961802
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 2016, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2016.dd', 'subgroup_hash': 8333125712768441886, 'subgroup_order': 2016, 'subgroup_tex': 'D_6\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253961813
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 2016, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2016.b', 'subgroup_hash': 7142504566083232834, 'subgroup_order': 2016, 'subgroup_tex': 'C_6\\times \\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253961824
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 2016, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2016.ei', 'subgroup_hash': 1362803657993387288, 'subgroup_order': 2016, 'subgroup_tex': 'C_6:\\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253961835
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 2016, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2016.eh', 'subgroup_hash': 6902341786253785745, 'subgroup_order': 2016, 'subgroup_tex': '\\PSL(2,7):C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 253961846
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 2016, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2016.ej', 'subgroup_hash': 9178613841147646726, 'subgroup_order': 2016, 'subgroup_tex': 'C_6.\\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253961857
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1008, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2016.dd', 'subgroup_hash': 8333125712768441886, 'subgroup_order': 2016, 'subgroup_tex': 'D_6\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253961868
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1008, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.4.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2016.cw', 'subgroup_hash': 117371359274444897, 'subgroup_order': 2016, 'subgroup_tex': 'S_3\\times \\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253961879
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': True, 'core_order': 1344, 'counter': 19, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '8064.cw.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1344.11295', 'subgroup_hash': 11295, 'subgroup_order': 1344, 'subgroup_tex': '\\GL(3,2):D_4', 'supersolvable': False, 'sylow': 0}
    • id: 253961891
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 672, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1344.11685', 'subgroup_hash': 11685, 'subgroup_order': 1344, 'subgroup_tex': 'C_2^3\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253961902
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 672, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1344.11295', 'subgroup_hash': 11295, 'subgroup_order': 1344, 'subgroup_tex': '\\GL(3,2):D_4', 'supersolvable': False, 'sylow': 0}
    • id: 253961913
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 672, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1344.11684', 'subgroup_hash': 11684, 'subgroup_order': 1344, 'subgroup_tex': 'C_2^2\\times \\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253961924
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 672, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1344.11294', 'subgroup_hash': 11294, 'subgroup_order': 1344, 'subgroup_tex': 'C_2^2.\\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253961935
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 672, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1344.11295', 'subgroup_hash': 11295, 'subgroup_order': 1344, 'subgroup_tex': '\\GL(3,2):D_4', 'supersolvable': False, 'sylow': 0}
    • id: 253961946
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 672, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1344.11295', 'subgroup_hash': 11295, 'subgroup_order': 1344, 'subgroup_tex': '\\GL(3,2):D_4', 'supersolvable': False, 'sylow': 0}
    • id: 253961957
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 1008, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': False, 'special_labels': ['D', 'S', 'L1', 'D1', 'D', 'S', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1008.884', 'subgroup_hash': 884, 'subgroup_order': 1008, 'subgroup_tex': 'C_6\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253961968
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1008, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1008.883', 'subgroup_hash': 883, 'subgroup_order': 1008, 'subgroup_tex': 'S_3\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253961979
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.8.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1008.552', 'subgroup_hash': 552, 'subgroup_order': 1008, 'subgroup_tex': 'D_{14}:C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 253961990
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 504, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1008.884', 'subgroup_hash': 884, 'subgroup_order': 1008, 'subgroup_tex': 'C_6\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253962002
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 504, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1008.883', 'subgroup_hash': 883, 'subgroup_order': 1008, 'subgroup_tex': 'S_3\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253962013
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 504, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1008.882', 'subgroup_hash': 882, 'subgroup_order': 1008, 'subgroup_tex': 'C_3\\times \\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253962024
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 504, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1008.881', 'subgroup_hash': 881, 'subgroup_order': 1008, 'subgroup_tex': 'C_3:\\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253962035
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 672, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.1255', 'subgroup_hash': 1255, 'subgroup_order': 672, 'subgroup_tex': 'C_2^2\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253962046
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 672, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.1254', 'subgroup_hash': 1254, 'subgroup_order': 672, 'subgroup_tex': 'C_2\\times \\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253962057
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 672, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.1043', 'subgroup_hash': 1043, 'subgroup_order': 672, 'subgroup_tex': '\\PSL(2,7):C_4', 'supersolvable': False, 'sylow': 0}
    • id: 253962068
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 336, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '672.1255', 'subgroup_hash': 1255, 'subgroup_order': 672, 'subgroup_tex': 'C_2^2\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253962079
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 336, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '672.1255', 'subgroup_hash': 1255, 'subgroup_order': 672, 'subgroup_tex': 'C_2^2\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253962090
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '672.1254', 'subgroup_hash': 1254, 'subgroup_order': 672, 'subgroup_tex': 'C_2\\times \\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253962101
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '672.1043', 'subgroup_hash': 1043, 'subgroup_order': 672, 'subgroup_tex': '\\PSL(2,7):C_4', 'supersolvable': False, 'sylow': 0}
    • id: 253962113
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 168, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '672.1255', 'subgroup_hash': 1255, 'subgroup_order': 672, 'subgroup_tex': 'C_2^2\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253962124
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '672.1254', 'subgroup_hash': 1254, 'subgroup_order': 672, 'subgroup_tex': 'C_2\\times \\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253962135
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.14.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8659', 'subgroup_hash': 8659, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2:D_6^2', 'supersolvable': False, 'sylow': 0}
    • id: 253962146
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 504, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': False, 'special_labels': ['L2', 'L2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '504.157', 'subgroup_hash': 157, 'subgroup_order': 504, 'subgroup_tex': 'C_3\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253962157
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '504.179', 'subgroup_hash': 179, 'subgroup_order': 504, 'subgroup_tex': 'C_2\\times C_{42}:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 253962168
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '504.79', 'subgroup_hash': 79, 'subgroup_order': 504, 'subgroup_tex': 'C_{14}.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 253962179
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '504.89', 'subgroup_hash': 89, 'subgroup_order': 504, 'subgroup_tex': 'D_{42}:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 253962190
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '504.162', 'subgroup_hash': 162, 'subgroup_order': 504, 'subgroup_tex': 'D_6\\times F_7', 'supersolvable': True, 'sylow': 0}
    • id: 253962201
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '504.68', 'subgroup_hash': 68, 'subgroup_order': 504, 'subgroup_tex': 'D_6.F_7', 'supersolvable': True, 'sylow': 0}
    • id: 253962212
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '504.70', 'subgroup_hash': 70, 'subgroup_order': 504, 'subgroup_tex': 'D_6:F_7', 'supersolvable': True, 'sylow': 0}
    • id: 253962224
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '504.72', 'subgroup_hash': 72, 'subgroup_order': 504, 'subgroup_tex': 'D_{42}:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 253962235
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.21.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '21.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 21, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.12576', 'subgroup_hash': 12576, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times D_4:D_4', 'supersolvable': True, 'sylow': 0}
    • id: 253962246
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 336, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': False, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.209', 'subgroup_hash': 209, 'subgroup_order': 336, 'subgroup_tex': 'C_2\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253962257
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '336.130', 'subgroup_hash': 130, 'subgroup_order': 336, 'subgroup_tex': 'C_2^3:F_7', 'supersolvable': True, 'sylow': 0}
    • id: 253962268
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '336.162', 'subgroup_hash': 162, 'subgroup_order': 336, 'subgroup_tex': 'D_6:D_{14}', 'supersolvable': True, 'sylow': 0}
    • id: 253962279
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 168, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.209', 'subgroup_hash': 209, 'subgroup_order': 336, 'subgroup_tex': 'C_2\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253962290
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 168, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.209', 'subgroup_hash': 209, 'subgroup_order': 336, 'subgroup_tex': 'C_2\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253962301
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 168, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.209', 'subgroup_hash': 209, 'subgroup_order': 336, 'subgroup_tex': 'C_2\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 253962312
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 168, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.208', 'subgroup_hash': 208, 'subgroup_order': 336, 'subgroup_tex': '\\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253962323
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.24.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.208', 'subgroup_hash': 208, 'subgroup_order': 336, 'subgroup_tex': '\\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253962335
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.28.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 253962346
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.28.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1037', 'subgroup_hash': 1037, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
    • id: 253962357
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.28.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1034', 'subgroup_hash': 1034, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6:S_4', 'supersolvable': False, 'sylow': 0}
    • id: 253962368
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.28.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1033', 'subgroup_hash': 1033, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
    • id: 253962379
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.28.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
    • id: 253962390
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.28.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
    • id: 253962401
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.28.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
    • id: 253962412
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.28.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
    • id: 253962423
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.28.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
    • id: 253962434
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.28.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
    • id: 253962446
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '252.38', 'subgroup_hash': 38, 'subgroup_order': 252, 'subgroup_tex': 'C_{42}:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 253962457
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '252.29', 'subgroup_hash': 29, 'subgroup_order': 252, 'subgroup_tex': 'C_{42}:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 253962468
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '252.29', 'subgroup_hash': 29, 'subgroup_order': 252, 'subgroup_tex': 'C_{42}:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 253962479
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '252.28', 'subgroup_hash': 28, 'subgroup_order': 252, 'subgroup_tex': 'C_6\\times F_7', 'supersolvable': True, 'sylow': 0}
    • id: 253962490
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '252.30', 'subgroup_hash': 30, 'subgroup_order': 252, 'subgroup_tex': 'C_{42}:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 253962501
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '252.16', 'subgroup_hash': 16, 'subgroup_order': 252, 'subgroup_tex': 'C_{21}:C_{12}', 'supersolvable': True, 'sylow': 0}
    • id: 253962512
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '252.18', 'subgroup_hash': 18, 'subgroup_order': 252, 'subgroup_tex': 'C_{21}:C_{12}', 'supersolvable': True, 'sylow': 0}
    • id: 253962523
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.32.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '252.29', 'subgroup_hash': 29, 'subgroup_order': 252, 'subgroup_tex': 'C_{42}:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 253962534
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.32.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '252.26', 'subgroup_hash': 26, 'subgroup_order': 252, 'subgroup_tex': 'S_3\\times F_7', 'supersolvable': True, 'sylow': 0}
    • id: 253962545
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1537', 'subgroup_hash': 1537, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3\\times S_4', 'supersolvable': False, 'sylow': 0}
    • id: 253962557
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1163', 'subgroup_hash': 1163, 'subgroup_order': 192, 'subgroup_tex': 'S_3\\times C_4:D_4', 'supersolvable': True, 'sylow': 0}
    • id: 253962568
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.283', 'subgroup_hash': 283, 'subgroup_order': 192, 'subgroup_tex': 'D_6.\\OD_{16}', 'supersolvable': True, 'sylow': 0}
    • id: 253962579
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1514', 'subgroup_hash': 1514, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:C_2^4', 'supersolvable': True, 'sylow': 0}
    • id: 253962590
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.595', 'subgroup_hash': 595, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}:D_4', 'supersolvable': True, 'sylow': 0}
    • id: 253962601
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.291', 'subgroup_hash': 291, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2:D_{24}', 'supersolvable': True, 'sylow': 0}
    • id: 253962612
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.880', 'subgroup_hash': 880, 'subgroup_order': 192, 'subgroup_tex': 'C_3\\times D_4:D_4', 'supersolvable': True, 'sylow': 0}
    • id: 253962623
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.776', 'subgroup_hash': 776, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_6):D_8', 'supersolvable': True, 'sylow': 0}
    • id: 253962634
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1313', 'subgroup_hash': 1313, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times D_8', 'supersolvable': True, 'sylow': 0}
    • id: 253962645
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.328', 'subgroup_hash': 328, 'subgroup_order': 192, 'subgroup_tex': 'D_6.D_8', 'supersolvable': True, 'sylow': 0}
    • id: 253962656
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1313', 'subgroup_hash': 1313, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times D_8', 'supersolvable': True, 'sylow': 0}
    • id: 253962668
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.328', 'subgroup_hash': 328, 'subgroup_order': 192, 'subgroup_tex': 'D_6.D_8', 'supersolvable': True, 'sylow': 0}
    • id: 253962679
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.715', 'subgroup_hash': 715, 'subgroup_order': 192, 'subgroup_tex': 'D_6:D_8', 'supersolvable': True, 'sylow': 0}
    • id: 253962690
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.332', 'subgroup_hash': 332, 'subgroup_order': 192, 'subgroup_tex': 'D_4:D_{12}', 'supersolvable': True, 'sylow': 0}
    • id: 253962701
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.715', 'subgroup_hash': 715, 'subgroup_order': 192, 'subgroup_tex': 'D_6:D_8', 'supersolvable': True, 'sylow': 0}
    • id: 253962712
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.42.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.332', 'subgroup_hash': 332, 'subgroup_order': 192, 'subgroup_tex': 'D_4:D_{12}', 'supersolvable': True, 'sylow': 0}
    • id: 253962723
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 168, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '8064.cw.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': True, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': True, 'solvable': False, 'special_labels': ['PC', 'D2', 'PC', 'D2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.42', 'subgroup_hash': 42, 'subgroup_order': 168, 'subgroup_tex': '\\PSL(2,7)', 'supersolvable': False, 'sylow': 0}
    • id: 253962734
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.51', 'subgroup_hash': 51, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 253962745
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 24, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.55', 'subgroup_hash': 55, 'subgroup_order': 168, 'subgroup_tex': 'D_6\\times C_{14}', 'supersolvable': True, 'sylow': 0}
    • id: 253962756
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.48.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.28', 'subgroup_hash': 28, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
    • id: 253962767
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.48.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.11', 'subgroup_hash': 11, 'subgroup_order': 168, 'subgroup_tex': 'D_{14}:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 253961740
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8064.cw', 'ambient_counter': 75, 'ambient_order': 8064, 'ambient_tex': 'S_3\\times \\GL(3,2):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8064.cw.48.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.11', 'subgroup_hash': 11, 'subgroup_order': 168, 'subgroup_tex': 'D_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 1040 matching records in this table.
    • id: 253961738
      {'ambient': '8064.cw', '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': '4032.a1', 'complements': ['8064.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1', '3.a1', '8.c1', '21.a1', '28.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8334, 4865, 2328, 4098], 'generators': [127370880, 93405312000, 87178291200, 174436810224, 93532721625, 40279680], 'label': '8064.cw.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '4032.ds'}
    • id: 253961739
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1', 'complements': ['2016.bo1', '2016.s1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '8.d1', '12.a1', '28.d1', '32.a1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7078, 7256, 2924, 7236], 'generators': [127370880, 40304029, 93405312000, 174483966355, 40279680], 'label': '8064.cw.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '12.a1', '672.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '4032.ds', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '672.1254'}
    • id: 253961740
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1344.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1'], 'contains': ['96.c1', '96.j1', '96.q1', '144.b1', '336.g1'], 'core': '2016.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9231, -1, 545, -1], 'generators': [127370880, 93492407816, 3630742, 40283611, 40279680], 'label': '8064.cw.48.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '48.f1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
    • id: 253961741
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '63.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['672.bq1', '672.bv1', '1008.f1', '1008.bg1', '1008.bp1', '1008.bq1', '1008.br1'], 'contains': ['4032.c1', '4032.e1', '4032.i1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5497, -1, 5663, -1], 'generators': [6354391680, 6227026255], 'label': '8064.cw.2016.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '2016.p1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961742
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '63.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['672.br1', '672.bw1', '1008.f1', '1008.bh1', '1008.br1', '1008.bs1', '1008.bt1', '1008.bu1', '1008.bv1', '1008.bw1', '1008.bx1'], 'contains': ['4032.c1', '4032.f1', '4032.i1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [4756, -1, 6729, -1], 'generators': [6354391680, 6354397135], 'label': '8064.cw.2016.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '2016.q1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.q1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961743
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['672.bs1', '672.bx1', '1008.g1', '1008.bg1', '1008.bh1', '1008.bp1', '1008.bs1'], 'contains': ['4032.c1', '4032.g1', '4032.j1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [5208, -1, 5876, -1], 'generators': [6354391680, 6314117455], 'label': '8064.cw.2016.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.c1', 'old_label': '2016.r1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.r1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961744
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.i1', '672.bt1', '672.bu1', '672.by1', '1008.h1', '1008.bq1', '1008.bt1'], 'contains': ['4032.c1', '4032.h1', '4032.k1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [7435, -1, 3329, -1], 'generators': [6230651542, 6227020800], 'label': '8064.cw.2016.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.t1', 'old_label': '2016.s1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.s1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961745
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.bz1', '672.cc1', '1008.j1', '1008.bg1', '1008.by1', '1008.bz1'], 'contains': ['4032.d1', '4032.e1', '4032.j1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5176, -1, 5801, -1], 'generators': [6267300480, 6314117455], 'label': '8064.cw.2016.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.c1', 'old_label': '2016.t1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.t1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961746
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.ca1', '672.cd1', '1008.j1', '1008.bh1', '1008.bz1', '1008.ca1', '1008.cb1', '1008.cc1', '1008.cd1', '1008.ce1'], 'contains': ['4032.d1', '4032.f1', '4032.j1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [4508, -1, 7035, -1], 'generators': [6267300480, 6267305935], 'label': '8064.cw.2016.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.c1', 'old_label': '2016.u1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.u1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961747
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['672.cb1', '672.ce1', '1008.k1', '1008.bg1', '1008.bh1', '1008.by1', '1008.ca1'], 'contains': ['4032.d1', '4032.g1', '4032.i1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [5411, -1, 5781, -1], 'generators': [87218570880, 87096655], 'label': '8064.cw.2016.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.c1', 'old_label': '2016.v1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.v1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961748
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.cf1', '1008.n1', '1008.bj1', '1008.bp1', '1008.by1'], 'contains': ['4032.e1', '4032.g1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [4616, -1, 6019, -1], 'generators': [127411073, 87096655], 'label': '8064.cw.2016.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.e1', 'old_label': '2016.w1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961749
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.cg1', '672.cl1', '1008.o1', '1008.bq1'], 'contains': ['4032.e1', '4032.h1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [5855, -1, 4519, -1], 'generators': [127376063, 123747459], 'label': '8064.cw.2016.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.t1', 'old_label': '2016.x1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961750
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '252.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.ch1', '1008.p1', '1008.bi1', '1008.br1', '1008.by1'], 'contains': ['4032.e1', '4032.i1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [4740, -1, 5945, -1], 'generators': [6227060993, 6354397135], 'label': '8064.cw.2016.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.c1', 'old_label': '2016.y1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.y1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961751
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '16.d1', '24.b1'], 'contains': ['96.b1', '96.k1', '96.p1', '144.c1', '336.l1'], 'core': '2016.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8659, -1, 745, -1], 'generators': [127370880, 87095816, 6230651542, 40283611, 40279680], 'label': '8064.cw.48.g1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '48.g1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
    • id: 253961752
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '252.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.ci1', '1008.q1', '1008.bi1', '1008.bp1', '1008.bz1'], 'contains': ['4032.e1', '4032.j1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [4678, -1, 5966, -1], 'generators': [127411073, 6314117455], 'label': '8064.cw.2016.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.c1', 'old_label': '2016.z1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.z1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961753
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.cj1', '672.cm1', '1008.r1', '1008.bq1'], 'contains': ['4032.e1', '4032.k1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [5870, -1, 4623, -1], 'generators': [127376063, 87302038659], 'label': '8064.cw.2016.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.m1', 'old_label': '2016.ba1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.ba1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961754
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.ck1', '1008.y1', '1008.bj1', '1008.br1', '1008.bz1', '1008.cf1', '1008.cg1', '1008.ch1', '1008.ci1', '1008.cj1'], 'contains': ['4032.e1', '4032.f1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [3140, -1, 7165, -1], 'generators': [127376335, 40193], 'label': '8064.cw.2016.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1', 'old_label': '2016.bb1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961755
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['672.cn1', '1008.n1', '1008.bj1', '1008.bo1', '1008.bs1', '1008.ca1', '1008.cf1', '1008.ck1', '1008.cl1', '1008.cm1', '1008.cn1', '1008.dc1'], 'contains': ['4032.f1', '4032.g1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [3020, -1, 7207, -1], 'generators': [40285135, 40193], 'label': '8064.cw.2016.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1', 'old_label': '2016.bc1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961756
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.co1', '672.cx1', '1008.o1', '1008.bt1', '1008.co1', '1008.cp1', '1008.cq1'], 'contains': ['4032.f1', '4032.h1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [4815, -1, 5703, -1], 'generators': [123747459, 5183], 'label': '8064.cw.2016.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.u1', 'old_label': '2016.bd1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.bd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961757
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '252.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['672.cp1', '1008.p1', '1008.bk1', '1008.br1', '1008.bx1', '1008.ca1', '1008.cg1', '1008.ck1', '1008.cr1', '1008.cs1', '1008.ct1', '1008.dd1'], 'contains': ['4032.f1', '4032.i1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [3311, -1, 7138, -1], 'generators': [6227026255, 40193], 'label': '8064.cw.2016.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.c1', 'old_label': '2016.be1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.be1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961758
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '252.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['672.cq1', '1008.q1', '1008.bk1', '1008.bs1', '1008.bz1', '1008.ce1', '1008.ch1', '1008.cl1', '1008.cr1', '1008.cu1', '1008.cv1', '1008.de1'], 'contains': ['4032.f1', '4032.j1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [3297, -1, 7237, -1], 'generators': [6314117455, 40193], 'label': '8064.cw.2016.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.c1', 'old_label': '2016.bf1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.bf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961759
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.cr1', '672.cy1', '1008.r1', '1008.bt1', '1008.co1', '1008.cw1', '1008.cx1'], 'contains': ['4032.f1', '4032.k1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [4849, -1, 5740, -1], 'generators': [5183, 87302038659], 'label': '8064.cw.2016.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.n1', 'old_label': '2016.bg1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.bg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961760
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '42.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.cs1', '1008.s1', '1008.bl1', '1008.bu1', '1008.cb1', '1008.ci1', '1008.cm1', '1008.cp1', '1008.cs1', '1008.cu1', '1008.cw1', '1008.cy1', '1008.cz1'], 'contains': ['4032.f1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [1804, -1, 8931, -1], 'generators': [127383097, 40193], 'label': '8064.cw.2016.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '2016.bh1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961761
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '42.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.ct1', '1008.s1', '1008.bm1', '1008.bv1', '1008.cc1', '1008.cj1', '1008.cn1', '1008.cq1', '1008.ct1', '1008.cv1', '1008.cx1', '1008.da1', '1008.db1', '1008.df1'], 'contains': ['4032.f1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [1877, -1, 8339, -1], 'generators': [12217, 40193], 'label': '8064.cw.2016.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '2016.bi1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.bi1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961762
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1', '24.c1'], 'contains': ['96.a1', '96.l1', '96.n1', '144.c1', '336.m1'], 'core': '672.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7541, -1, 2630, -1], 'generators': [127370880, 93405312000, 174396866011, 6230651542, 40279680], 'label': '8064.cw.48.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '48.h1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1', 'subgroup_fusion': None, 'weyl_group': '504.162'}
    • id: 253961763
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.cu1', '1008.u1', '1008.bl1', '1008.bm1', '1008.bw1', '1008.cd1', '1008.cf1', '1008.cr1', '1008.dc1'], 'contains': ['4032.f1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [2596, -1, 7392, -1], 'generators': [87103417, 40193], 'label': '8064.cw.2016.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1', 'old_label': '2016.bj1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.bj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961764
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['672.cv1', '1008.v1', '1008.bn1', '1008.bu1', '1008.bv1', '1008.cd1', '1008.cg1', '1008.cl1', '1008.co1', '1008.dd1'], 'contains': ['4032.f1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [2486, -1, 7371, -1], 'generators': [180710986297, 40193], 'label': '8064.cw.2016.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '2016.bk1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.bk1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961765
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '252.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.cw1', '1008.x1', '1008.bn1', '1008.bw1', '1008.cb1', '1008.cc1', '1008.ch1', '1008.ck1', '1008.de1'], 'contains': ['4032.f1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [2520, -1, 7491, -1], 'generators': [180670706617, 40193], 'label': '8064.cw.2016.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.c1', 'old_label': '2016.bl1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.bl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961766
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.cz1', '672.da1', '672.db1', '1008.y1', '1008.bo1', '1008.bx1', '1008.ce1', '1008.ci1', '1008.dc1', '1008.dd1', '1008.de1', '1008.df1'], 'contains': ['4032.f1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3098, -1, 7106, -1], 'generators': [5455, 40193], 'label': '8064.cw.2016.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '2016.bm1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.bm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 253961767
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '252.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['672.dc1', '1008.ba1', '1008.bi1', '1008.bk1', '1008.bp1', '1008.bs1', '1008.by1', '1008.ca1'], 'contains': ['4032.g1', '4032.i1', '4032.j1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 1008, 'diagramx': [4773, -1, 5986, -1], 'generators': [6314117455, 6354431873], 'label': '8064.cw.2016.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.c1', 'old_label': '2016.bn1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.bn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961768
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2016.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['672.dd1', '672.de1', '672.df1', '672.dg1', '1008.bc1', '1008.bq1', '1008.bt1'], 'contains': ['4032.h1', '4032.i1', '4032.k1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 1008, 'diagramx': [7351, -1, 3389, -1], 'generators': [87305667263, 87302038659], 'label': '8064.cw.2016.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '504.k1', 'old_label': '2016.bo1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.bo1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961769
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2688.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': ['3.a1'], 'conjugacy_class_count': 1, 'contained_in': ['384.a1', '896.a1', '1344.a1', '1344.b1', '1344.e1', '1344.j1', '1344.k1', '1344.m1', '1344.o1', '1344.q1', '1344.u1', '1344.x1', '1344.bb1'], 'contains': ['8064.a1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5994, 8589, 4804, 9093], 'generators': [93405312000], 'label': '8064.cw.2688.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '2688.a1', 'normal_contained_in': ['16.a1', '1344.a1', '1344.b1'], 'normal_contains': ['8064.a1'], 'normalizer': '1.a1', 'old_label': '2688.a1', 'projective_image': '8064.cw', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1344.11295', 'quotient_action_kernel_order': 1344, 'quotient_fusion': None, 'short_label': '2688.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961770
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2688.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.b1', '672.da1', '896.a1', '1344.c1', '1344.f1', '1344.h1', '1344.i1', '1344.l1', '1344.n1', '1344.p1', '1344.r1', '1344.t1', '1344.v1', '1344.y1', '1344.ba1', '1344.bc1'], 'contains': ['8064.a1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [6638, -1, 4587, -1], 'generators': [39894], 'label': '8064.cw.2688.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '2688.b1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2688.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961771
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '2688.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.c1', '672.db1', '896.a1', '1344.d1', '1344.g1', '1344.s1', '1344.w1', '1344.z1', '1344.bd1'], 'contains': ['8064.a1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [6799, -1, 4051, -1], 'generators': [93405351894], 'label': '8064.cw.2688.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.g1', 'old_label': '2688.c1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2688.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 253961772
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4032.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['576.a1', '1344.a1', '1344.c1', '1344.d1', '2016.a1', '2016.b1', '2016.c1', '2016.d1', '2016.e1', '2016.f1', '2016.g1', '2016.h1', '2016.i1', '2016.j1', '2016.k1'], 'contains': ['8064.a1'], 'core': '4032.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8241, 8885, 2531, 9421], 'generators': [127370880], 'label': '8064.cw.4032.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '4032.a1', 'normal_contained_in': ['24.a1', '1344.a1', '2016.a1'], 'normal_contains': ['8064.a1'], 'normalizer': '1.a1', 'old_label': '4032.a1', 'projective_image': '4032.ds', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4032.ds', 'quotient_action_kernel_order': 4032, 'quotient_fusion': None, 'short_label': '4032.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961773
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '16.e1', '24.b1'], 'contains': ['96.d1', '96.i1', '96.k1', '96.t1', '144.d1', '336.r1'], 'core': '4032.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8501, -1, 1261, -1], 'generators': [127370880, 127375496, 6230651542, 6227020800, 6227024731], 'label': '8064.cw.48.i1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '48.i1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
    • id: 253961774
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4032.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.b1', '1344.e1', '1344.f1', '1344.g1', '2016.a1', '2016.l1', '2016.m1', '2016.n1', '2016.o1'], 'contains': ['8064.a1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6201, -1, 4768, -1], 'generators': [87091200], 'label': '8064.cw.4032.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2016.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4032.b1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961775
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4032.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.c1', '1344.b1', '1344.h1', '2016.b1', '2016.l1', '2016.p1', '2016.q1', '2016.r1', '2016.s1'], 'contains': ['8064.a1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6214, -1, 4750, -1], 'generators': [87178291200], 'label': '8064.cw.4032.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1344.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '4032.c1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961776
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4032.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.d1', '1344.i1', '1344.j1', '2016.c1', '2016.l1', '2016.t1', '2016.u1', '2016.v1'], 'contains': ['8064.a1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6166, -1, 4786, -1], 'generators': [87218570880], 'label': '8064.cw.4032.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '672.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '4032.d1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961777
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4032.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1344.k1', '1344.l1', '2016.d1', '2016.m1', '2016.p1', '2016.t1', '2016.w1', '2016.x1', '2016.y1', '2016.z1', '2016.ba1', '2016.bb1'], 'contains': ['8064.a1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [5176, -1, 5760, -1], 'generators': [127376335], 'label': '8064.cw.4032.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '4032.e1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961778
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4032.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1344.m1', '1344.n1', '2016.d1', '2016.n1', '2016.q1', '2016.u1', '2016.bb1', '2016.bc1', '2016.bd1', '2016.be1', '2016.bf1', '2016.bg1', '2016.bh1', '2016.bi1', '2016.bj1', '2016.bk1', '2016.bl1', '2016.bm1'], 'contains': ['8064.a1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [3311, -1, 7106, -1], 'generators': [5455], 'label': '8064.cw.4032.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '4032.f1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961779
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4032.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '42.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1344.o1', '1344.p1', '2016.e1', '2016.m1', '2016.n1', '2016.r1', '2016.v1', '2016.w1', '2016.bc1', '2016.bn1'], 'contains': ['8064.a1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [5149, -1, 5857, -1], 'generators': [87096655], 'label': '8064.cw.4032.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1', 'old_label': '4032.g1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961780
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4032.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.e1', '1344.q1', '1344.r1', '1344.s1', '1344.t1', '2016.f1', '2016.s1', '2016.x1', '2016.bd1', '2016.bo1'], 'contains': ['8064.a1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [7264, -1, 3321, -1], 'generators': [3630742], 'label': '8064.cw.4032.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.i1', 'old_label': '4032.h1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961781
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4032.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '63.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1344.u1', '1344.v1', '1344.w1', '2016.g1', '2016.o1', '2016.p1', '2016.q1', '2016.v1', '2016.y1', '2016.be1', '2016.bn1', '2016.bo1'], 'contains': ['8064.a1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5498, -1, 5663, -1], 'generators': [6227026255], 'label': '8064.cw.4032.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '4032.i1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961782
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4032.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1344.x1', '1344.y1', '1344.z1', '2016.h1', '2016.o1', '2016.r1', '2016.t1', '2016.u1', '2016.z1', '2016.bf1', '2016.bn1'], 'contains': ['8064.a1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5230, -1, 5810, -1], 'generators': [6314117455], 'label': '8064.cw.4032.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.c1', 'old_label': '4032.j1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961783
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4032.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.f1', '1344.ba1', '1344.bb1', '1344.bc1', '1344.bd1', '2016.i1', '2016.s1', '2016.ba1', '2016.bg1', '2016.bo1'], 'contains': ['8064.a1'], 'core': '8064.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [7435, -1, 3338, -1], 'generators': [6230651542], 'label': '8064.cw.4032.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.t1', 'old_label': '4032.k1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961784
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '16.f1', '24.b1'], 'contains': ['96.d1', '96.o1', '96.p1', '144.e1', '336.t1'], 'core': '4032.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9344, -1, 508, -1], 'generators': [127370880, 127375496, 6227020800, 6274197142, 6227024731], 'label': '8064.cw.48.j1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '48.j1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
    • id: 253961785
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '8064.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1152.a1', '2688.a1', '2688.b1', '2688.c1', '4032.a1', '4032.b1', '4032.c1', '4032.d1', '4032.e1', '4032.f1', '4032.g1', '4032.h1', '4032.i1', '4032.j1', '4032.k1'], 'contains': [], 'core': '8064.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6201, 8740, 4768, 9257], 'generators': [], 'label': '8064.cw.8064.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '8064.a1', 'normal_contained_in': ['48.a1', '2688.a1', '4032.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '8064.a1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8064.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 253961786
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '24.c1'], 'contains': ['96.e1', '96.h1', '96.l1', '96.u1', '144.d1', '336.x1'], 'core': '672.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [7384, -1, 3109, -1], 'generators': [127370880, 93405312000, 87178291200, 180583607131, 6230651542], 'label': '8064.cw.48.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '48.k1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1', 'subgroup_fusion': None, 'weyl_group': '504.162'}
    • id: 253961787
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1', '24.c1'], 'contains': ['96.e1', '96.m1', '96.n1', '144.e1', '336.y1'], 'core': '672.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [8705, -1, 1813, -1], 'generators': [127370880, 93405312000, 87178291200, 180583607131, 6274197142], 'label': '8064.cw.48.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '48.l1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1', 'subgroup_fusion': None, 'weyl_group': '504.162'}
    • id: 253961788
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '16.g1', '24.b1'], 'contains': ['96.f1', '96.i1', '96.p1', '144.f1', '336.bb1'], 'core': '4032.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8765, -1, 684, -1], 'generators': [127370880, 6267300480, 6267304411, 3630742, 6314116616], 'label': '8064.cw.48.m1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '48.m1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
    • id: 253961789
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '16.h1', '24.b1'], 'contains': ['96.f1', '96.k1', '96.o1', '144.g1', '336.bd1'], 'core': '4032.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8826, -1, 657, -1], 'generators': [127370880, 6267300480, 6267304411, 6230651542, 6314116616], 'label': '8064.cw.48.n1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '48.n1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
    • id: 253961790
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1', '24.c1'], 'contains': ['96.g1', '96.h1', '96.n1', '144.f1', '336.bh1'], 'core': '672.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [7693, -1, 2601, -1], 'generators': [180623886811, 127370880, 87218570880, 93408942742, 93405312000], 'label': '8064.cw.48.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '48.o1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1', 'subgroup_fusion': None, 'weyl_group': '504.162'}
    • id: 253961791
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.d1', '2.e1'], 'contains': ['8.a1', '8.b1', '12.d1', '28.f1', '32.b1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6868, 2323, 2996, 627], 'generators': [127370880, 93405312000, 87178291200, 180710987155, 87178315549], 'label': '8064.cw.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.d1', '2.e1'], 'normal_contains': ['8.a1', '8.b1', '672.b1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '2016.cw'}
    • id: 253961792
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1', '24.c1'], 'contains': ['96.g1', '96.l1', '96.m1', '144.g1', '336.bi1'], 'core': '672.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [7563, -1, 2659, -1], 'generators': [180623886811, 127370880, 87218570880, 93405312000, 6230651542], 'label': '8064.cw.48.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '48.p1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1', 'subgroup_fusion': None, 'weyl_group': '504.162'}
    • id: 253961793
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1', '28.a1'], 'contains': ['112.a1', '112.b1', '112.e1', '112.h1', '112.i1', '112.n1', '112.o1', '112.bk1', '112.bl1', '168.a1', '168.d1'], 'core': '336.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [5996, -1, 4076, -1], 'generators': [127370880, 93405312000, 87178291200, 6314117455, 6354391984, 40279680], 'label': '8064.cw.56.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.a1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 253961794
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1344.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '28.a1'], 'contains': ['112.a1', '112.c1', '112.f1', '112.j1', '112.l1', '112.p1', '112.r1', '168.b1', '168.e1'], 'core': '336.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [7861, -1, 2067, -1], 'generators': [127370880, 93405312000, 93492407816, 87178291200, 6230651542, 40279680], 'label': '8064.cw.56.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.b1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
    • id: 253961795
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1'], 'contains': ['112.a1', '112.d1', '112.g1', '112.k1', '112.m1', '112.q1', '112.s1', '168.c1', '168.e1'], 'core': '336.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [8140, -1, 2113, -1], 'generators': [127370880, 93405312000, 87178291200, 174356606935, 180630792113, 40279680], 'label': '8064.cw.56.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.c1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
    • id: 253961796
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1344.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '28.a1'], 'contains': ['112.b1', '112.c1', '112.d1', '112.t1', '112.v1', '112.y1', '112.z1', '168.f1', '168.k1'], 'core': '672.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [8580, -1, 2210, -1], 'generators': [127370880, 174403771313, 93405312000, 93485545359, 174356606935, 40279680], 'label': '8064.cw.56.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.d1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
    • id: 253961797
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '28.a1'], 'contains': ['112.b1', '112.f1', '112.g1', '112.u1', '112.w1', '112.ba1', '112.bb1', '168.h1', '168.l1'], 'core': '672.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [7985, -1, 2441, -1], 'generators': [127370880, 93405312000, 6307254159, 174356606935, 180630792113, 40279680], 'label': '8064.cw.56.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.e1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
    • id: 253961798
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.b1', '28.c1', '28.d1'], 'contains': ['112.x1', '112.bm1', '168.m1', '168.n1', '168.o1', '224.a1'], 'core': '672.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [5001, -1, 4877, -1], 'generators': [127370880, 127410774, 93405312000, 93405352193, 93445608376, 40279680], 'label': '8064.cw.56.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.f1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.f1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
    • id: 253961799
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1'], 'contains': ['112.c1', '112.e1', '112.g1', '112.bc1', '112.bd1', '112.bg1', '112.bj1', '168.p1', '168.q1', '168.r1'], 'core': '672.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [8972, -1, 1592, -1], 'generators': [127370880, 93405312000, 93485545359, 174356606935, 180630792113, 40279680], 'label': '8064.cw.56.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.g1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.g1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
    • id: 253961800
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1'], 'contains': ['112.d1', '112.e1', '112.f1', '112.be1', '112.bf1', '112.bh1', '112.bi1', '168.p1', '168.s1'], 'core': '672.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [8195, -1, 2368, -1], 'generators': [127370880, 174403771313, 93405312000, 6307254159, 174356606935, 40279680], 'label': '8064.cw.56.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.h1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.h1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
    • id: 253961801
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '28.a1'], 'contains': ['112.h1', '112.j1', '112.k1', '112.t1', '112.u1', '112.bc1', '112.be1', '112.bn1', '112.bo1', '168.t1', '168.z1'], 'core': '672.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [7252, -1, 3100, -1], 'generators': [127370880, 180587246513, 93405312000, 87178291200, 6350799759, 174356606935], 'label': '8064.cw.56.i1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.i1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 253961802
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': ['2016.bo1', '2016.s1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.f1', '2.g1'], 'contains': ['8.a1', '8.e1', '12.e1', '28.h1', '32.c1'], 'core': '4.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6815, 742, 3068, 1964], 'generators': [87218595229, 127370880, 87218570880, 93405312000, 174483966355], 'label': '8064.cw.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.f1', '2.g1'], 'normal_contains': ['8.a1', '672.c1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '4032.ds', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '2016.cw'}
    • id: 253961803
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '28.a1'], 'contains': ['112.h1', '112.l1', '112.m1', '112.v1', '112.w1', '112.bg1', '112.bh1', '168.u1', '168.bb1'], 'core': '672.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [8891, -1, 1631, -1], 'generators': [127370880, 93405312000, 87178291200, 6307254159, 174356606935, 180630792113], 'label': '8064.cw.56.j1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.j1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.j1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 253961804
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.b1', '28.e1', '28.f1'], 'contains': ['112.x1', '112.bp1', '168.v1', '168.bd1', '224.b1'], 'core': '672.b1', 'coset_action_label': None, 'count': 14, 'diagramx': [4595, -1, 4969, -1], 'generators': [127370880, 93405312000, 87178291200, 6227037496, 93405352193, 87305701974], 'label': '8064.cw.56.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.k1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.k1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
    • id: 253961805
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1'], 'contains': ['112.i1', '112.j1', '112.m1', '112.y1', '112.ba1', '112.bd1', '112.bi1', '168.w1', '168.be1'], 'core': '672.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [8369, -1, 2256, -1], 'generators': [127370880, 93405312000, 87178291200, 6350799759, 174356606935, 180630792113], 'label': '8064.cw.56.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.l1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.l1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
    • id: 253961806
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1'], 'contains': ['112.i1', '112.k1', '112.l1', '112.z1', '112.bb1', '112.bf1', '112.bj1', '168.x1', '168.be1'], 'core': '672.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [8319, -1, 2297, -1], 'generators': [127370880, 180587246513, 93405312000, 87178291200, 6307254159, 174356606935], 'label': '8064.cw.56.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.m1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.m1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
    • id: 253961807
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1', '28.a1'], 'contains': ['112.n1', '112.p1', '112.q1', '112.t1', '112.w1', '112.bd1', '112.bf1', '168.bf1', '168.bl1'], 'core': '672.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [7936, -1, 2400, -1], 'generators': [127370880, 87218570880, 93405312000, 6307254159, 174356606935, 180630792113], 'label': '8064.cw.56.n1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.n1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.n1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
    • id: 253961808
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1', '28.a1'], 'contains': ['112.n1', '112.r1', '112.s1', '112.u1', '112.v1', '112.bi1', '112.bj1', '168.bg1', '168.bm1'], 'core': '672.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [8061, -1, 2337, -1], 'generators': [127370880, 87218570880, 174403771313, 93405312000, 93485545359, 174356606935], 'label': '8064.cw.56.o1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.o1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.o1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
    • id: 253961809
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.b1', '28.g1', '28.h1'], 'contains': ['112.x1', '112.bq1', '168.bh1', '168.bp1', '224.c1'], 'core': '672.c1', 'coset_action_label': None, 'count': 14, 'diagramx': [4905, -1, 5021, -1], 'generators': [127370880, 127410774, 87218570880, 93405312000, 6267317176, 93405352193], 'label': '8064.cw.56.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.p1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.p1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
    • id: 253961810
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1'], 'contains': ['112.o1', '112.p1', '112.s1', '112.y1', '112.bb1', '112.bc1', '112.bh1', '168.bi1', '168.bq1'], 'core': '672.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [8236, -1, 2145, -1], 'generators': [127370880, 87218570880, 174403771313, 93405312000, 6307254159, 174356606935], 'label': '8064.cw.56.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.q1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.q1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
    • id: 253961811
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1'], 'contains': ['112.o1', '112.q1', '112.r1', '112.z1', '112.ba1', '112.be1', '112.bg1', '168.bj1', '168.bq1'], 'core': '672.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [8105, -1, 2170, -1], 'generators': [127370880, 87218570880, 93405312000, 93485545359, 174356606935, 180630792113], 'label': '8064.cw.56.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1', 'old_label': '56.r1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.r1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
    • id: 253961812
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.d1', '28.e1', '28.g1'], 'contains': ['112.x1', '112.bs1', '168.cl1', '168.cm1', '224.e1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4710, -1, 5144, -1], 'generators': [127370880, 93492408655, 127410774, 93405312000, 93405352193, 93405328696], 'label': '8064.cw.56.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.s1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.s1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
    • id: 253961813
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1344.a1', 'complements': ['2016.bn1', '2016.v1', '2016.r1', '2016.o1', '2016.l1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.d1', '2.f1'], 'contains': ['8.a1', '8.f1', '12.b1', '32.d1', '84.bw1', '112.t1'], 'core': '4.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7192, 4585, 2735, 4221], 'generators': [127370880, 93405312000, 93532721625, 174480355824], 'label': '8064.cw.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.b1', '2.d1', '2.f1'], 'normal_contains': ['8.a1', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '4032.ds', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '1344.11684'}
    • id: 253961814
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.c1', '28.f1', '28.g1'], 'contains': ['112.x1', '112.bt1', '168.cn1', '168.co1', '168.cp1', '224.h1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4771, -1, 4923, -1], 'generators': [127370880, 127410774, 93405312000, 93405352193, 6354397135, 93405328696], 'label': '8064.cw.56.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.t1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.t1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
    • id: 253961815
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.c1', '28.e1', '28.h1'], 'contains': ['112.x1', '112.bu1', '168.cq1', '168.cr1', '168.cs1', '224.i1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4840, -1, 5067, -1], 'generators': [127370880, 127410774, 93405312000, 6314117455, 93405352193, 93405328696], 'label': '8064.cw.56.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.u1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.u1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
    • id: 253961816
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '28.d1', '28.f1', '28.h1'], 'contains': ['112.x1', '112.br1', '112.bv1', '168.ct1', '168.cu1', '224.d1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4955, -1, 5393, -1], 'generators': [127370880, 127410774, 93405312000, 93532688335, 93405352193, 93405328696], 'label': '8064.cw.56.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.v1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.v1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
    • id: 253961817
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.b1', '28.i1', '28.j1'], 'contains': ['112.bm1', '112.bp1', '112.bq1', '168.cv1', '168.cz1', '224.p1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 56, 'diagramx': [4806, -1, 5186, -1], 'generators': [93405312000, 87178291200, 6227037496, 87265422294, 87091200, 93405352193], 'label': '8064.cw.56.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.w1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.w1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
    • id: 253961818
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['28.d1', '28.i1'], 'contains': ['112.bm1', '112.br1', '112.bs1', '168.db1', '168.dd1', '224.q1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4563, -1, 5327, -1], 'generators': [93492419896, 93445597135, 39894, 93405312000, 87091200, 93405352193], 'label': '8064.cw.56.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.x1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.x1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
    • id: 253961819
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.c1', '28.i1', '28.j1'], 'contains': ['112.bm1', '112.bt1', '112.bu1', '168.dg1', '168.dh1', '168.di1', '224.s1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [4738, -1, 5107, -1], 'generators': [39894, 93405312000, 6314117455, 93405352193, 93445608376, 40279680], 'label': '8064.cw.56.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.y1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.y1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
    • id: 253961820
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '28.d1', '28.j1'], 'contains': ['112.bm1', '112.bs1', '112.bv1', '168.dj1', '168.dk1', '224.r1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [5045, -1, 5460, -1], 'generators': [93492419896, 93492408655, 39894, 93405312000, 87091200, 93405352193], 'label': '8064.cw.56.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.z1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.z1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
    • id: 253961821
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['28.f1', '28.i1'], 'contains': ['112.bp1', '112.br1', '112.bt1', '168.dl1', '168.dp1', '224.t1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [4493, -1, 5229, -1], 'generators': [87178331094, 93405312000, 87178291200, 6227037496, 93405352193, 6354397135], 'label': '8064.cw.56.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.ba1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.ba1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
    • id: 253961822
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.e1', '28.i1', '28.j1'], 'contains': ['112.bp1', '112.bs1', '112.bu1', '168.dm1', '168.dx1', '224.v1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 56, 'diagramx': [4367, -1, 5294, -1], 'generators': [87305662080, 93405312000, 6354408376, 6314117455, 93405352193, 87305701974], 'label': '8064.cw.56.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.bb1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bb1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
    • id: 253961823
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '28.f1', '28.j1'], 'contains': ['112.bp1', '112.bt1', '112.bv1', '168.dn1', '168.dy1', '224.u1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [4626, -1, 5426, -1], 'generators': [87178331094, 93405312000, 87178291200, 6227037496, 6227026255, 93405352193], 'label': '8064.cw.56.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.bc1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
    • id: 253961824
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': ['2016.v1', '2016.l1', '2016.r1', '2016.o1', '2016.bn1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.d1', '2.g1'], 'contains': ['8.a1', '8.g1', '12.f1', '32.e1', '84.bx1', '112.u1'], 'core': '4.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [7233, 5810, 2800, 3186], 'generators': [127370880, 93405312000, 180707376624, 93532721625], 'label': '8064.cw.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.c1', '2.d1', '2.g1'], 'normal_contains': ['8.a1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '4032.ds', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '4032.ds'}
    • id: 253961825
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['28.h1', '28.i1'], 'contains': ['112.bq1', '112.br1', '112.bu1', '168.dz1', '168.ed1', '224.y1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4650, -1, 5360, -1], 'generators': [39894, 93405312000, 6314128696, 6267305935, 93405352193, 87265382400], 'label': '8064.cw.56.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.bd1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bd1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
    • id: 253961826
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.g1', '28.i1', '28.j1'], 'contains': ['112.bq1', '112.bs1', '112.bt1', '168.ea1', '168.eh1', '224.ba1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [4538, -1, 5261, -1], 'generators': [93492408655, 39894, 93405312000, 6314128696, 93405352193, 87265382400], 'label': '8064.cw.56.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.be1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.be1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
    • id: 253961827
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '56.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '28.h1', '28.j1'], 'contains': ['112.bq1', '112.bu1', '112.bv1', '168.eb1', '168.ei1', '224.z1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4873, -1, 5493, -1], 'generators': [87218570880, 39894, 93405312000, 6267317176, 6267305935, 93405352193], 'label': '8064.cw.56.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.bf1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bf1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
    • id: 253961828
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '63.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '21.a1'], 'contains': ['126.a1', '126.b1', '126.c1', '126.d1', '126.e1', '126.f1', '126.g1', '126.h1', '126.i1', '126.j1', '126.k1', '126.l1', '126.m1', '126.n1', '126.o1'], 'core': '2016.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [1305, -1, 8919, -1], 'generators': [127370880, 87258493059, 87178291200, 40284863, 127409625, 87305691590, 40279680], 'label': '8064.cw.63.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '63.a1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '63.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
    • id: 253961829
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '32.a1', '32.b1', '32.c1', '32.d1', '32.e1', '32.f1', '32.g1'], 'contains': ['128.a1', '192.a1', '192.b1', '192.c1', '448.a1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7763, -1, 2035, -1], 'generators': [127370880, 93405312000, 127388033, 37070], 'label': '8064.cw.64.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '64.a1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
    • id: 253961830
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '32.a1', '32.h1'], 'contains': ['128.a1', '192.d1', '192.e1', '192.f1', '448.b1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6773, -1, 3060, -1], 'generators': [87128270, 93405312000, 87108353, 87091200], 'label': '8064.cw.64.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '64.b1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
    • id: 253961831
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '32.b1', '32.h1', '32.i1'], 'contains': ['128.a1', '192.g1', '192.h1', '448.c1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [6688, -1, 3417, -1], 'generators': [87305662080, 93405312000, 37070, 17153], 'label': '8064.cw.64.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '64.c1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1', 'subgroup_fusion': None, 'weyl_group': '252.26'}
    • id: 253961832
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '32.c1', '32.h1'], 'contains': ['128.a1', '192.i1', '192.j1', '448.d1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6527, -1, 3205, -1], 'generators': [87218570880, 87218588033, 93405312000, 87218607950], 'label': '8064.cw.64.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '64.d1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1', 'subgroup_fusion': None, 'weyl_group': '126.8'}
    • id: 253961833
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1344.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1', '32.d1', '32.i1'], 'contains': ['128.a1', '192.k1', '192.l1', '192.m1', '448.h1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7185, -1, 2593, -1], 'generators': [93405316616, 93408942742, 93405312000, 174356586331], 'label': '8064.cw.64.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.e1', 'old_label': '64.e1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
    • id: 253961834
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1', '32.e1', '32.i1'], 'contains': ['128.a1', '192.n1', '192.o1', '448.l1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7121, -1, 2942, -1], 'generators': [93405316616, 93405312000, 6230651542, 174356586331], 'label': '8064.cw.64.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.e1', 'old_label': '64.f1', 'projective_image': '8064.cw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1', 'subgroup_fusion': None, 'weyl_group': '252.26'}
    • id: 253961835
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1344.a1', 'complements': ['2016.bo1', '2016.s1', '2016.o1', '2016.bn1', '2016.l1', '2016.r1', '2016.v1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.e1', '2.g1'], 'contains': ['8.a1', '12.c1', '32.f1', '84.by1', '112.v1'], 'core': '4.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [8758, 8703, 2134, 6014], 'generators': [127370880, 93405312000, 174436810224, 93532721625], 'label': '8064.cw.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.b1', '2.e1', '2.g1'], 'normal_contains': ['8.a1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '4032.ds', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '1344.11684'}
    • id: 253961836
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.c1'], 'contains': ['144.a1', '144.b1', '144.c1', '144.d1', '144.e1', '144.f1', '144.g1', '504.b1'], 'core': '2016.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9370, -1, 583, -1], 'generators': [127370880, 6267304411, 6230651542, 6227020800, 40279680], 'label': '8064.cw.72.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '72.a1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
    • id: 253961837
      {'ambient': '8064.cw', 'aut_centralizer_order': None, 'aut_label': '84.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '28.a1'], 'contains': ['168.a1', '168.b1', '168.c1', '168.k1', '168.l1', '168.q1', '168.s1', '168.t1', '168.u1', '168.w1', '168.x1', '168.bf1', '168.bg1', '168.bi1', '168.bj1', '252.a1'], 'core': '2016.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [9101, -1, 1305, -1], 'generators': [127370880, 180583603200, 180663836559, 24535, 180630792113, 40279680], 'label': '8064.cw.84.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1', 'old_label': '84.a1', 'projective_image': '4032.ds', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}