Formats: - HTML - YAML - JSON - 2026-07-24T15:35:03.872839
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [8, 12, 6, 6, 24], 'aut_gens': [[1, 2, 48, 144, 432, 1296, 3888, 11664], [26829, 17746, 7008, 14256, 3168, 21792, 21120, 17328], [31977, 386, 30384, 32064, 5328, 30096, 12672, 22464], [27129, 26710, 21888, 11904, 14448, 12528, 14592, 25296], [18513, 25654, 96, 7392, 31680, 29712, 33168, 480], [28221, 14306, 8544, 15936, 9840, 21792, 28992, 9456]], 'aut_group': '20480.sl', 'aut_hash': 3343538436977119361, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 419904, 'aut_permdeg': 1782, 'aut_perms': 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'aut_phi_ratio': 36.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 324, 1, 1], [2, 729, 1, 1], [3, 8, 1, 2], [3, 8, 2, 1], [3, 16, 1, 1], [3, 16, 2, 1], [3, 18, 1, 1], [3, 24, 3, 1], [3, 24, 6, 1], [3, 48, 3, 1], [3, 48, 6, 1], [3, 144, 1, 2], [3, 144, 2, 2], [3, 144, 4, 1], [4, 1458, 1, 1], [4, 8748, 1, 1], [6, 648, 1, 2], [6, 648, 2, 1], [6, 648, 3, 1], [6, 648, 6, 1], [6, 1458, 1, 1], [8, 1458, 1, 2], [12, 1458, 2, 1], [24, 1458, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_2^5.C_2\\wr F_5', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': None, 'autcentquo_hash': 3343538436977119361, 'autcentquo_nilpotent': False, 'autcentquo_order': 419904, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^6.C_3.C_{12}.C_2^4', 'cc_stats': [[1, 1, 1], [2, 324, 1], [2, 729, 1], [3, 8, 4], [3, 16, 3], [3, 18, 1], [3, 24, 9], [3, 48, 9], [3, 144, 10], [4, 1458, 1], [4, 8748, 1], [6, 648, 13], [6, 1458, 1], [8, 1458, 2], [12, 1458, 2], [24, 1458, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '34992.gv', 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 11, 'conjugacy_classes_known': True, 'counter': 178, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 324, 1, 1], [2, 729, 1, 1], [3, 8, 1, 4], [3, 16, 1, 3], [3, 18, 1, 1], [3, 24, 1, 9], [3, 48, 1, 9], [3, 144, 1, 4], [3, 144, 2, 3], [4, 1458, 1, 1], [4, 8748, 1, 1], [6, 648, 1, 13], [6, 1458, 1, 1], [8, 1458, 2, 1], [12, 1458, 2, 1], [24, 1458, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 576, 'exponent': 24, 'exponents_of_order': [7, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 1, 12], [48, 1, 9]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '3888.ct', 'hash': 8428647213182937126, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [6, 24, 3, 3, 3, 3, 3, 3], 'inner_gens': [[1, 26134, 48, 31152, 1728, 2592, 14112, 26400], [9485, 2, 7008, 9696, 14016, 11760, 1536, 1104], [1, 10034, 48, 144, 432, 1296, 3888, 11664], [15793, 7442, 48, 144, 432, 1296, 3888, 11664], [2593, 27170, 48, 144, 432, 1296, 3888, 11664], [2593, 24674, 48, 144, 432, 1296, 3888, 11664], [30385, 6818, 48, 144, 432, 1296, 3888, 11664], [25585, 12434, 48, 144, 432, 1296, 3888, 11664]], 'inner_hash': 8428647213182937126, 'inner_nilpotent': False, 'inner_order': 34992, 'inner_split': True, 'inner_tex': 'C_3^5:S_3.D_{12}', 'inner_used': [1, 2], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 4], [2, 11], [8, 8], [16, 13], [24, 18], [48, 9]], 'label': '34992.gv', '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': None, 'name': 'C3^5:S3.D12', 'ngens': 11, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 31, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 63, 'number_divisions': 55, 'number_normal_subgroups': 19, 'number_subgroup_autclasses': 1944, 'number_subgroup_classes': 8521, 'number_subgroups': 2552154, 'old_label': None, 'order': 34992, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1053], [3, 2186], [4, 10206], [6, 9882], [8, 2916], [12, 2916], [24, 5832]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 34, 18912, 10704, 27552, 14736, 9456, 17232], [15889, 2, 18912, 11904, 12960, 12144, 13104, 33840]], 'outer_group': '12.4', 'outer_hash': 4, 'outer_nilpotent': False, 'outer_order': 12, 'outer_permdeg': 5, 'outer_perms': [6, 31], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 2], [8, 9], [16, 7], [24, 18], [32, 3], [48, 9]], 'representations': {'PC': {'code': '54543240441001891528817350557579409525418953877514635091832537952814262430339541145050063021784439188836981765306558921645045570644025624826340707285093771372224399516478392674671425663', 'gens': [1, 2, 6, 7, 8, 9, 10, 11], 'pres': [11, -2, -2, -2, -2, -3, -3, 3, 3, 3, 3, 3, 34320, 574949, 56, 714254, 90, 874019, 124, 1480164, 231280, 141795, 830, 2398710, 373313, 461104, 52245, 25460, 152071, 616722, 79229, 307864, 151587, 256616, 582139, 238818, 217445, 100735, 1552329, 84500, 504271, 476562, 211583, 3194410, 66813, 877040, 437095, 130371]}, 'Perm': {'d': 36, 'gens': [116697261490772295116603936582471915879759, 64118440377246744272995272286192040366131]}}, 'schur_multiplier': [3], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^5:S_3.D_{12}', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    • id: 160483002
      {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 178, 'group_order': 34992, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 160483013
      {'aut_label': '2A', 'centralizer': '324.BP', 'counter': 2, 'group_counter': 178, 'group_order': 34992, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 34417, 'size': 324}
    • id: 160483024
      {'aut_label': '2B', 'centralizer': '729.a1', 'counter': 3, 'group_counter': 178, 'group_order': 34992, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 33672, 'size': 729}
    • id: 160483035
      {'aut_label': '3A', 'centralizer': '8.B', 'counter': 4, 'group_counter': 178, 'group_order': 34992, 'label': '3A', 'order': 3, 'powers': [4, 1], 'representative': 4896, 'size': 8}
    • id: 160483046
      {'aut_label': '3B', 'centralizer': '8.B', 'counter': 5, 'group_counter': 178, 'group_order': 34992, 'label': '3B', 'order': 3, 'powers': [5, 1], 'representative': 10560, 'size': 8}
    • id: 160483057
      {'aut_label': '3C', 'centralizer': '8.B', 'counter': 6, 'group_counter': 178, 'group_order': 34992, 'label': '3C', 'order': 3, 'powers': [6, 1], 'representative': 31584, 'size': 8}
    • id: 160483062
      {'aut_label': '3A', 'centralizer': '8.B', 'counter': 7, 'group_counter': 178, 'group_order': 34992, 'label': '3D', 'order': 3, 'powers': [7, 1], 'representative': 96, 'size': 8}
    • id: 160483063
      {'aut_label': '3E', 'centralizer': '16.a1', 'counter': 8, 'group_counter': 178, 'group_order': 34992, 'label': '3E', 'order': 3, 'powers': [8, 1], 'representative': 23472, 'size': 16}
    • id: 160483064
      {'aut_label': '3E', 'centralizer': '16.a1', 'counter': 9, 'group_counter': 178, 'group_order': 34992, 'label': '3F', 'order': 3, 'powers': [9, 1], 'representative': 13392, 'size': 16}
    • id: 160483003
      {'aut_label': '3G', 'centralizer': '16.a1', 'counter': 10, 'group_counter': 178, 'group_order': 34992, 'label': '3G', 'order': 3, 'powers': [10, 1], 'representative': 1920, 'size': 16}
    • id: 160483004
      {'aut_label': '3H', 'centralizer': '18.E', 'counter': 11, 'group_counter': 178, 'group_order': 34992, 'label': '3H', 'order': 3, 'powers': [11, 1], 'representative': 5584, 'size': 18}
    • id: 160483005
      {'aut_label': '3I', 'centralizer': '24.H', 'counter': 12, 'group_counter': 178, 'group_order': 34992, 'label': '3I', 'order': 3, 'powers': [12, 1], 'representative': 34272, 'size': 24}
    • id: 160483006
      {'aut_label': '3I', 'centralizer': '24.H', 'counter': 13, 'group_counter': 178, 'group_order': 34992, 'label': '3J', 'order': 3, 'powers': [13, 1], 'representative': 6240, 'size': 24}
    • id: 160483007
      {'aut_label': '3K', 'centralizer': '24.H', 'counter': 14, 'group_counter': 178, 'group_order': 34992, 'label': '3K', 'order': 3, 'powers': [14, 1], 'representative': 14352, 'size': 24}
    • id: 160483008
      {'aut_label': '3K', 'centralizer': '24.H', 'counter': 15, 'group_counter': 178, 'group_order': 34992, 'label': '3L', 'order': 3, 'powers': [15, 1], 'representative': 5040, 'size': 24}
    • id: 160483009
      {'aut_label': '3I', 'centralizer': '24.H', 'counter': 16, 'group_counter': 178, 'group_order': 34992, 'label': '3M', 'order': 3, 'powers': [16, 1], 'representative': 30336, 'size': 24}
    • id: 160483010
      {'aut_label': '3I', 'centralizer': '24.H', 'counter': 17, 'group_counter': 178, 'group_order': 34992, 'label': '3N', 'order': 3, 'powers': [17, 1], 'representative': 2256, 'size': 24}
    • id: 160483011
      {'aut_label': '3I', 'centralizer': '24.H', 'counter': 18, 'group_counter': 178, 'group_order': 34992, 'label': '3O', 'order': 3, 'powers': [18, 1], 'representative': 20256, 'size': 24}
    • id: 160483012
      {'aut_label': '3K', 'centralizer': '24.H', 'counter': 19, 'group_counter': 178, 'group_order': 34992, 'label': '3P', 'order': 3, 'powers': [19, 1], 'representative': 28800, 'size': 24}
    • id: 160483014
      {'aut_label': '3I', 'centralizer': '24.H', 'counter': 20, 'group_counter': 178, 'group_order': 34992, 'label': '3Q', 'order': 3, 'powers': [20, 1], 'representative': 33792, 'size': 24}
    • id: 160483015
      {'aut_label': '3R', 'centralizer': '48.A', 'counter': 21, 'group_counter': 178, 'group_order': 34992, 'label': '3R', 'order': 3, 'powers': [21, 1], 'representative': 11664, 'size': 48}
    • id: 160483016
      {'aut_label': '3R', 'centralizer': '48.A', 'counter': 22, 'group_counter': 178, 'group_order': 34992, 'label': '3S', 'order': 3, 'powers': [22, 1], 'representative': 3888, 'size': 48}
    • id: 160483017
      {'aut_label': '3R', 'centralizer': '48.A', 'counter': 23, 'group_counter': 178, 'group_order': 34992, 'label': '3T', 'order': 3, 'powers': [23, 1], 'representative': 432, 'size': 48}
    • id: 160483018
      {'aut_label': '3R', 'centralizer': '48.A', 'counter': 24, 'group_counter': 178, 'group_order': 34992, 'label': '3U', 'order': 3, 'powers': [24, 1], 'representative': 15552, 'size': 48}
    • id: 160483019
      {'aut_label': '3R', 'centralizer': '48.A', 'counter': 25, 'group_counter': 178, 'group_order': 34992, 'label': '3V', 'order': 3, 'powers': [25, 1], 'representative': 12960, 'size': 48}
    • id: 160483020
      {'aut_label': '3W', 'centralizer': '48.A', 'counter': 26, 'group_counter': 178, 'group_order': 34992, 'label': '3W', 'order': 3, 'powers': [26, 1], 'representative': 5184, 'size': 48}
    • id: 160483021
      {'aut_label': '3W', 'centralizer': '48.A', 'counter': 27, 'group_counter': 178, 'group_order': 34992, 'label': '3X', 'order': 3, 'powers': [27, 1], 'representative': 12096, 'size': 48}
    • id: 160483022
      {'aut_label': '3R', 'centralizer': '48.A', 'counter': 28, 'group_counter': 178, 'group_order': 34992, 'label': '3Y', 'order': 3, 'powers': [28, 1], 'representative': 11712, 'size': 48}
    • id: 160483023
      {'aut_label': '3W', 'centralizer': '48.A', 'counter': 29, 'group_counter': 178, 'group_order': 34992, 'label': '3Z', 'order': 3, 'powers': [29, 1], 'representative': 1344, 'size': 48}
    • id: 160483025
      {'aut_label': '3AA', 'centralizer': '144.BS', 'counter': 30, 'group_counter': 178, 'group_order': 34992, 'label': '3AA', 'order': 3, 'powers': [30, 1], 'representative': 1312, 'size': 144}
    • id: 160483026
      {'aut_label': '3AB', 'centralizer': '144.BS', 'counter': 31, 'group_counter': 178, 'group_order': 34992, 'label': '3AB', 'order': 3, 'powers': [31, 1], 'representative': 160, 'size': 144}
    • id: 160483027
      {'aut_label': '3AC', 'centralizer': '144.A', 'counter': 32, 'group_counter': 178, 'group_order': 34992, 'label': '3AC', 'order': 3, 'powers': [32, 1], 'representative': 64, 'size': 144}
    • id: 160483028
      {'aut_label': '3AB', 'centralizer': '144.BS', 'counter': 33, 'group_counter': 178, 'group_order': 34992, 'label': '3AD', 'order': 3, 'powers': [33, 1], 'representative': 4336, 'size': 144}
    • id: 160483029
      {'aut_label': '3AE1', 'centralizer': '144.BS', 'counter': 34, 'group_counter': 178, 'group_order': 34992, 'label': '3AE1', 'order': 3, 'powers': [35, 1], 'representative': 11680, 'size': 144}
    • id: 160483030
      {'aut_label': '3AE1', 'centralizer': '144.BS', 'counter': 35, 'group_counter': 178, 'group_order': 34992, 'label': '3AE-1', 'order': 3, 'powers': [34, 1], 'representative': 11696, 'size': 144}
    • id: 160483031
      {'aut_label': '3AE1', 'centralizer': '144.BS', 'counter': 36, 'group_counter': 178, 'group_order': 34992, 'label': '3AF1', 'order': 3, 'powers': [37, 1], 'representative': 3904, 'size': 144}
    • id: 160483032
      {'aut_label': '3AE1', 'centralizer': '144.BS', 'counter': 37, 'group_counter': 178, 'group_order': 34992, 'label': '3AF-1', 'order': 3, 'powers': [36, 1], 'representative': 448, 'size': 144}
    • id: 160483033
      {'aut_label': '3AG1', 'centralizer': '144.BS', 'counter': 38, 'group_counter': 178, 'group_order': 34992, 'label': '3AG1', 'order': 3, 'powers': [39, 1], 'representative': 5200, 'size': 144}
    • id: 160483034
      {'aut_label': '3AG1', 'centralizer': '144.BS', 'counter': 39, 'group_counter': 178, 'group_order': 34992, 'label': '3AG-1', 'order': 3, 'powers': [38, 1], 'representative': 11824, 'size': 144}
    • id: 160483036
      {'aut_label': '4A', 'centralizer': '1458.C', 'counter': 40, 'group_counter': 178, 'group_order': 34992, 'label': '4A', 'order': 4, 'powers': [3, 40], 'representative': 5844, 'size': 1458}
    • id: 160483037
      {'aut_label': '4B', 'centralizer': '8748.C', 'counter': 41, 'group_counter': 178, 'group_order': 34992, 'label': '4B', 'order': 4, 'powers': [3, 41], 'representative': 9767, 'size': 8748}
    • id: 160483038
      {'aut_label': '6A', 'centralizer': '648.A', 'counter': 42, 'group_counter': 178, 'group_order': 34992, 'label': '6A', 'order': 6, 'powers': [12, 2], 'representative': 145, 'size': 648}
    • id: 160483039
      {'aut_label': '6A', 'centralizer': '648.A', 'counter': 43, 'group_counter': 178, 'group_order': 34992, 'label': '6B', 'order': 6, 'powers': [13, 2], 'representative': 9337, 'size': 648}
    • id: 160483040
      {'aut_label': '6C', 'centralizer': '648.A', 'counter': 44, 'group_counter': 178, 'group_order': 34992, 'label': '6C', 'order': 6, 'powers': [14, 2], 'representative': 2225, 'size': 648}
    • id: 160483041
      {'aut_label': '6C', 'centralizer': '648.A', 'counter': 45, 'group_counter': 178, 'group_order': 34992, 'label': '6D', 'order': 6, 'powers': [15, 2], 'representative': 12869, 'size': 648}
    • id: 160483042
      {'aut_label': '6E', 'centralizer': '648.A', 'counter': 46, 'group_counter': 178, 'group_order': 34992, 'label': '6E', 'order': 6, 'powers': [4, 2], 'representative': 5269, 'size': 648}
    • id: 160483043
      {'aut_label': '6A', 'centralizer': '648.A', 'counter': 47, 'group_counter': 178, 'group_order': 34992, 'label': '6F', 'order': 6, 'powers': [16, 2], 'representative': 2821, 'size': 648}
    • id: 160483044
      {'aut_label': '6A', 'centralizer': '648.A', 'counter': 48, 'group_counter': 178, 'group_order': 34992, 'label': '6G', 'order': 6, 'powers': [17, 2], 'representative': 13009, 'size': 648}
    • id: 160483045
      {'aut_label': '6H', 'centralizer': '648.A', 'counter': 49, 'group_counter': 178, 'group_order': 34992, 'label': '6H', 'order': 6, 'powers': [5, 2], 'representative': 9581, 'size': 648}
    • id: 160483047
      {'aut_label': '6I', 'centralizer': '648.A', 'counter': 50, 'group_counter': 178, 'group_order': 34992, 'label': '6I', 'order': 6, 'powers': [6, 2], 'representative': 26981, 'size': 648}
    • id: 160483048
      {'aut_label': '6A', 'centralizer': '648.A', 'counter': 51, 'group_counter': 178, 'group_order': 34992, 'label': '6J', 'order': 6, 'powers': [18, 2], 'representative': 1877, 'size': 648}
    • id: 160483049
      {'aut_label': '6C', 'centralizer': '648.A', 'counter': 52, 'group_counter': 178, 'group_order': 34992, 'label': '6K', 'order': 6, 'powers': [19, 2], 'representative': 10341, 'size': 648}
    • id: 160483050
      {'aut_label': '6E', 'centralizer': '648.A', 'counter': 53, 'group_counter': 178, 'group_order': 34992, 'label': '6L', 'order': 6, 'powers': [7, 2], 'representative': 34465, 'size': 648}
    • id: 160483051
      {'aut_label': '6A', 'centralizer': '648.A', 'counter': 54, 'group_counter': 178, 'group_order': 34992, 'label': '6M', 'order': 6, 'powers': [20, 2], 'representative': 31221, 'size': 648}
    • id: 160483052
      {'aut_label': '6N', 'centralizer': '1458.C', 'counter': 55, 'group_counter': 178, 'group_order': 34992, 'label': '6N', 'order': 6, 'powers': [11, 3], 'representative': 26984, 'size': 1458}
    • id: 160483053
      {'aut_label': '8A1', 'centralizer': '1458.C', 'counter': 56, 'group_counter': 178, 'group_order': 34992, 'label': '8A1', 'order': 8, 'powers': [40, 56], 'representative': 4218, 'size': 1458}
    • id: 160483054
      {'aut_label': '8A-1', 'centralizer': '1458.C', 'counter': 57, 'group_counter': 178, 'group_order': 34992, 'label': '8A-1', 'order': 8, 'powers': [40, 57], 'representative': 23910, 'size': 1458}
    • id: 160483055
      {'aut_label': '12A1', 'centralizer': '1458.C', 'counter': 58, 'group_counter': 178, 'group_order': 34992, 'label': '12A1', 'order': 12, 'powers': [55, 40], 'representative': 1180, 'size': 1458}
    • id: 160483056
      {'aut_label': '12A1', 'centralizer': '1458.C', 'counter': 59, 'group_counter': 178, 'group_order': 34992, 'label': '12A5', 'order': 12, 'powers': [55, 40], 'representative': 19580, 'size': 1458}
    • id: 160483058
      {'aut_label': '24A1', 'centralizer': '1458.C', 'counter': 60, 'group_counter': 178, 'group_order': 34992, 'label': '24A1', 'order': 24, 'powers': [58, 56], 'representative': 30206, 'size': 1458}
    • id: 160483059
      {'aut_label': '24A-1', 'centralizer': '1458.C', 'counter': 61, 'group_counter': 178, 'group_order': 34992, 'label': '24A-1', 'order': 24, 'powers': [58, 57], 'representative': 6514, 'size': 1458}
    • id: 160483060
      {'aut_label': '24A-1', 'centralizer': '1458.C', 'counter': 62, 'group_counter': 178, 'group_order': 34992, 'label': '24A5', 'order': 24, 'powers': [59, 57], 'representative': 21046, 'size': 1458}
    • id: 160483061
      {'aut_label': '24A1', 'centralizer': '1458.C', 'counter': 63, 'group_counter': 178, 'group_order': 34992, 'label': '24A-5', 'order': 24, 'powers': [59, 56], 'representative': 17642, 'size': 1458}
  • gps_qchar • Show schema
    • id: 15774688
      {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.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], 'schur_index': 1}
    • id: 15774699
      {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.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], 'schur_index': 1}
    • id: 15774710
      {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.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], 'schur_index': 1}
    • id: 15774721
      {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.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], 'schur_index': 1}
    • id: 15774732
      {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 15774739
      {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774740
      {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, -2, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 15774741
      {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.2d', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, 0, -4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774742
      {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.2e', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, 0, 4, 4, 4, 4, 4, 4, 4, 4, -2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 2, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774689
      {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.2f', 'multiplicity': 4, 'nt': [24, 35], 'qdim': 8, 'qvalues': [8, 0, -8, 8, 8, 8, 8, 8, 8, 8, -4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774690
      {'cdim': 8, 'counter': 11, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.8a', 'multiplicity': 1, 'nt': [9, 19], 'qdim': 8, 'qvalues': [8, 2, 0, -1, 8, -1, -1, -1, -1, -1, 8, -1, -1, 8, 8, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774691
      {'cdim': 8, 'counter': 12, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.8b', 'multiplicity': 1, 'nt': [9, 19], 'qdim': 8, 'qvalues': [8, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774692
      {'cdim': 8, 'counter': 13, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.8c', 'multiplicity': 1, 'nt': [12, 212], 'qdim': 8, 'qvalues': [8, 2, 0, -1, 8, -1, -1, -1, -1, -1, 8, 2, 2, -1, -1, 5, 5, 2, -1, 5, -4, 2, 2, -4, -4, -1, -1, 2, -1, -1, 2, -1, 5, -4, -4, 2, 2, -1, -1, 0, 0, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774693
      {'cdim': 8, 'counter': 14, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.8d', 'multiplicity': 1, 'nt': [12, 212], 'qdim': 8, 'qvalues': [8, 2, 0, -1, 8, -1, -1, -1, -1, -1, 8, 5, 5, -1, -1, 2, 2, 5, -1, 2, 2, -4, -4, 2, 2, -1, -1, -4, -1, -1, 5, -1, 2, 2, 2, -4, -4, -1, -1, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774694
      {'cdim': 8, 'counter': 15, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.8e', 'multiplicity': 1, 'nt': [18, 68], 'qdim': 8, 'qvalues': [8, -2, 0, -1, 8, -1, -1, -1, -1, -1, 8, -1, -1, 8, 8, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 1, 1, -2, -2, 1, 1, 1, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774695
      {'cdim': 8, 'counter': 16, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.8f', 'multiplicity': 1, 'nt': [18, 68], 'qdim': 8, 'qvalues': [8, -2, 0, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1, -2, 1, 1, -2, -2, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774696
      {'cdim': 8, 'counter': 17, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.8g', 'multiplicity': 1, 'nt': [24, 2890], 'qdim': 8, 'qvalues': [8, -2, 0, -1, 8, -1, -1, -1, -1, -1, 8, 2, 2, -1, -1, 5, 5, 2, -1, 5, -4, 2, 2, -4, -4, -1, -1, 2, -1, -1, 2, -1, 5, -4, -4, 2, 2, -1, -1, 0, 0, -2, -2, 1, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774697
      {'cdim': 8, 'counter': 18, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.8h', 'multiplicity': 1, 'nt': [24, 2890], 'qdim': 8, 'qvalues': [8, -2, 0, -1, 8, -1, -1, -1, -1, -1, 8, 5, 5, -1, -1, 2, 2, 5, -1, 2, 2, -4, -4, 2, 2, -1, -1, -4, -1, -1, 5, -1, 2, 2, 2, -4, -4, -1, -1, 0, 0, 1, 1, 1, 1, 1, -2, -2, -2, 1, 1, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774698
      {'cdim': 16, 'counter': 19, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.16a', 'multiplicity': 1, 'nt': [18, 318], 'qdim': 16, 'qvalues': [16, 0, 0, -2, 16, -2, -2, -2, -2, -2, 16, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 7, 7, -2, 7, -2, -2, -2, -2, -2, -2, -2, -2, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774700
      {'cdim': 16, 'counter': 20, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.16b', 'multiplicity': 1, 'nt': [24, 1333], 'qdim': 16, 'qvalues': [16, 0, 0, -2, 16, -2, -2, -2, -2, -2, -8, -2, -2, 16, 16, -2, -2, -2, 16, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774701
      {'cdim': 16, 'counter': 21, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.16c', 'multiplicity': 1, 'nt': [24, 1333], 'qdim': 16, 'qvalues': [16, 0, 0, 16, 16, 16, 16, 16, 16, 16, -8, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, -8, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774702
      {'cdim': 16, 'counter': 22, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.16d', 'multiplicity': 1, 'nt': [24, 2932], 'qdim': 16, 'qvalues': [16, 0, 0, -2, 16, -2, -2, -2, -2, -2, 16, -8, -8, -2, -2, 4, 4, -8, -2, 4, 4, 1, 1, 4, 4, -2, -2, 1, -2, -2, -8, -2, 4, 4, 4, 1, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774703
      {'cdim': 16, 'counter': 23, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.16e', 'multiplicity': 1, 'nt': [24, 2932], 'qdim': 16, 'qvalues': [16, 0, 0, -2, 16, -2, -2, -2, -2, -2, 16, 4, 4, -2, -2, -8, -8, 4, -2, -8, 1, 4, 4, 1, 1, -2, -2, 4, -2, -2, 4, -2, -8, 1, 1, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774704
      {'cdim': 16, 'counter': 24, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.16f', 'multiplicity': 1, 'nt': [24, 7282], 'qdim': 16, 'qvalues': [16, 0, 0, -2, 16, -2, -2, -2, -2, -2, -8, 4, 4, -2, -2, 10, 10, 4, -2, 10, -8, 4, 4, -8, -8, -2, -2, 4, -2, 1, -2, 1, -5, 4, 4, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774705
      {'cdim': 16, 'counter': 25, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.16g', 'multiplicity': 1, 'nt': [24, 7282], 'qdim': 16, 'qvalues': [16, 0, 0, -2, 16, -2, -2, -2, -2, -2, -8, 10, 10, -2, -2, 4, 4, 10, -2, 4, 4, -8, -8, 4, 4, -2, -2, -8, -2, 1, -5, 1, -2, -2, -2, 4, 4, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774709
      {'cdim': 24, 'counter': 29, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24a', 'multiplicity': 1, 'nt': [27, 545], 'qdim': 24, 'qvalues': [24, 2, 0, -3, -3, 24, -3, -3, -3, -3, 0, -3, -3, -3, 6, -3, -3, 6, -3, 6, -3, -3, -3, -3, 6, 6, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774711
      {'cdim': 24, 'counter': 30, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24b', 'multiplicity': 1, 'nt': [27, 545], 'qdim': 24, 'qvalues': [24, 2, 0, -3, -3, 24, -3, -3, -3, -3, 0, -3, 6, 6, -3, 6, -3, -3, -3, -3, 6, -3, 6, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774712
      {'cdim': 24, 'counter': 31, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24c', 'multiplicity': 1, 'nt': [27, 545], 'qdim': 24, 'qvalues': [24, 2, 0, -3, -3, 24, -3, -3, -3, -3, 0, 6, -3, -3, -3, -3, 6, -3, 6, -3, -3, 6, -3, 6, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774713
      {'cdim': 24, 'counter': 32, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24d', 'multiplicity': 1, 'nt': [36, 13963], 'qdim': 24, 'qvalues': [24, 2, 0, 6, -3, -3, 15, 6, -12, -3, 0, -3, -3, -3, -3, 6, -3, 6, 6, -3, 6, -3, -3, -3, -3, -3, -3, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774714
      {'cdim': 24, 'counter': 33, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24e', 'multiplicity': 1, 'nt': [36, 13963], 'qdim': 24, 'qvalues': [24, 2, 0, 6, -3, -3, 15, 6, -12, -3, 0, -3, 6, -3, 6, -3, 6, -3, -3, -3, -3, -3, 6, 6, -3, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774715
      {'cdim': 24, 'counter': 34, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24f', 'multiplicity': 1, 'nt': [36, 13963], 'qdim': 24, 'qvalues': [24, 2, 0, 6, -3, -3, 15, 6, -12, -3, 0, 6, -3, 6, -3, -3, -3, -3, -3, 6, -3, 6, -3, -3, 6, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774716
      {'cdim': 24, 'counter': 35, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24g', 'multiplicity': 1, 'nt': [36, 13963], 'qdim': 24, 'qvalues': [24, 2, 0, 15, -3, -3, 6, -12, 6, -3, 0, -3, -3, 6, -3, -3, 6, 6, -3, -3, -3, -3, -3, 6, -3, -3, 6, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774717
      {'cdim': 24, 'counter': 36, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24h', 'multiplicity': 1, 'nt': [36, 13963], 'qdim': 24, 'qvalues': [24, 2, 0, 15, -3, -3, 6, -12, 6, -3, 0, -3, 6, -3, -3, -3, -3, -3, 6, 6, -3, -3, 6, -3, 6, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774718
      {'cdim': 24, 'counter': 37, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24i', 'multiplicity': 1, 'nt': [36, 13963], 'qdim': 24, 'qvalues': [24, 2, 0, 15, -3, -3, 6, -12, 6, -3, 0, 6, -3, -3, 6, 6, -3, -3, -3, -3, 6, 6, -3, -3, -3, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774719
      {'cdim': 24, 'counter': 38, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24j', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 24, 'qvalues': [24, -2, 0, -3, -3, 24, -3, -3, -3, -3, 0, -3, -3, -3, 6, -3, -3, 6, -3, 6, -3, -3, -3, -3, 6, 6, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -2, 1, 1, 1, 1, -2, -2, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774720
      {'cdim': 24, 'counter': 39, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24k', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 24, 'qvalues': [24, -2, 0, -3, -3, 24, -3, -3, -3, -3, 0, -3, 6, 6, -3, 6, -3, -3, -3, -3, 6, -3, 6, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, 1, 1, -2, 1, 1, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774722
      {'cdim': 24, 'counter': 40, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24l', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 24, 'qvalues': [24, -2, 0, -3, -3, 24, -3, -3, -3, -3, 0, 6, -3, -3, -3, -3, 6, -3, 6, -3, -3, 6, -3, 6, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1, 1, 1, -2, 1, -2, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774723
      {'cdim': 24, 'counter': 41, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24m', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -2, 0, 6, -3, -3, 15, 6, -12, -3, 0, -3, -3, -3, -3, 6, -3, 6, 6, -3, 6, -3, -3, -3, -3, -3, -3, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -2, -2, 1, 1, 1, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774724
      {'cdim': 24, 'counter': 42, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24n', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -2, 0, 6, -3, -3, 15, 6, -12, -3, 0, -3, 6, -3, 6, -3, 6, -3, -3, -3, -3, -3, 6, 6, -3, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, -2, -2, 1, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774725
      {'cdim': 24, 'counter': 43, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24o', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -2, 0, 6, -3, -3, 15, 6, -12, -3, 0, 6, -3, 6, -3, -3, -3, -3, -3, 6, -3, 6, -3, -3, 6, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, -2, 1, -2, 1, 1, 1, 1, 1, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774726
      {'cdim': 24, 'counter': 44, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24p', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -2, 0, 15, -3, -3, 6, -12, 6, -3, 0, -3, -3, 6, -3, -3, 6, 6, -3, -3, -3, -3, -3, 6, -3, -3, 6, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 1, 1, 1, -2, 1, 1, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774727
      {'cdim': 24, 'counter': 45, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24q', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -2, 0, 15, -3, -3, 6, -12, 6, -3, 0, -3, 6, -3, -3, -3, -3, -3, 6, 6, -3, -3, 6, -3, 6, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774728
      {'cdim': 24, 'counter': 46, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.24r', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -2, 0, 15, -3, -3, 6, -12, 6, -3, 0, 6, -3, -3, 6, 6, -3, -3, -3, -3, 6, 6, -3, -3, -3, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -2, 1, -2, 1, 1, 1, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774706
      {'cdim': 16, 'counter': 26, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.16h', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 32, 'qvalues': [32, 0, 0, -4, 32, -4, -4, -4, -4, -4, -16, -16, -16, -4, -4, 8, 8, -16, -4, 8, 8, 2, 2, 8, 8, -4, -4, 2, -4, 2, 8, 2, -4, -4, -4, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774707
      {'cdim': 16, 'counter': 27, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.16i', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 32, 'qvalues': [32, 0, 0, -4, 32, -4, -4, -4, -4, -4, -16, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 14, 14, -4, 14, 2, 2, 2, 2, 2, 2, 2, 2, -7, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774708
      {'cdim': 16, 'counter': 28, 'faithful': False, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.16j', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 32, 'qvalues': [32, 0, 0, -4, 32, -4, -4, -4, -4, -4, -16, 8, 8, -4, -4, -16, -16, 8, -4, -16, 2, 8, 8, 2, 2, -4, -4, 8, -4, 2, -4, 2, 8, -1, -1, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774729
      {'cdim': 48, 'counter': 47, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.48a', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 48, 'qvalues': [48, 0, 0, -6, -6, -6, -6, -6, -6, 21, 0, -6, -6, -6, 12, -6, -6, 12, -6, 12, 3, 3, 3, 3, -6, -6, 3, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774730
      {'cdim': 48, 'counter': 48, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.48b', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 48, 'qvalues': [48, 0, 0, -6, -6, -6, -6, -6, -6, 21, 0, -6, 12, 12, -6, 12, -6, -6, -6, -6, -6, 3, -6, 3, 3, 3, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774731
      {'cdim': 48, 'counter': 49, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.48c', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 48, 'qvalues': [48, 0, 0, -6, -6, -6, -6, -6, -6, 21, 0, 12, -6, -6, -6, -6, 12, -6, 12, -6, 3, -6, 3, -6, 3, 3, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774733
      {'cdim': 48, 'counter': 50, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.48d', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, -24, -6, -6, 12, 3, 12, -6, 0, -6, -6, 12, -6, -6, 12, 12, -6, -6, 3, 3, 3, -6, 3, 3, -6, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774734
      {'cdim': 48, 'counter': 51, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.48e', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, -24, -6, -6, 12, 3, 12, -6, 0, -6, 12, -6, -6, -6, -6, -6, 12, 12, 3, 3, -6, 3, -6, 3, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774735
      {'cdim': 48, 'counter': 52, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.48f', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, -24, -6, -6, 12, 3, 12, -6, 0, 12, -6, -6, 12, 12, -6, -6, -6, -6, -6, -6, 3, 3, 3, -6, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774736
      {'cdim': 48, 'counter': 53, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.48g', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 12, -6, -6, -24, 12, 3, -6, 0, -6, -6, -6, -6, 12, -6, 12, 12, -6, -6, 3, 3, 3, 3, 3, 3, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774737
      {'cdim': 48, 'counter': 54, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.48h', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 12, -6, -6, -24, 12, 3, -6, 0, -6, 12, -6, 12, -6, 12, -6, -6, -6, 3, 3, -6, -6, 3, -6, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15774738
      {'cdim': 48, 'counter': 55, 'faithful': True, 'group': '34992.gv', 'group_order': 34992, 'image': None, 'label': '34992.gv.48i', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 12, -6, -6, -24, 12, 3, -6, 0, 12, -6, 12, -6, -6, -6, -6, -6, 12, 3, -6, 3, 3, -6, 3, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • gps_char • Show schema
    • id: 35746879
      {'center': None, 'center_index': 1, 'center_order': 34992, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': None, 'kernel_order': 34992, 'label': '34992.gv.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 35746890
      {'center': None, 'center_index': 1, 'center_order': 34992, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 17496, 'label': '34992.gv.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 35746901
      {'center': None, 'center_index': 1, 'center_order': 34992, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 17496, 'label': '34992.gv.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 35746912
      {'center': None, 'center_index': 1, 'center_order': 34992, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 17496, 'label': '34992.gv.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 35746923
      {'center': None, 'center_index': 6, 'center_order': 5832, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': None, 'kernel_order': 5832, 'label': '34992.gv.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 35746934
      {'center': None, 'center_index': 4, 'center_order': 8748, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': None, 'kernel_order': 4374, 'label': '34992.gv.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746939
      {'center': None, 'center_index': 6, 'center_order': 5832, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 2916, 'label': '34992.gv.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 35746940
      {'center': None, 'center_index': 8, 'center_order': 4374, 'counter': 8, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': None, 'kernel_order': 2187, 'label': '34992.gv.2d1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
    • id: 35746941
      {'center': None, 'center_index': 8, 'center_order': 4374, 'counter': 9, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': None, 'kernel_order': 2187, 'label': '34992.gv.2d2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
    • id: 35746880
      {'center': None, 'center_index': 12, 'center_order': 2916, 'counter': 10, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 1458, 'label': '34992.gv.2e1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
    • id: 35746881
      {'center': None, 'center_index': 12, 'center_order': 2916, 'counter': 11, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 1458, 'label': '34992.gv.2e2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
    • id: 35746882
      {'center': None, 'center_index': 24, 'center_order': 1458, 'counter': 12, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 729, 'label': '34992.gv.2f1', 'nt': [24, 35], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]]]}
    • id: 35746883
      {'center': None, 'center_index': 24, 'center_order': 1458, 'counter': 13, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 729, 'label': '34992.gv.2f2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]]]}
    • id: 35746884
      {'center': None, 'center_index': 24, 'center_order': 1458, 'counter': 14, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 729, 'label': '34992.gv.2f3', 'nt': [24, 35], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]]]}
    • id: 35746885
      {'center': None, 'center_index': 24, 'center_order': 1458, 'counter': 15, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 729, 'label': '34992.gv.2f4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]]]}
    • id: 35746886
      {'center': None, 'center_index': 144, 'center_order': 243, 'counter': 16, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '144.182', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 243, 'label': '34992.gv.8a', 'nt': [9, 19], 'q_character': None, 'values': [[[8, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 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]]]}
    • id: 35746887
      {'center': None, 'center_index': 144, 'center_order': 243, 'counter': 17, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '144.182', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 243, 'label': '34992.gv.8b', 'nt': [9, 19], 'q_character': None, 'values': [[[8, 0]], [[2, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746888
      {'center': None, 'center_index': 1296, 'center_order': 27, 'counter': 18, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '1296.3522', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '34992.gv.8c', 'nt': [12, 212], 'q_character': None, 'values': [[[8, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[5, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[5, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 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]]]}
    • id: 35746889
      {'center': None, 'center_index': 1296, 'center_order': 27, 'counter': 19, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '1296.3522', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '34992.gv.8d', 'nt': [12, 212], 'q_character': None, 'values': [[[8, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[5, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746891
      {'center': None, 'center_index': 144, 'center_order': 243, 'counter': 20, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '144.182', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 243, 'label': '34992.gv.8e', 'nt': [18, 68], 'q_character': None, 'values': [[[8, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 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]]]}
    • id: 35746892
      {'center': None, 'center_index': 144, 'center_order': 243, 'counter': 21, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '144.182', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 243, 'label': '34992.gv.8f', 'nt': [18, 68], 'q_character': None, 'values': [[[8, 0]], [[-2, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746893
      {'center': None, 'center_index': 1296, 'center_order': 27, 'counter': 22, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '1296.3522', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '34992.gv.8g', 'nt': [24, 2890], 'q_character': None, 'values': [[[8, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[5, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[5, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 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]]]}
    • id: 35746894
      {'center': None, 'center_index': 1296, 'center_order': 27, 'counter': 23, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '1296.3522', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '34992.gv.8h', 'nt': [24, 2890], 'q_character': None, 'values': [[[8, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[5, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746895
      {'center': None, 'center_index': 1296, 'center_order': 27, 'counter': 24, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '1296.3522', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '34992.gv.16a', 'nt': [18, 318], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[7, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[7, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35746896
      {'center': None, 'center_index': 432, 'center_order': 81, 'counter': 25, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '432.740', 'image_order': 432, 'indicator': 1, 'kernel': None, 'kernel_order': 81, 'label': '34992.gv.16b', 'nt': [24, 1333], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35746897
      {'center': None, 'center_index': 432, 'center_order': 81, 'counter': 26, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '432.740', 'image_order': 432, 'indicator': 1, 'kernel': None, 'kernel_order': 81, 'label': '34992.gv.16c', 'nt': [24, 1333], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-8, 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]], [[0, 0]], [[0, 0]], [[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: 35746898
      {'center': None, 'center_index': 1296, 'center_order': 27, 'counter': 27, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '1296.3522', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '34992.gv.16d', 'nt': [24, 2932], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-8, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746899
      {'center': None, 'center_index': 1296, 'center_order': 27, 'counter': 28, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '1296.3522', 'image_order': 1296, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '34992.gv.16e', 'nt': [24, 2932], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[-8, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-8, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746900
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 29, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.16f', 'nt': [24, 7282], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[10, 0]], [[10, 0]], [[4, 0]], [[-2, 0]], [[10, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-5, 0]], [[4, 0]], [[4, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35746902
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 30, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.16g', 'nt': [24, 7282], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[10, 0]], [[10, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[10, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[1, 0]], [[-5, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[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: 35746903
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 31, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.16h1', 'nt': [48, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-5, 0], [-6, 1]], [[1, 0], [6, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-6, 1]], [[4, 0], [6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746904
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 32, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.16h2', 'nt': [48, 2], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [6, 1]], [[-5, 0], [-6, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[4, 0], [6, 1]], [[-2, 0], [-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746905
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 33, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.16i1', 'nt': [48, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[7, 0]], [[-2, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-6, 1]], [[4, 0], [6, 1]], [[4, 0], [6, 1]], [[-2, 0], [-6, 1]], [[-2, 0], [3, 1]], [[-5, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746906
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 34, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.16i2', 'nt': [48, 2], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[7, 0]], [[7, 0]], [[-2, 0]], [[7, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[4, 0], [6, 1]], [[-2, 0], [-6, 1]], [[-2, 0], [-6, 1]], [[4, 0], [6, 1]], [[-5, 0], [-3, 1]], [[-2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746907
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 35, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.16j1', 'nt': [48, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[-8, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-5, 0], [-6, 1]], [[1, 0], [6, 1]], [[4, 0], [6, 1]], [[-2, 0], [-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746908
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 36, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.16j2', 'nt': [48, 2], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[-8, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [6, 1]], [[-5, 0], [-6, 1]], [[-2, 0], [-6, 1]], [[4, 0], [6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746909
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 37, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.24a', 'nt': [27, 545], 'q_character': None, 'values': [[[24, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746910
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 38, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.24b', 'nt': [27, 545], 'q_character': None, 'values': [[[24, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 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]]]}
    • id: 35746911
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 39, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.24c', 'nt': [27, 545], 'q_character': None, 'values': [[[24, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 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]]]}
    • id: 35746913
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 40, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.24d', 'nt': [36, 13963], 'q_character': None, 'values': [[[24, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[15, 0]], [[6, 0]], [[-12, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 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]]]}
    • id: 35746914
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 41, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.24e', 'nt': [36, 13963], 'q_character': None, 'values': [[[24, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[15, 0]], [[6, 0]], [[-12, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 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]]]}
    • id: 35746915
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 42, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.24f', 'nt': [36, 13963], 'q_character': None, 'values': [[[24, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[15, 0]], [[6, 0]], [[-12, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746916
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 43, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.24g', 'nt': [36, 13963], 'q_character': None, 'values': [[[24, 0]], [[2, 0]], [[0, 0]], [[15, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-12, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746917
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 44, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.24h', 'nt': [36, 13963], 'q_character': None, 'values': [[[24, 0]], [[2, 0]], [[0, 0]], [[15, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-12, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746918
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 45, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.24i', 'nt': [36, 13963], 'q_character': None, 'values': [[[24, 0]], [[2, 0]], [[0, 0]], [[15, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-12, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746919
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 46, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.24j', 'nt': [54, 0], 'q_character': None, 'values': [[[24, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746920
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 47, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.24k', 'nt': [54, 0], 'q_character': None, 'values': [[[24, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 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]]]}
    • id: 35746921
      {'center': None, 'center_index': 3888, 'center_order': 9, 'counter': 48, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': None, 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 9, 'label': '34992.gv.24l', 'nt': [54, 0], 'q_character': None, 'values': [[[24, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 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]]]}
    • id: 35746922
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 49, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.24m', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[15, 0]], [[6, 0]], [[-12, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 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]]]}
    • id: 35746924
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 50, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.24n', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[15, 0]], [[6, 0]], [[-12, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 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]]]}
    • id: 35746925
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 51, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.24o', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[15, 0]], [[6, 0]], [[-12, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746926
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 52, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.24p', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-2, 0]], [[0, 0]], [[15, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-12, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746927
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 53, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.24q', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-2, 0]], [[0, 0]], [[15, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-12, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746928
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 54, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.24r', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-2, 0]], [[0, 0]], [[15, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-12, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746929
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 55, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.48a', 'nt': [54, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[21, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[12, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746930
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 56, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.48b', 'nt': [54, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[21, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746931
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 57, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.48c', 'nt': [54, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[21, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35746932
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 58, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.48d', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[3, 0]], [[12, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35746933
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 59, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.48e', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[3, 0]], [[12, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[12, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35746935
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 60, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.48f', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[3, 0]], [[12, 0]], [[-6, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35746936
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 61, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.48g', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-24, 0]], [[12, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35746937
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 62, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.48h', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-24, 0]], [[12, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35746938
      {'center': None, 'center_index': 34992, 'center_order': 1, 'counter': 63, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '34992.gv', 'group_counter': 178, 'group_order': 34992, 'image': None, 'image_isoclass': '34992.gv', 'image_order': 34992, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '34992.gv.48i', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-24, 0]], [[12, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • gps_subgroup_search • Show schema
    Showing the first 100 of 1944 matching records in this table.
    • id: 202394137
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 34992, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '34992.gv.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': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '34992.gv', 'subgroup_hash': 8428647213182937126, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^5:S_3.D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202395193
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 17496, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.2.A', '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': True, 'special_labels': ['C1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5871189794871100326, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^3.C_3^4.D_4', 'supersolvable': False, 'sylow': 0}
    • id: 202395304
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 17496, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.2.B', '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2619031437592766887, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^5.C_3^2.Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202395415
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 17496, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.2.C', 'maximal': True, 'maximal_normal': True, 'metabelian': True, '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 586965764121700021, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6.C_{24}', 'supersolvable': False, 'sylow': 0}
    • id: 202395526
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 5832, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2057021129983316444, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.\\SD_{16}', 'supersolvable': False, 'sylow': 0}
    • id: 202395637
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 8748, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.4.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7900436537566606106, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^6.C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202395748
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4374, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.4.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 439701937686982138, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^6.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 202395859
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4374, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.4.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6056940396142048557, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^5.C_3^2.C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202395970
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 5832, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.6.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 411900616617040455, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^6.C_8', 'supersolvable': False, 'sylow': 0}
    • id: 202394138
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2916, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.6.B', '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2117018362642351523, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^6.D_4', 'supersolvable': False, 'sylow': 0}
    • id: 202394249
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2916, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.6.C', '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5832.nf', 'subgroup_hash': 8308808951802383450, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^6:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202394360
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 4374, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.8.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C3'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5596956082708510582, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^6.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202394471
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 2187, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.8.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': None, 'subgroup_hash': 6130571682709182221, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^3.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 202394582
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.9.A', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7434716613647403538, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^5.\\SD_{16}', 'supersolvable': False, 'sylow': 0}
    • id: 202394693
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.9.B', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.eo', 'subgroup_hash': 8859155090492874013, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^2:F_9:S_3', 'supersolvable': False, 'sylow': 0}
    • id: 202394804
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2916, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.12.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6218027514413146265, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^6.C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202394915
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1458, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.12.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8908903677108408947, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 202395026
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.12.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2699779245324637352, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^4:C_3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 202395137
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.12.D', '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2699779245324637352, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^4:C_3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 202395194
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.12.E', '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 442920119945899729, 'subgroup_order': 2916, 'subgroup_tex': 'C_3.C_3^5.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395205
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1458, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.12.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6218027514413146265, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^6.C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202395216
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 2187, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '34992.gv.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['F', 'L3', 'C4'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.9106', 'subgroup_hash': 5920808883286947445, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^2\\times C_3^4:C_3', 'supersolvable': True, 'sylow': 3}
    • id: 202395227
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.18.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3922', 'subgroup_hash': 3922, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202395238
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.18.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2324', 'subgroup_hash': 2324, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202395249
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.18.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2324', 'subgroup_hash': 2324, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202395260
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.18.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3931', 'subgroup_hash': 3931, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202395271
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.18.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3889', 'subgroup_hash': 3889, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:C_{24}', 'supersolvable': False, 'sylow': 0}
    • id: 202395282
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.18.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2336', 'subgroup_hash': 2336, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 202395293
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.18.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2298', 'subgroup_hash': 2298, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:C_{24}', 'supersolvable': False, 'sylow': 0}
    • id: 202395305
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.18.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2336', 'subgroup_hash': 2336, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 202395316
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1458, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1795', 'subgroup_hash': 1795, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395327
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '1458.1468', 'subgroup_hash': 1468, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395338
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '1458.1468', 'subgroup_hash': 1468, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395349
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.D', '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1468', 'subgroup_hash': 1468, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395360
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.E', '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1468', 'subgroup_hash': 1468, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395371
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1756', 'subgroup_hash': 1756, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202395382
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1756', 'subgroup_hash': 1756, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202395393
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 729, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1798', 'subgroup_hash': 1798, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
    • id: 202395404
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '1458.1470', 'subgroup_hash': 1470, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395416
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '1458.1470', 'subgroup_hash': 1470, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395427
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '1458.1759', 'subgroup_hash': 1759, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395438
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '1458.1465', 'subgroup_hash': 1465, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202395449
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '1458.1465', 'subgroup_hash': 1465, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202395460
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '1458.1465', 'subgroup_hash': 1465, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202395471
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '1458.1465', 'subgroup_hash': 1465, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202395482
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.24.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '1458.1758', 'subgroup_hash': 1758, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202395493
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.27.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3522', 'subgroup_hash': 3522, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
    • id: 202395504
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.27.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3521', 'subgroup_hash': 3521, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
    • id: 202395515
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.27.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3522', 'subgroup_hash': 3522, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
    • id: 202395527
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.891', 'subgroup_hash': 891, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395538
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.891', 'subgroup_hash': 891, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395549
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.891', 'subgroup_hash': 891, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395560
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.891', 'subgroup_hash': 891, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395571
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.891', 'subgroup_hash': 891, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395582
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.815', 'subgroup_hash': 815, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395593
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.815', 'subgroup_hash': 815, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395604
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.815', 'subgroup_hash': 815, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395615
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.815', 'subgroup_hash': 815, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395626
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.893', 'subgroup_hash': 893, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395638
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.474', 'subgroup_hash': 474, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395649
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.474', 'subgroup_hash': 474, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395660
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.474', 'subgroup_hash': 474, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395671
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.474', 'subgroup_hash': 474, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395682
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.806', 'subgroup_hash': 806, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 202395693
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.882', 'subgroup_hash': 882, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202395704
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.883', 'subgroup_hash': 883, 'subgroup_order': 972, 'subgroup_tex': 'C_3^5:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202395715
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.414', 'subgroup_hash': 414, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_3:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202395726
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.406', 'subgroup_hash': 406, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202395737
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.406', 'subgroup_hash': 406, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202395749
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.414', 'subgroup_hash': 414, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_3:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202395760
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.406', 'subgroup_hash': 406, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202395771
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.414', 'subgroup_hash': 414, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_3:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202395782
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.406', 'subgroup_hash': 406, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 202395793
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.36.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.414', 'subgroup_hash': 414, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_3:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 202395804
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': True, 'core_order': 729, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.48.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}:C_2', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C5'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 202395815
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.48.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395826
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.48.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395837
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.48.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395848
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.48.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395860
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.48.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395871
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.48.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395882
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.48.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395893
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.48.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395904
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.48.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '729.498', 'subgroup_hash': 498, 'subgroup_order': 729, 'subgroup_tex': 'C_3^3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395915
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.48.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '729.498', 'subgroup_hash': 498, 'subgroup_order': 729, 'subgroup_tex': 'C_3^3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
    • id: 202395926
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.54.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.725', 'subgroup_hash': 725, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 202395937
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.54.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.725', 'subgroup_hash': 725, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 202395948
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.54.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.725', 'subgroup_hash': 725, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 202395959
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.54.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.725', 'subgroup_hash': 725, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 202395971
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.54.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.725', 'subgroup_hash': 725, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 202395982
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.54.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202395993
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.54.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.712', 'subgroup_hash': 712, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
    • id: 202396004
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.54.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202396015
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.54.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.711', 'subgroup_hash': 711, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
    • id: 202396026
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.54.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202396037
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.54.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202396048
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.54.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.712', 'subgroup_hash': 712, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
    • id: 202396059
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.54.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 202396070
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.72.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.257', 'subgroup_hash': 257, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 202394139
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '34992.gv', 'ambient_counter': 178, 'ambient_order': 34992, 'ambient_tex': 'C_3^5:S_3.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '34992.gv.72.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.257', 'subgroup_hash': 257, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 1944 matching records in this table.
    • id: 202394137
      {'ambient': '34992.gv', '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': '34992.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.A', '2.B', '2.C', '3.a1', '9.A', '9.B'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9917, 5174, 9731, 5271], 'generators': [3121, 11664, 26896, 6912, 13440, 6, 17112, 27216, 28512, 33408, 1884], 'label': '34992.gv.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.A', '2.B', '2.C'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '34992.gv', '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': None}
    • id: 202394138
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '6.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.A', '3.a1'], 'contains': ['12.A', '12.B', '54.A', '54.B', '54.C', '54.D', '54.E'], 'core': '12.A', 'coset_action_label': None, 'count': 3, 'diagramx': [9753, -1, 9666, -1], 'generators': [3121, 11664, 27792, 25056, 24876, 12144, 27216, 12960, 17112], 'label': '34992.gv.6.B', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.B', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 202394139
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '72.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.BM', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.H', '36.B'], 'contains': ['144.N', '216.A', '216.B', '216.D', '216.K', '216.M', '216.X', '216.CE', '216.CF', '216.CI', '216.CJ', '216.CK', '216.CL'], 'core': '34992.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [2871, -1, 5162, -1], 'generators': [3121, 30384, 31440, 3024, 3888, 11664], 'label': '34992.gv.72.B', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '72.b1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.B', 'subgroup_fusion': None, 'weyl_group': '36.13'}
    • id: 202394140
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.GW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EE', '216.EH', '216.EM', '216.EV', '216.FH', '216.FI', '216.FL', '216.FO', '216.FY'], 'contains': ['1296.DX', '1944.CX', '1944.CY', '1944.DD', '1944.DF', '1944.EV', '1944.EW', '1944.EX', '1944.EY', '1944.EZ'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [6846, -1, 7463, -1], 'generators': [29832, 12384, 12336, 33408], 'label': '34992.gv.648.GW', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.GW', 'old_label': '648.gh1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.GW', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394141
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.GX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EF', '216.EH', '216.EK', '216.EX', '216.FF', '216.FJ', '216.FL', '216.FQ', '216.FY'], 'contains': ['1296.DY', '1944.CX', '1944.DA', '1944.DD', '1944.DE', '1944.EV', '1944.EW', '1944.EX', '1944.EY', '1944.EZ'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [6871, -1, 7491, -1], 'generators': [4392, 16272, 22752, 13440], 'label': '34992.gv.648.GX', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.GX', 'old_label': '648.gh2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.GX', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394142
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.GY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EG', '216.EI', '216.EJ', '216.EW', '216.FE', '216.FK', '216.FM', '216.FP', '216.FY'], 'contains': ['1296.DZ', '1944.CW', '1944.CZ', '1944.DB', '1944.DG', '1944.EV', '1944.EW', '1944.EX', '1944.EY', '1944.EZ'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7078, -1, 7519, -1], 'generators': [21192, 432, 12624, 33408], 'label': '34992.gv.648.GY', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.GY', 'old_label': '648.gh3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.GY', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394143
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.GZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EG', '216.EI', '216.EL', '216.EU', '216.FG', '216.FK', '216.FM', '216.FN', '216.FY'], 'contains': ['1296.EA', '1944.CV', '1944.CZ', '1944.DC', '1944.DH', '1944.EV', '1944.EW', '1944.EX', '1944.EY', '1944.EZ'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [6866, -1, 7477, -1], 'generators': [23256, 20160, 25632, 28416], 'label': '34992.gv.648.GZ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.GZ', 'old_label': '648.gh4', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.GZ', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394144
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EE', '216.EM', '216.EW', '216.FH', '216.FI', '216.FP', '216.FZ', '324.L'], 'contains': ['1296.EB', '1944.CW', '1944.CY', '1944.DG', '1944.FA', '1944.FB', '1944.FC', '1944.FD'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6544, -1, 7221, -1], 'generators': [17784, 20880, 21120, 13440], 'label': '34992.gv.648.HA', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.L', 'old_label': '648.gi1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HA', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394145
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EF', '216.EL', '216.EX', '216.FG', '216.FJ', '216.FQ', '216.FZ', '324.K'], 'contains': ['1296.EC', '1944.CV', '1944.DA', '1944.DH', '1944.FA', '1944.FB', '1944.FC', '1944.FD'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6643, -1, 7207, -1], 'generators': [27864, 432, 1296, 13440], 'label': '34992.gv.648.HB', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.K', 'old_label': '648.gi2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HB', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394146
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EH', '216.EI', '216.EJ', '216.EU', '216.FE', '216.FL', '216.FM', '216.FN', '216.FZ'], 'contains': ['1296.ED', '1944.CX', '1944.CZ', '1944.DE', '1944.DF', '1944.FA', '1944.FB', '1944.FC', '1944.FD'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [6876, -1, 7420, -1], 'generators': [12600, 13056, 26112, 33408], 'label': '34992.gv.648.HC', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HC', 'old_label': '648.gi3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HC', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394147
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EE', '216.EG', '216.EJ', '216.EX', '216.FE', '216.FI', '216.FK', '216.FQ', '216.GA'], 'contains': ['1296.EE', '1944.CW', '1944.DD', '1944.DE', '1944.DH', '1944.FE', '1944.FF', '1944.FG', '1944.FH', '1944.FI'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7132, -1, 7675, -1], 'generators': [7416, 20832, 30192, 33408], 'label': '34992.gv.648.HD', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HD', 'old_label': '648.gj1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HD', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394148
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EE', '216.EI', '216.EK', '216.EU', '216.FF', '216.FI', '216.FM', '216.FN', '216.GA'], 'contains': ['1296.EF', '1944.CX', '1944.DC', '1944.DE', '1944.DG', '1944.FE', '1944.FF', '1944.FG', '1944.FH', '1944.FI'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7288, -1, 7633, -1], 'generators': [30168, 144, 9456, 13440], 'label': '34992.gv.648.HE', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HE', 'old_label': '648.gj2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HE', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394149
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EF', '216.EG', '216.EM', '216.EU', '216.FH', '216.FJ', '216.FK', '216.FN', '216.GA'], 'contains': ['1296.EG', '1944.CV', '1944.DD', '1944.DF', '1944.DG', '1944.FE', '1944.FF', '1944.FG', '1944.FH', '1944.FI'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7106, -1, 7661, -1], 'generators': [3528, 26064, 192, 33408], 'label': '34992.gv.648.HF', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HF', 'old_label': '648.gj3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HF', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394150
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '72.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.B', '24.C', '24.F', '36.O'], 'contains': ['144.Q', '216.E', '216.F', '216.Z', '216.BH', '216.BQ', '216.BR'], 'core': '1296.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1818, -1, 3081, -1], 'generators': [3121, 13440, 26896, 31248, 4608, 33408], 'label': '34992.gv.72.C', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.O', 'old_label': '72.c1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.C', 'subgroup_fusion': None, 'weyl_group': '108.17'}
    • id: 202394151
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EF', '216.EI', '216.EJ', '216.EV', '216.FE', '216.FJ', '216.FM', '216.FO', '216.GA'], 'contains': ['1296.EH', '1944.CX', '1944.DB', '1944.DF', '1944.DH', '1944.FE', '1944.FF', '1944.FG', '1944.FH', '1944.FI'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7307, -1, 7647, -1], 'generators': [23448, 24240, 12384, 33408], 'label': '34992.gv.648.HG', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HG', 'old_label': '648.gj4', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HG', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394152
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EG', '216.EM', '216.EX', '216.FH', '216.FK', '216.FQ', '216.GB', '324.M'], 'contains': ['1296.ER', '1944.CV', '1944.CW', '1944.DD', '1944.FJ', '1944.FK', '1944.FL', '1944.FM'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6555, -1, 7179, -1], 'generators': [2424, 24768, 192, 33408], 'label': '34992.gv.648.HH', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.M', 'old_label': '648.gk1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HH', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394153
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['216.EI', '216.EK', '216.EV', '216.FF', '216.FM', '216.FO', '216.GB'], 'contains': ['1296.ES', '1944.CX', '1944.DB', '1944.DC', '1944.FJ', '1944.FK', '1944.FL', '1944.FM'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6891, -1, 7292, -1], 'generators': [19080, 144, 12384, 33408], 'label': '34992.gv.648.HI', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HI', 'old_label': '648.gk2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HI', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394154
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EE', '216.EI', '216.EJ', '216.EX', '216.FE', '216.FI', '216.FM', '216.FQ', '216.GC'], 'contains': ['1296.ET', '1944.CW', '1944.CX', '1944.DE', '1944.DH', '1944.FN', '1944.FO', '1944.FP', '1944.FQ'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7232, -1, 7590, -1], 'generators': [19800, 28656, 9456, 13440], 'label': '34992.gv.648.HJ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HJ', 'old_label': '648.gl1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HJ', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394155
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EF', '216.EI', '216.EM', '216.EU', '216.FH', '216.FJ', '216.FM', '216.FN', '216.GC'], 'contains': ['1296.EU', '1944.CV', '1944.CX', '1944.DF', '1944.DG', '1944.FN', '1944.FO', '1944.FP', '1944.FQ'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7169, -1, 7562, -1], 'generators': [18264, 432, 30768, 33408], 'label': '34992.gv.648.HK', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HK', 'old_label': '648.gl2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HK', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394156
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EI', '216.EM', '216.EX', '216.FH', '216.FM', '216.FQ', '216.GD', '324.N'], 'contains': ['1296.EV', '1944.CV', '1944.CW', '1944.CX', '1944.FR', '1944.FS', '1944.FT'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6657, -1, 7122, -1], 'generators': [28392, 28944, 3072, 28416], 'label': '34992.gv.648.HL', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.N', 'old_label': '648.gm1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HL', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394157
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['216.EE', '216.EL', '216.EV', '216.FG', '216.FI', '216.FO', '216.GE'], 'contains': ['1296.EW', '1944.CY', '1944.DC', '1944.DH', '1944.FU', '1944.FV', '1944.FW', '1944.FX'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6782, -1, 7392, -1], 'generators': [19080, 21168, 24288, 33408], 'label': '34992.gv.648.HM', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HM', 'old_label': '648.gn1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HM', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394158
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['216.EF', '216.EK', '216.EW', '216.FF', '216.FJ', '216.FP', '216.GE'], 'contains': ['1296.EX', '1944.DA', '1944.DB', '1944.DG', '1944.FU', '1944.FV', '1944.FW', '1944.FX'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6825, -1, 7434, -1], 'generators': [32760, 22464, 16272, 13440], 'label': '34992.gv.648.HN', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HN', 'old_label': '648.gn2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HN', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394159
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EG', '216.EH', '216.EJ', '216.EU', '216.FE', '216.FK', '216.FL', '216.FN', '216.GE'], 'contains': ['1296.EY', '1944.CZ', '1944.DD', '1944.DE', '1944.DF', '1944.FU', '1944.FV', '1944.FW', '1944.FX'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [6814, -1, 7534, -1], 'generators': [9432, 27648, 26928, 13440], 'label': '34992.gv.648.HO', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HO', 'old_label': '648.gn3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HO', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394160
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['216.EH', '216.EL', '216.EW', '216.FG', '216.FL', '216.FP', '216.GF', '324.O'], 'contains': ['1296.FG', '1944.CY', '1944.CZ', '1944.DA', '1944.FY', '1944.FZ', '1944.GA'], 'core': '34992.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [6518, -1, 6892, -1], 'generators': [16200, 11760, 24288, 13440], 'label': '34992.gv.648.HP', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.O', 'old_label': '648.go1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HP', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394161
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '72.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.D', '24.E', '24.F'], 'contains': ['144.BD', '216.E', '216.G', '216.BA', '216.BO', '216.BU', '216.CB'], 'core': '3888.A', 'coset_action_label': None, 'count': 72, 'diagramx': [1255, -1, 1634, -1], 'generators': [3121, 13440, 21904, 31248, 4608, 33408], 'label': '34992.gv.72.D', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.D', 'old_label': '72.d1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.D', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 202394162
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EE', '216.EG', '216.EK', '216.EU', '216.FF', '216.FI', '216.FK', '216.FN', '216.GG'], 'contains': ['1296.FQ', '1944.DC', '1944.DD', '1944.DE', '1944.DG', '1944.GB', '1944.GC', '1944.GD', '1944.GE'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7055, -1, 7761, -1], 'generators': [8424, 9216, 20160, 28416], 'label': '34992.gv.648.HQ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HQ', 'old_label': '648.gp1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HQ', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394163
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EF', '216.EG', '216.EJ', '216.EV', '216.FE', '216.FJ', '216.FK', '216.FO', '216.GG'], 'contains': ['1296.FR', '1944.DB', '1944.DD', '1944.DF', '1944.DH', '1944.GB', '1944.GC', '1944.GD', '1944.GE'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [6886, -1, 7690, -1], 'generators': [29928, 6576, 9456, 33408], 'label': '34992.gv.648.HR', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HR', 'old_label': '648.gp2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HR', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394164
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['216.EG', '216.EK', '216.EV', '216.FF', '216.FK', '216.FO', '216.GH'], 'contains': ['1296.FS', '1944.DB', '1944.DC', '1944.DD', '1944.GF', '1944.GG', '1944.GH'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [7293, -1, 7548, -1], 'generators': [648, 1440, 20160, 28416], 'label': '34992.gv.648.HS', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HS', 'old_label': '648.gq1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HS', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394165
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EE', '216.EF', '216.EJ', '216.EU', '216.FE', '216.FI', '216.FJ', '216.FN', '216.GI'], 'contains': ['1296.GG', '1944.DE', '1944.DF', '1944.DG', '1944.DH', '1944.GI', '1944.GJ', '1944.GK'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7174, -1, 7931, -1], 'generators': [9432, 32496, 18528, 28416], 'label': '34992.gv.648.HT', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HT', 'old_label': '648.gr1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HT', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394166
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EE', '216.EF', '216.EJ', '216.EU', '216.FE', '216.FI', '216.FJ', '216.FN', '216.GJ'], 'contains': ['1296.GH', '1944.DE', '1944.DF', '1944.DG', '1944.DH', '1944.GL', '1944.GM', '1944.GN', '1944.GO'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7221, -1, 8030, -1], 'generators': [29928, 13104, 26112, 33408], 'label': '34992.gv.648.HU', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.HU', 'old_label': '648.gr2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HU', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394167
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.DZ', '216.FR', '216.FS', '216.FT', '216.FU', '216.FV', '216.FW', '216.FX', '324.P'], 'contains': ['1296.GI', '1944.CP', '1944.CQ', '1944.CR', '1944.CS', '1944.CT', '1944.CU', '1944.DI'], 'core': '3888.A', 'coset_action_label': None, 'count': 108, 'diagramx': [4063, -1, 5708, -1], 'generators': [22968, 10512, 10560, 33408], 'label': '34992.gv.648.HV', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.BG', 'old_label': '648.gs1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HV', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394168
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.EA', '216.FR', '216.FS', '216.FT', '216.FY', '216.FZ', '216.GA', '216.GB', '216.GC', '216.GD', '324.Q'], 'contains': ['1296.GJ', '1944.CV', '1944.CW', '1944.CX', '1944.DI'], 'core': '3888.A', 'coset_action_label': None, 'count': 216, 'diagramx': [5566, -1, 5757, -1], 'generators': [16536, 9072, 13440, 33408], 'label': '34992.gv.648.HW', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.BH', 'old_label': '648.gt1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HW', 'subgroup_fusion': None, 'weyl_group': '324.121'}
    • id: 202394169
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.EB', '216.FT', '216.FU', '216.FV', '216.FY', '216.FZ', '216.GE', '216.GF', '324.R'], 'contains': ['1296.GK', '1944.CY', '1944.CZ', '1944.DA', '1944.DI'], 'core': '3888.A', 'coset_action_label': None, 'count': 108, 'diagramx': [4804, -1, 5722, -1], 'generators': [4056, 13056, 10560, 33408], 'label': '34992.gv.648.HX', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.BI', 'old_label': '648.gu1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HX', 'subgroup_fusion': None, 'weyl_group': '324.121'}
    • id: 202394170
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.EC', '216.FR', '216.FU', '216.FW', '216.FY', '216.GA', '216.GB', '216.GE', '216.GG', '216.GH'], 'contains': ['1296.GL', '1944.DB', '1944.DC', '1944.DD', '1944.DI'], 'core': '3888.A', 'coset_action_label': None, 'count': 216, 'diagramx': [6120, -1, 5771, -1], 'generators': [4392, 28176, 28416, 33408], 'label': '34992.gv.648.HY', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.EC', 'old_label': '648.gv1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HY', 'subgroup_fusion': None, 'weyl_group': '162.40'}
    • id: 202394171
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.HZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ED', '216.FR', '216.FS', '216.FV', '216.FW', '216.FY', '216.FZ', '216.GA', '216.GC', '216.GE', '216.GG', '216.GI', '216.GJ'], 'contains': ['1296.GM', '1944.DE', '1944.DF', '1944.DG', '1944.DH', '1944.DI'], 'core': '3888.A', 'coset_action_label': None, 'count': 432, 'diagramx': [6125, -1, 6424, -1], 'generators': [10008, 32544, 10560, 33408], 'label': '34992.gv.648.HZ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ED', 'old_label': '648.gw1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.HZ', 'subgroup_fusion': None, 'weyl_group': '162.40'}
    • id: 202394172
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '72.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.E', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.D', '24.E', '24.G'], 'contains': ['144.BE', '216.E', '216.H', '216.BB', '216.BM', '216.BW', '216.BX', '216.CA'], 'core': '3888.A', 'coset_action_label': None, 'count': 144, 'diagramx': [1084, -1, 1344, -1], 'generators': [3121, 13440, 13264, 31248, 4608, 33408], 'label': '34992.gv.72.E', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.E', 'old_label': '72.e1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.E', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 202394173
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EN', '216.ET', '216.FA', '216.FC', '216.GK', '216.GL', '216.GM', '216.GN', '216.GO'], 'contains': ['1296.GT', '1944.DJ', '1944.DO', '1944.DR', '1944.DW', '1944.EA', '1944.EE', '1944.EG', '1944.EL', '1944.EQ'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7127, -1, 7718, -1], 'generators': [29976, 96, 3072, 2784], 'label': '34992.gv.648.IA', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IA', 'old_label': '648.gx1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IA', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394174
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EO', '216.ES', '216.EZ', '216.FB', '216.GK', '216.GL', '216.GM', '216.GN', '216.GO'], 'contains': ['1296.GU', '1944.DJ', '1944.DM', '1944.DQ', '1944.DX', '1944.DZ', '1944.ED', '1944.EH', '1944.EO', '1944.ES'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7203, -1, 7704, -1], 'generators': [29640, 96, 192, 3552], 'label': '34992.gv.648.IB', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IB', 'old_label': '648.gx2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IB', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394175
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EP', '216.ER', '216.EZ', '216.FD', '216.GK', '216.GL', '216.GM', '216.GN', '216.GO'], 'contains': ['1296.GV', '1944.DJ', '1944.DM', '1944.DQ', '1944.DY', '1944.EB', '1944.ED', '1944.EH', '1944.EN', '1944.EP'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7165, -1, 7746, -1], 'generators': [29976, 432, 960, 2304], 'label': '34992.gv.648.IC', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IC', 'old_label': '648.gx3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IC', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394176
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.ID', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EQ', '216.ET', '216.EY', '216.FC', '216.GK', '216.GL', '216.GM', '216.GN', '216.GO'], 'contains': ['1296.GW', '1944.DJ', '1944.DN', '1944.DP', '1944.DW', '1944.EA', '1944.EF', '1944.EI', '1944.EM', '1944.ER'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7158, -1, 7732, -1], 'generators': [29976, 96, 1296, 672], 'label': '34992.gv.648.ID', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.ID', 'old_label': '648.gx4', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ID', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394177
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EN', '216.EQ', '216.EZ', '216.FC', '216.GP', '216.GQ', '216.GR', '216.GS'], 'contains': ['1296.HC', '1944.DK', '1944.DM', '1944.DQ', '1944.DW', '1944.EA', '1944.EN', '1944.EO', '1944.EP', '1944.ES'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [6881, -1, 7576, -1], 'generators': [7896, 144, 16848, 17232], 'label': '34992.gv.648.IE', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IE', 'old_label': '648.gy1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IE', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394178
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EO', '216.FA', '216.FB', '216.GP', '216.GQ', '216.GR', '216.GS', '324.T'], 'contains': ['1296.HD', '1944.DK', '1944.DO', '1944.DR', '1944.DX', '1944.DZ', '1944.EL', '1944.EQ'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6653, -1, 7321, -1], 'generators': [29976, 16992, 720, 17328], 'label': '34992.gv.648.IF', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.T', 'old_label': '648.gy2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IF', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394179
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EP', '216.EY', '216.FD', '216.GP', '216.GQ', '216.GR', '216.GS', '324.S'], 'contains': ['1296.HE', '1944.DK', '1944.DN', '1944.DP', '1944.DY', '1944.EB', '1944.EM', '1944.ER'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6662, -1, 7335, -1], 'generators': [29976, 34128, 34704, 672], 'label': '34992.gv.648.IG', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.S', 'old_label': '648.gy3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IG', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394180
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EN', '216.EO', '216.ET', '216.FD', '216.GT', '216.GU', '216.GV', '216.GW', '216.GX'], 'contains': ['1296.HJ', '1944.DL', '1944.DO', '1944.DR', '1944.ED', '1944.EH', '1944.EM', '1944.EN', '1944.EP', '1944.ER'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7881, -1, 8229, -1], 'generators': [29976, 96, 720, 22752], 'label': '34992.gv.648.IH', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IH', 'old_label': '648.gz1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IH', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394181
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.II', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EN', '216.EP', '216.ES', '216.FC', '216.GT', '216.GU', '216.GV', '216.GW', '216.GX'], 'contains': ['1296.HK', '1944.DL', '1944.DM', '1944.DQ', '1944.EE', '1944.EG', '1944.EM', '1944.EO', '1944.ER', '1944.ES'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [8147, -1, 8201, -1], 'generators': [29976, 432, 15264, 14448], 'label': '34992.gv.648.II', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.II', 'old_label': '648.gz2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.II', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394182
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EO', '216.EQ', '216.ER', '216.FC', '216.GT', '216.GU', '216.GV', '216.GW', '216.GX'], 'contains': ['1296.HL', '1944.DL', '1944.DM', '1944.DQ', '1944.EF', '1944.EI', '1944.EL', '1944.EN', '1944.EP', '1944.EQ'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [8152, -1, 8215, -1], 'generators': [29976, 432, 960, 28992], 'label': '34992.gv.648.IJ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IJ', 'old_label': '648.gz3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IJ', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394183
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '72.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.B', '24.E', '24.G'], 'contains': ['144.BF', '216.E', '216.I', '216.BC', '216.BN', '216.BV', '216.CC'], 'core': '3888.A', 'coset_action_label': None, 'count': 72, 'diagramx': [578, -1, 1288, -1], 'generators': [3121, 13440, 7984, 31248, 4608, 33408], 'label': '34992.gv.72.F', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.F', 'old_label': '72.f1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.F', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 202394184
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EP', '216.EQ', '216.ET', '216.FB', '216.GT', '216.GU', '216.GV', '216.GW', '216.GX'], 'contains': ['1296.HM', '1944.DL', '1944.DN', '1944.DP', '1944.ED', '1944.EH', '1944.EL', '1944.EO', '1944.EQ', '1944.ES'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [8157, -1, 8087, -1], 'generators': [29976, 14688, 14736, 672], 'label': '34992.gv.648.IK', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IK', 'old_label': '648.gz4', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IK', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394185
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EE', '216.EF', '216.EJ', '216.EU', '216.GK', '216.GL', '216.GP', '216.GV', '216.GW', '216.HA', '216.HD', '216.HE', '216.HH'], 'contains': ['1296.HR', '1944.DM', '1944.DN', '1944.DQ', '1944.DR', '1944.EV', '1944.FA', '1944.FE', '1944.FF', '1944.FN', '1944.FU', '1944.GB', '1944.GI', '1944.GL'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7988, -1, 8731, -1], 'generators': [29976, 432, 960, 20640], 'label': '34992.gv.648.IL', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IL', 'old_label': '648.ha1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IL', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394186
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EE', '216.EF', '216.EJ', '216.EU', '216.GK', '216.GM', '216.GP', '216.GU', '216.GX', '216.GY', '216.HC', '216.HD', '216.HH'], 'contains': ['1296.HS', '1944.DM', '1944.DN', '1944.DQ', '1944.DR', '1944.EV', '1944.FB', '1944.FE', '1944.FG', '1944.FO', '1944.FV', '1944.GC', '1944.GI', '1944.GL'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7992, -1, 8716, -1], 'generators': [1656, 28944, 28992, 22224], 'label': '34992.gv.648.IM', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IM', 'old_label': '648.ha2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IM', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394187
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EE', '216.EF', '216.EJ', '216.EU', '216.GL', '216.GM', '216.GR', '216.GV', '216.GX', '216.GZ', '216.HD', '216.HG'], 'contains': ['1296.HT', '1944.DM', '1944.DN', '1944.DQ', '1944.DR', '1944.EW', '1944.FB', '1944.FH', '1944.FO', '1944.FU', '1944.GB', '1944.GJ', '1944.GM'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [8018, -1, 8773, -1], 'generators': [29976, 432, 960, 26112], 'label': '34992.gv.648.IN', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IN', 'old_label': '648.ha3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IN', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394188
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EE', '216.EF', '216.EJ', '216.EU', '216.GL', '216.GN', '216.GQ', '216.GW', '216.GX', '216.GZ', '216.HE', '216.HF', '216.HH'], 'contains': ['1296.HU', '1944.DM', '1944.DN', '1944.DQ', '1944.DR', '1944.EX', '1944.FB', '1944.FF', '1944.FI', '1944.FN', '1944.FW', '1944.GB', '1944.GI', '1944.GN'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [8005, -1, 8546, -1], 'generators': [21192, 96, 20736, 30528], 'label': '34992.gv.648.IO', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IO', 'old_label': '648.ha4', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IO', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394189
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EE', '216.EF', '216.EJ', '216.EU', '216.GL', '216.GO', '216.GS', '216.GT', '216.GW', '216.GY', '216.HD', '216.HE', '216.HG'], 'contains': ['1296.HV', '1944.DM', '1944.DN', '1944.DQ', '1944.DR', '1944.EY', '1944.FB', '1944.FF', '1944.FH', '1944.FP', '1944.FX', '1944.GD', '1944.GJ', '1944.GL'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [8142, -1, 8674, -1], 'generators': [29976, 432, 960, 25632], 'label': '34992.gv.648.IP', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IP', 'old_label': '648.ha5', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IP', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394190
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EE', '216.EF', '216.EJ', '216.EU', '216.GM', '216.GN', '216.GQ', '216.GT', '216.GU', '216.HA', '216.HC', '216.HD', '216.HG'], 'contains': ['1296.HW', '1944.DM', '1944.DN', '1944.DQ', '1944.DR', '1944.EX', '1944.FC', '1944.FG', '1944.FH', '1944.FQ', '1944.FU', '1944.GE', '1944.GJ', '1944.GL'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7811, -1, 8518, -1], 'generators': [29976, 432, 960, 22752], 'label': '34992.gv.648.IQ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IQ', 'old_label': '648.ha6', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IQ', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394191
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EE', '216.EF', '216.EJ', '216.EU', '216.GM', '216.GO', '216.GS', '216.GU', '216.GV', '216.GZ', '216.HC', '216.HF', '216.HH'], 'contains': ['1296.HX', '1944.DM', '1944.DN', '1944.DQ', '1944.DR', '1944.EY', '1944.FD', '1944.FG', '1944.FI', '1944.FO', '1944.FU', '1944.GC', '1944.GI', '1944.GN'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [8059, -1, 8532, -1], 'generators': [1656, 22464, 22512, 22224], 'label': '34992.gv.648.IR', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IR', 'old_label': '648.ha7', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IR', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394192
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EE', '216.EF', '216.EJ', '216.EU', '216.GN', '216.GO', '216.GP', '216.GU', '216.GW', '216.GZ', '216.HD', '216.HI'], 'contains': ['1296.HY', '1944.DM', '1944.DN', '1944.DQ', '1944.DR', '1944.EZ', '1944.FD', '1944.FE', '1944.FQ', '1944.FW', '1944.GD', '1944.GK', '1944.GM'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7842, -1, 8560, -1], 'generators': [29976, 432, 960, 3888], 'label': '34992.gv.648.IS', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IS', 'old_label': '648.ha8', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IS', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394193
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EE', '216.EF', '216.EJ', '216.EU', '216.GN', '216.GO', '216.GP', '216.GV', '216.GX', '216.HB', '216.HC', '216.HE', '216.HG'], 'contains': ['1296.HZ', '1944.DM', '1944.DN', '1944.DQ', '1944.DR', '1944.EZ', '1944.FC', '1944.FF', '1944.FG', '1944.FO', '1944.FX', '1944.GB', '1944.GJ', '1944.GO'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7903, -1, 8589, -1], 'generators': [29976, 432, 960, 13968], 'label': '34992.gv.648.IT', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IT', 'old_label': '648.ha9', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IT', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394194
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '72.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.BM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.B', '24.D', '24.H', '36.C'], 'contains': ['144.BG', '216.A', '216.E', '216.J', '216.BD', '216.BL', '216.BT', '216.CD'], 'core': '432.B', 'coset_action_label': None, 'count': 36, 'diagramx': [2249, -1, 3809, -1], 'generators': [3121, 1296, 14736, 7920, 432, 11664], 'label': '34992.gv.72.G', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.C', 'old_label': '72.g1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.G', 'subgroup_fusion': None, 'weyl_group': '36.13'}
    • id: 202394195
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EG', '216.EK', '216.EV', '216.GK', '216.GN', '216.GS', '216.GU', '216.GX', '216.GZ', '216.HD', '216.HE', '216.HG'], 'contains': ['1296.IA', '1944.DM', '1944.DP', '1944.DR', '1944.EW', '1944.EX', '1944.FG', '1944.FH', '1944.FJ', '1944.FX', '1944.GB', '1944.GD', '1944.GF'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7806, -1, 8475, -1], 'generators': [29976, 96, 1296, 2304], 'label': '34992.gv.648.IU', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IU', 'old_label': '648.hb1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IU', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394196
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EG', '216.EK', '216.EV', '216.GL', '216.GO', '216.GP', '216.GT', '216.GV', '216.GZ', '216.HC', '216.HD', '216.HH'], 'contains': ['1296.IB', '1944.DM', '1944.DP', '1944.DR', '1944.EV', '1944.EY', '1944.FE', '1944.FI', '1944.FJ', '1944.FU', '1944.GB', '1944.GC', '1944.GG'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [8088, -1, 8504, -1], 'generators': [29976, 96, 30288, 21120], 'label': '34992.gv.648.IV', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IV', 'old_label': '648.hb2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IV', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394197
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EG', '216.EK', '216.EV', '216.GL', '216.GQ', '216.GU', '216.HB', '216.HD', '216.HH'], 'contains': ['1296.IC', '1944.DM', '1944.DP', '1944.DR', '1944.EV', '1944.FG', '1944.FK', '1944.FW', '1944.GB', '1944.GG'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7477, -1, 8101, -1], 'generators': [29976, 96, 22416, 28992], 'label': '34992.gv.648.IW', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IW', 'old_label': '648.hb3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IW', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394198
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EG', '216.EK', '216.EV', '216.GM', '216.GO', '216.GP', '216.GW', '216.GX', '216.HA', '216.HD', '216.HF', '216.HG'], 'contains': ['1296.ID', '1944.DM', '1944.DP', '1944.DR', '1944.EY', '1944.EZ', '1944.FF', '1944.FH', '1944.FL', '1944.FU', '1944.GB', '1944.GE', '1944.GF'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7953, -1, 8461, -1], 'generators': [29976, 9504, 720, 7440], 'label': '34992.gv.648.IX', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IX', 'old_label': '648.hb4', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IX', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394199
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EG', '216.EK', '216.EV', '216.GM', '216.GQ', '216.GV', '216.GY', '216.HE', '216.HI'], 'contains': ['1296.IE', '1944.DM', '1944.DP', '1944.DR', '1944.EZ', '1944.FE', '1944.FM', '1944.FW', '1944.GD', '1944.GH'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7629, -1, 8144, -1], 'generators': [29976, 144, 192, 3888], 'label': '34992.gv.648.IY', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IY', 'old_label': '648.hb5', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IY', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394200
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.IZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EG', '216.EK', '216.EV', '216.GN', '216.GR', '216.GW', '216.GY', '216.HC', '216.HH'], 'contains': ['1296.IF', '1944.DM', '1944.DP', '1944.DR', '1944.EX', '1944.FF', '1944.FM', '1944.FV', '1944.GC', '1944.GG'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7496, -1, 8044, -1], 'generators': [29976, 14688, 720, 14448], 'label': '34992.gv.648.IZ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.IZ', 'old_label': '648.hb6', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.IZ', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394201
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EH', '216.EL', '216.EW', '216.GK', '216.GR', '216.GT', '216.HB', '216.HF', '216.HI', '324.U'], 'contains': ['1296.IG', '1944.DO', '1944.DP', '1944.DQ', '1944.EZ', '1944.FD', '1944.FW', '1944.FY'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [7216, -1, 7505, -1], 'generators': [34632, 432, 4608, 5088], 'label': '34992.gv.648.JA', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.U', 'old_label': '648.hc1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JA', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394202
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EH', '216.EL', '216.EW', '216.GL', '216.GM', '216.GP', '216.GU', '216.GW', '216.GZ', '216.HC', '216.HE', '216.HG'], 'contains': ['1296.IH', '1944.DO', '1944.DP', '1944.DQ', '1944.EW', '1944.EX', '1944.EY', '1944.EZ', '1944.FB', '1944.FC', '1944.FU', '1944.FX', '1944.FZ'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7682, -1, 8186, -1], 'generators': [21192, 96, 30192, 30528], 'label': '34992.gv.648.JB', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JB', 'old_label': '648.hc2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JB', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394203
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EH', '216.EL', '216.EW', '216.GN', '216.GS', '216.GV', '216.HA', '216.HD', '216.HH', '324.V'], 'contains': ['1296.II', '1944.DO', '1944.DP', '1944.DQ', '1944.EV', '1944.EX', '1944.FA', '1944.FD', '1944.FU', '1944.GA'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7303, -1, 7803, -1], 'generators': [29640, 20592, 1296, 21120], 'label': '34992.gv.648.JC', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.V', 'old_label': '648.hc3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JC', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394204
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EH', '216.EL', '216.EW', '216.GO', '216.GQ', '216.GX', '216.GY', '216.HD', '216.HH'], 'contains': ['1296.IJ', '1944.DO', '1944.DP', '1944.DQ', '1944.EV', '1944.EY', '1944.FB', '1944.FV', '1944.FW', '1944.GA'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7368, -1, 7974, -1], 'generators': [6648, 96, 960, 11664], 'label': '34992.gv.648.JD', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JD', 'old_label': '648.hc4', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JD', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394205
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '72.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.BM', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.C', '24.E', '24.H', '36.D'], 'contains': ['144.BH', '216.B', '216.E', '216.L', '216.BF', '216.BJ', '216.BS', '216.BY', '216.BZ'], 'core': '3888.A', 'coset_action_label': None, 'count': 72, 'diagramx': [2261, -1, 3833, -1], 'generators': [3121, 27792, 6240, 23760, 24624, 27216], 'label': '34992.gv.72.H', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.D', 'old_label': '72.h1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.H', 'subgroup_fusion': None, 'weyl_group': '36.13'}
    • id: 202394206
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EI', '216.EM', '216.EX', '216.GK', '216.GO', '216.GQ', '216.GV', '216.GW', '216.GZ', '216.HC', '216.HD', '216.HG'], 'contains': ['1296.IK', '1944.DM', '1944.DN', '1944.DO', '1944.EW', '1944.EY', '1944.FC', '1944.FF', '1944.FH', '1944.FJ', '1944.FO', '1944.FQ', '1944.FR'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [8047, -1, 8333, -1], 'generators': [29976, 96, 9072, 672], 'label': '34992.gv.648.JE', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JE', 'old_label': '648.hd1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JE', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394207
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EI', '216.EM', '216.EX', '216.GL', '216.GN', '216.GP', '216.GU', '216.GV', '216.GY', '216.HD', '216.HF', '216.HG'], 'contains': ['1296.IL', '1944.DM', '1944.DN', '1944.DO', '1944.EX', '1944.EZ', '1944.FB', '1944.FG', '1944.FH', '1944.FL', '1944.FO', '1944.FP', '1944.FR'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [8293, -1, 8347, -1], 'generators': [29976, 1440, 2976, 672], 'label': '34992.gv.648.JF', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JF', 'old_label': '648.hd2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JF', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394208
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EI', '216.EM', '216.EX', '216.GL', '216.GS', '216.GX', '216.HA', '216.HC', '216.HI', '324.X'], 'contains': ['1296.IM', '1944.DM', '1944.DN', '1944.DO', '1944.EZ', '1944.FD', '1944.FE', '1944.FM', '1944.FQ', '1944.FS'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7546, -1, 7959, -1], 'generators': [27864, 432, 1296, 22752], 'label': '34992.gv.648.JG', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.X', 'old_label': '648.hd3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JG', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394209
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EI', '216.EM', '216.EX', '216.GM', '216.GN', '216.GP', '216.GT', '216.GX', '216.GZ', '216.HD', '216.HE', '216.HH'], 'contains': ['1296.IN', '1944.DM', '1944.DN', '1944.DO', '1944.EV', '1944.EX', '1944.FB', '1944.FE', '1944.FI', '1944.FJ', '1944.FN', '1944.FO', '1944.FT'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [8001, -1, 8447, -1], 'generators': [29976, 96, 30192, 672], 'label': '34992.gv.648.JH', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JH', 'old_label': '648.hd4', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JH', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394210
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EI', '216.EM', '216.EX', '216.GM', '216.GS', '216.GW', '216.HB', '216.HD', '216.HH', '324.Y'], 'contains': ['1296.IO', '1944.DM', '1944.DN', '1944.DO', '1944.EV', '1944.FD', '1944.FF', '1944.FK', '1944.FO', '1944.FT'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7442, -1, 7874, -1], 'generators': [29976, 96, 24624, 672], 'label': '34992.gv.648.JI', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.Y', 'old_label': '648.hd5', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JI', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394211
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EI', '216.EM', '216.EX', '216.GO', '216.GR', '216.GU', '216.HA', '216.HE', '216.HH', '324.W'], 'contains': ['1296.IP', '1944.DM', '1944.DN', '1944.DO', '1944.EY', '1944.FA', '1944.FG', '1944.FM', '1944.FN', '1944.FT'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7376, -1, 7888, -1], 'generators': [1176, 4320, 34704, 17328], 'label': '34992.gv.648.JJ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.W', 'old_label': '648.hd6', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JJ', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394212
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['216.ER', '216.ES', '216.FC', '216.GY', '216.GZ', '216.HA', '216.HB'], 'contains': ['1296.IR', '1944.DM', '1944.DQ', '1944.DS', '1944.EE', '1944.EF', '1944.EG', '1944.EI'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6896, -1, 7363, -1], 'generators': [29976, 432, 960, 21120], 'label': '34992.gv.648.JK', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JK', 'old_label': '648.he1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JK', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394213
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.ET', '216.FB', '216.FD', '216.GY', '216.GZ', '216.HA', '216.HB', '324.Z'], 'contains': ['1296.IS', '1944.DN', '1944.DO', '1944.DP', '1944.DR', '1944.DS', '1944.ED', '1944.EH'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6667, -1, 7193, -1], 'generators': [29976, 96, 20736, 672], 'label': '34992.gv.648.JL', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.Z', 'old_label': '648.he2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JL', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394214
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EN', '216.EO', '216.FC', '216.FD', '216.HC', '216.HD', '216.HE', '216.HF'], 'contains': ['1296.IW', '1944.DM', '1944.DO', '1944.DQ', '1944.DR', '1944.DT', '1944.EM', '1944.EN', '1944.EP', '1944.ER'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7568, -1, 7846, -1], 'generators': [29976, 96, 23520, 12336], 'label': '34992.gv.648.JM', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JM', 'old_label': '648.hf1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JM', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394215
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EP', '216.EQ', '216.FB', '216.FC', '216.HC', '216.HD', '216.HE', '216.HF'], 'contains': ['1296.IX', '1944.DM', '1944.DN', '1944.DP', '1944.DQ', '1944.DT', '1944.EL', '1944.EO', '1944.EQ', '1944.ES'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7602, -1, 7945, -1], 'generators': [29976, 9216, 6864, 672], 'label': '34992.gv.648.JN', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JN', 'old_label': '648.hf2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JN', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394216
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '72.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.BM', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.F', '24.G', '24.H', '36.E'], 'contains': ['144.BR', '216.C', '216.D', '216.E', '216.S', '216.W', '216.BI', '216.BK', '216.BP'], 'core': '432.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1995, -1, 3728, -1], 'generators': [3121, 30384, 13440, 23760, 24624, 3888], 'label': '34992.gv.72.I', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.E', 'old_label': '72.i1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.I', 'subgroup_fusion': None, 'weyl_group': '36.13'}
    • id: 202394217
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.FB', '216.FC', '216.FD', '216.HG', '216.HH', '216.HI', '324.BA'], 'contains': ['1296.JB', '1944.DM', '1944.DN', '1944.DO', '1944.DP', '1944.DQ', '1944.DR', '1944.DU'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6105, -1, 7094, -1], 'generators': [34632, 144, 192, 5088], 'label': '34992.gv.648.JO', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.BA', 'old_label': '648.hg1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JO', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394218
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EN', '216.EQ', '216.ET', '216.EZ', '216.HJ', '216.HK', '216.HL', '216.HM'], 'contains': ['1296.JE', '1944.DV', '1944.DW', '1944.EA', '1944.ED', '1944.EH', '1944.EN', '1944.EO', '1944.EP', '1944.ES'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7613, -1, 7832, -1], 'generators': [7896, 16992, 192, 3552], 'label': '34992.gv.648.JP', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JP', 'old_label': '648.hh1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JP', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394219
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['216.EO', '216.ES', '216.EY', '216.HJ', '216.HK', '216.HL', '216.HM'], 'contains': ['1296.JF', '1944.DV', '1944.DX', '1944.DZ', '1944.EF', '1944.EI', '1944.EM', '1944.ER'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [8518, -1, 7789, -1], 'generators': [6648, 13392, 15264, 3552], 'label': '34992.gv.648.JQ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JQ', 'old_label': '648.hh2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JQ', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394220
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['216.EP', '216.ER', '216.FA', '216.HJ', '216.HK', '216.HL', '216.HM'], 'contains': ['1296.JG', '1944.DV', '1944.DY', '1944.EB', '1944.EE', '1944.EG', '1944.EL', '1944.EQ'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [8523, -1, 7775, -1], 'generators': [1656, 22128, 16512, 31776], 'label': '34992.gv.648.JR', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JR', 'old_label': '648.hh3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JR', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394221
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EU', '216.FE', '216.FI', '216.FJ', '216.GK', '216.GL', '216.GM', '216.GN', '216.GP', '216.GS', '216.HK', '216.HM', '216.HN'], 'contains': ['1296.JK', '1944.DW', '1944.DX', '1944.EA', '1944.EB', '1944.EX', '1944.FD', '1944.FE', '1944.FH', '1944.FO', '1944.FX', '1944.GB', '1944.GI', '1944.GL'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7624, -1, 8319, -1], 'generators': [11544, 432, 19104, 17232], 'label': '34992.gv.648.JS', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JS', 'old_label': '648.hi1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JS', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394222
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EU', '216.FE', '216.FI', '216.FJ', '216.GK', '216.GL', '216.GM', '216.GO', '216.GP', '216.GQ', '216.HK', '216.HL', '216.HN'], 'contains': ['1296.JL', '1944.DW', '1944.DX', '1944.EA', '1944.EB', '1944.EY', '1944.FC', '1944.FE', '1944.FH', '1944.FO', '1944.FW', '1944.GB', '1944.GI', '1944.GL'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7597, -1, 8418, -1], 'generators': [11304, 10800, 30816, 14448], 'label': '34992.gv.648.JT', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JT', 'old_label': '648.hi2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JT', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394223
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EU', '216.FE', '216.FI', '216.FJ', '216.GL', '216.GM', '216.GN', '216.GO', '216.GP', '216.GR', '216.HL', '216.HM', '216.HP'], 'contains': ['1296.JM', '1944.DW', '1944.DX', '1944.EA', '1944.EB', '1944.EZ', '1944.FB', '1944.FF', '1944.FG', '1944.FN', '1944.FU', '1944.GC', '1944.GJ', '1944.GM'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7770, -1, 8404, -1], 'generators': [9528, 13104, 11376, 5664], 'label': '34992.gv.648.JU', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JU', 'old_label': '648.hi3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JU', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394224
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EU', '216.FE', '216.FI', '216.FJ', '216.GL', '216.GM', '216.GN', '216.GO', '216.GQ', '216.GS', '216.HJ', '216.HK', '216.HP'], 'contains': ['1296.JN', '1944.DW', '1944.DX', '1944.EA', '1944.EB', '1944.EV', '1944.FB', '1944.FF', '1944.FG', '1944.FQ', '1944.FU', '1944.GD', '1944.GJ', '1944.GN'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7778, -1, 8362, -1], 'generators': [19800, 432, 2304, 30528], 'label': '34992.gv.648.JV', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JV', 'old_label': '648.hi4', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JV', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394225
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EU', '216.FE', '216.FI', '216.FJ', '216.GN', '216.GO', '216.GP', '216.HK', '216.HO'], 'contains': ['1296.JO', '1944.DW', '1944.DX', '1944.EA', '1944.EB', '1944.EW', '1944.FA', '1944.FI', '1944.FP', '1944.FV', '1944.GE', '1944.GK', '1944.GO'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7455, -1, 8158, -1], 'generators': [6120, 1440, 2304, 11664], 'label': '34992.gv.648.JW', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JW', 'old_label': '648.hi5', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JW', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394226
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EV', '216.FF', '216.FK', '216.GK', '216.GM', '216.GN', '216.GO', '216.GP', '216.GS', '216.HK', '216.HL', '216.HP'], 'contains': ['1296.JP', '1944.DW', '1944.DZ', '1944.EB', '1944.EV', '1944.EZ', '1944.FF', '1944.FG', '1944.FJ', '1944.FU', '1944.GC', '1944.GD', '1944.GF'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7763, -1, 8390, -1], 'generators': [9528, 21168, 24288, 9456], 'label': '34992.gv.648.JX', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JX', 'old_label': '648.hj1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JX', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394227
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '72.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.E', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.F', '36.F'], 'contains': ['144.I', '216.S', '216.Z', '216.BA', '216.CP', '216.CQ', '216.CV'], 'core': '3888.B', 'coset_action_label': None, 'count': 36, 'diagramx': [1801, -1, 3054, -1], 'generators': [3121, 13440, 8592, 24624, 3888, 26896], 'label': '34992.gv.72.J', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '72.j1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.J', 'subgroup_fusion': None, 'weyl_group': '324.124'}
    • id: 202394228
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EV', '216.FF', '216.FK', '216.GL', '216.GN', '216.GP', '216.HJ', '216.HM', '216.HN'], 'contains': ['1296.JQ', '1944.DW', '1944.DZ', '1944.EB', '1944.EX', '1944.FE', '1944.FL', '1944.FX', '1944.GB', '1944.GG'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7541, -1, 8016, -1], 'generators': [13320, 33840, 192, 19104], 'label': '34992.gv.648.JY', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JY', 'old_label': '648.hj2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JY', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394229
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.JZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EV', '216.FF', '216.FK', '216.GL', '216.GO', '216.GQ', '216.GR', '216.HK', '216.HN'], 'contains': ['1296.JR', '1944.DW', '1944.DZ', '1944.EB', '1944.EY', '1944.FH', '1944.FM', '1944.FW', '1944.GB', '1944.GG'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7333, -1, 7917, -1], 'generators': [9528, 18576, 12384, 12336], 'label': '34992.gv.648.JZ', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.JZ', 'old_label': '648.hj3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.JZ', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394230
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.KA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['216.EV', '216.FF', '216.FK', '216.GM', '216.GQ', '216.HM', '216.HO'], 'contains': ['1296.JS', '1944.DW', '1944.DZ', '1944.EB', '1944.EW', '1944.FI', '1944.FK', '1944.FV', '1944.GE', '1944.GH'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [7354, -1, 8002, -1], 'generators': [9528, 24240, 9072, 12336], 'label': '34992.gv.648.KA', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.KA', 'old_label': '648.hj4', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.KA', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394231
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.KB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['216.EW', '216.FG', '216.FL', '216.GK', '216.GR', '216.HJ', '216.HO', '324.BB'], 'contains': ['1296.JT', '1944.DY', '1944.DZ', '1944.EA', '1944.EW', '1944.FA', '1944.FV', '1944.FY'], 'core': '34992.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [6810, -1, 7349, -1], 'generators': [15096, 144, 14640, 11088], 'label': '34992.gv.648.KB', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.BB', 'old_label': '648.hk1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.KB', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394232
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.KC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EW', '216.FG', '216.FL', '216.GL', '216.GM', '216.GP', '216.HK', '216.HP'], 'contains': ['1296.JU', '1944.DY', '1944.DZ', '1944.EA', '1944.EV', '1944.EZ', '1944.FB', '1944.FU', '1944.FZ'], 'core': '34992.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7349, -1, 7860, -1], 'generators': [16200, 11808, 26928, 12336], 'label': '34992.gv.648.KC', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.KC', 'old_label': '648.hk2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.KC', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394233
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.KD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['216.EW', '216.FG', '216.FL', '216.GN', '216.GQ', '216.HL', '216.HN'], 'contains': ['1296.JV', '1944.DY', '1944.DZ', '1944.EA', '1944.EX', '1944.FC', '1944.FW', '1944.GA'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6805, -1, 7448, -1], 'generators': [29640, 432, 34704, 31776], 'label': '34992.gv.648.KD', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.KD', 'old_label': '648.hk3', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.KD', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394234
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.KE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EW', '216.FG', '216.FL', '216.GO', '216.GS', '216.HM', '216.HN', '324.BC'], 'contains': ['1296.JW', '1944.DY', '1944.DZ', '1944.EA', '1944.EY', '1944.FD', '1944.FX', '1944.GA'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6759, -1, 7377, -1], 'generators': [15096, 144, 20736, 5664], 'label': '34992.gv.648.KE', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.BC', 'old_label': '648.hk4', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.KE', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 202394235
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.KF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.EX', '216.FH', '216.FM', '216.GK', '216.GL', '216.GN', '216.GO', '216.GP', '216.GQ', '216.HK', '216.HM', '216.HP'], 'contains': ['1296.JX', '1944.DW', '1944.DX', '1944.DY', '1944.EV', '1944.EZ', '1944.FB', '1944.FF', '1944.FG', '1944.FJ', '1944.FN', '1944.FQ', '1944.FR'], 'core': '34992.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': [7837, -1, 8305, -1], 'generators': [9528, 12816, 12624, 7440], 'label': '34992.gv.648.KF', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.KF', 'old_label': '648.hl1', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.KF', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 202394236
      {'ambient': '34992.gv', 'aut_centralizer_order': None, 'aut_label': '648.KG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34992.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['216.EX', '216.FH', '216.FM', '216.GL', '216.GS', '216.HL', '216.HO', '324.BE'], 'contains': ['1296.JY', '1944.DW', '1944.DX', '1944.DY', '1944.EW', '1944.FA', '1944.FI', '1944.FK', '1944.FP', '1944.FS'], 'core': '34992.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [7259, -1, 7604, -1], 'generators': [13320, 33840, 192, 22752], 'label': '34992.gv.648.KG', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.BE', 'old_label': '648.hl2', 'projective_image': '34992.gv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.KG', 'subgroup_fusion': None, 'weyl_group': '108.39'}