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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2519424.jt', 'ambient_counter': 254, 'ambient_order': 2519424, 'ambient_tex': 'C_3^7.A_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 69984, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2519424.jt.12.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': 4748967431074108681, 'subgroup_order': 209952, 'subgroup_tex': 'C_3^6.A_4^2.C_2', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '2519424.jt', 'aut_centralizer_order': None, 'aut_label': '12.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '36.B', 'coset_action_label': None, 'count': 2, 'diagramx': [1412, -1, 1237, -1], 'generators': [9860011207183393224, 144, 189706711622424, 852633951300996624, 3392308100079624, 858465045665297544, 12930504771122882040, 9860201001072172800, 10014214958406086640, 30992187830559747123, 189706712388480, 9860200900960838400, 9860200900965233424], 'label': '2519424.jt.12.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '12.o1', 'projective_image': '2519424.jt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.O', 'subgroup_fusion': None, 'weyl_group': '419904.b'}
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label None does not appear in gps_groups
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 36, 'aut_gen_orders': [12, 12, 6, 18], 'aut_gens': [[5232167387746550642, 2696555690010087963], [41750869757302441442, 19894337257702851484], [20022739166065106405, 6513126578572644964], [41795331997799461085, 40694472011850472948], [23175333029989537946, 20759035103680892403]], 'aut_group': '10077696.cr', 'aut_hash': 1455092669202348314, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10077696, 'aut_permdeg': 846, 'aut_perms': 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'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 54, 1, 2], [2, 81, 1, 1], [2, 162, 1, 1], [2, 486, 1, 1], [2, 648, 1, 1], [2, 729, 1, 2], [2, 1458, 1, 1], [2, 4374, 1, 1], [3, 2, 1, 1], [3, 12, 1, 1], [3, 16, 1, 1], [3, 24, 1, 2], [3, 32, 1, 1], [3, 36, 1, 1], [3, 48, 1, 1], [3, 64, 1, 1], [3, 64, 2, 1], [3, 72, 1, 1], [3, 72, 2, 1], [3, 96, 1, 1], [3, 144, 1, 2], [3, 144, 2, 1], [3, 192, 1, 2], [3, 288, 1, 2], [3, 384, 1, 1], [3, 432, 2, 1], [3, 576, 2, 1], [3, 864, 2, 2], [3, 1152, 2, 1], [3, 1296, 2, 1], [3, 1728, 2, 1], [3, 2592, 1, 1], [3, 2592, 2, 1], [3, 5184, 1, 1], [4, 17496, 1, 2], [4, 52488, 1, 1], [6, 108, 1, 2], [6, 108, 2, 1], [6, 162, 1, 1], [6, 216, 1, 2], [6, 324, 1, 2], [6, 324, 2, 2], [6, 432, 1, 2], [6, 648, 1, 6], [6, 648, 2, 5], [6, 864, 1, 2], [6, 864, 2, 1], [6, 972, 1, 2], [6, 972, 2, 1], [6, 1296, 1, 8], [6, 1296, 2, 2], [6, 1458, 1, 2], [6, 1728, 1, 2], [6, 1944, 1, 2], [6, 1944, 2, 4], [6, 2592, 1, 3], [6, 2592, 2, 1], [6, 2916, 1, 3], [6, 2916, 2, 1], [6, 3888, 1, 2], [6, 3888, 2, 9], [6, 5184, 1, 1], [6, 5184, 2, 2], [6, 5832, 1, 3], [6, 5832, 2, 3], [6, 7776, 1, 1], [6, 7776, 2, 7], [6, 8748, 1, 1], [6, 11664, 1, 1], [6, 11664, 2, 2], [6, 15552, 2, 1], [6, 17496, 2, 1], [6, 23328, 1, 1], [6, 23328, 2, 4], [6, 23328, 4, 1], [6, 34992, 2, 1], [6, 46656, 1, 1], [9, 144, 2, 1], [9, 288, 2, 1], [9, 864, 2, 1], [9, 1152, 2, 1], [9, 1152, 4, 1], [9, 1728, 2, 2], [9, 3456, 2, 1], [9, 5184, 2, 3], [9, 5184, 4, 1], [9, 10368, 1, 1], [9, 10368, 2, 3], [12, 17496, 2, 1], [12, 34992, 1, 1], [12, 34992, 2, 2], [12, 69984, 1, 1], [12, 209952, 2, 1], [18, 3888, 2, 2], [18, 7776, 2, 4], [18, 11664, 2, 1], [18, 15552, 2, 2], [18, 46656, 2, 3], [18, 46656, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^6.C_2^6:S_3^3', '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': 36, 'autcentquo_group': '10077696.cr', 'autcentquo_hash': 1455092669202348314, 'autcentquo_nilpotent': False, 'autcentquo_order': 10077696, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^6.C_2^6:S_3^3', 'cc_stats': [[1, 1, 1], [2, 54, 2], [2, 81, 1], [2, 162, 1], [2, 486, 1], [2, 648, 1], [2, 729, 2], [2, 1458, 1], [2, 4374, 1], [3, 2, 1], [3, 12, 1], [3, 16, 1], [3, 24, 2], [3, 32, 1], [3, 36, 1], [3, 48, 1], [3, 64, 3], [3, 72, 3], [3, 96, 1], [3, 144, 4], [3, 192, 2], [3, 288, 2], [3, 384, 1], [3, 432, 2], [3, 576, 2], [3, 864, 4], [3, 1152, 2], [3, 1296, 2], [3, 1728, 2], [3, 2592, 3], [3, 5184, 1], [4, 17496, 2], [4, 52488, 1], [6, 108, 4], [6, 162, 1], [6, 216, 2], [6, 324, 6], [6, 432, 2], [6, 648, 16], [6, 864, 4], [6, 972, 4], [6, 1296, 12], [6, 1458, 2], [6, 1728, 2], [6, 1944, 10], [6, 2592, 5], [6, 2916, 5], [6, 3888, 20], [6, 5184, 5], [6, 5832, 9], [6, 7776, 15], [6, 8748, 1], [6, 11664, 5], [6, 15552, 2], [6, 17496, 2], [6, 23328, 13], [6, 34992, 2], [6, 46656, 1], [9, 144, 2], [9, 288, 2], [9, 864, 2], [9, 1152, 6], [9, 1728, 4], [9, 3456, 2], [9, 5184, 10], [9, 10368, 7], [12, 17496, 2], [12, 34992, 5], [12, 69984, 1], [12, 209952, 2], [18, 3888, 4], [18, 7776, 8], [18, 11664, 2], [18, 15552, 4], [18, 46656, 10]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '2519424.jt', 'commutator_count': 1, 'commutator_label': '209952.ib', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 16, 'conjugacy_classes_known': True, 'counter': 254, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 54, 1, 2], [2, 81, 1, 1], [2, 162, 1, 1], [2, 486, 1, 1], [2, 648, 1, 1], [2, 729, 1, 2], [2, 1458, 1, 1], [2, 4374, 1, 1], [3, 2, 1, 1], [3, 12, 1, 1], [3, 16, 1, 1], [3, 24, 1, 2], [3, 32, 1, 1], [3, 36, 1, 1], [3, 48, 1, 1], [3, 64, 1, 1], [3, 64, 2, 1], [3, 72, 1, 1], [3, 72, 2, 1], [3, 96, 1, 1], [3, 144, 1, 2], [3, 144, 2, 1], [3, 192, 1, 2], [3, 288, 1, 2], [3, 384, 1, 1], [3, 432, 2, 1], [3, 576, 2, 1], [3, 864, 2, 2], [3, 1152, 2, 1], [3, 1296, 2, 1], [3, 1728, 2, 1], [3, 2592, 1, 1], [3, 2592, 2, 1], [3, 5184, 1, 1], [4, 17496, 1, 2], [4, 52488, 1, 1], [6, 108, 1, 4], [6, 162, 1, 1], [6, 216, 1, 2], [6, 324, 1, 6], [6, 432, 1, 2], [6, 648, 1, 12], [6, 648, 2, 2], [6, 864, 1, 4], [6, 972, 1, 4], [6, 1296, 1, 12], [6, 1458, 1, 2], [6, 1728, 1, 2], [6, 1944, 1, 4], [6, 1944, 2, 3], [6, 2592, 1, 5], [6, 2916, 1, 5], [6, 3888, 1, 2], [6, 3888, 2, 9], [6, 5184, 1, 1], [6, 5184, 2, 2], [6, 5832, 1, 5], [6, 5832, 2, 2], [6, 7776, 1, 1], [6, 7776, 2, 7], [6, 8748, 1, 1], [6, 11664, 1, 1], [6, 11664, 2, 2], [6, 15552, 2, 1], [6, 17496, 2, 1], [6, 23328, 1, 1], [6, 23328, 2, 6], [6, 34992, 2, 1], [6, 46656, 1, 1], [9, 144, 2, 1], [9, 288, 2, 1], [9, 864, 2, 1], [9, 1152, 2, 3], [9, 1728, 2, 2], [9, 3456, 2, 1], [9, 5184, 2, 5], [9, 10368, 1, 1], [9, 10368, 2, 3], [12, 17496, 2, 1], [12, 34992, 1, 3], [12, 34992, 2, 1], [12, 69984, 1, 1], [12, 209952, 2, 1], [18, 3888, 2, 2], [18, 7776, 2, 4], [18, 11664, 2, 1], [18, 15552, 2, 2], [18, 46656, 2, 5]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [9, 7], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 0, 8], [24, 1, 4], [32, 0, 8], [32, 1, 1], [48, 0, 4], [48, 1, 2], [64, 0, 12], [72, 0, 4], [72, 1, 8], [96, 0, 2], [96, 1, 1], [128, 0, 6], [144, 1, 4], [192, 0, 4], [192, 1, 2], [288, 0, 2], [288, 1, 6], [384, 0, 2], [384, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '2519424.jt', 'hash': 1436482011940253895, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [12, 18], 'inner_gens': [[5232167387746550642, 23386589906599382524], [42040728687231934561, 2696555690010087963]], 'inner_hash': 1436482011940253895, 'inner_nilpotent': False, 'inner_order': 2519424, 'inner_split': True, 'inner_tex': 'C_3^7.A_4^2:D_4', 'inner_used': [1, 2], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 12], [2, 27], [4, 6], [6, 12], [9, 4], [12, 30], [16, 18], [18, 5], [24, 24], [32, 9], [36, 16], [48, 12], [64, 18], [72, 22], [96, 15], [128, 9], [144, 16], [192, 12], [288, 9], [384, 3]], 'label': '2519424.jt', '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': 'C3^7.A4^2:D4', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 179, 'number_characteristic_subgroups': 35, 'number_conjugacy_classes': 279, 'number_divisions': 198, 'number_normal_subgroups': 35, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 2519424, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 8775], [3, 29402], [4, 87480], [6, 916326], [9, 147744], [12, 699840], [18, 629856]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[5232167300568259466, 20637388664106966148], [5232167387746550642, 2696555690010087964]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 4], [2, 9], [4, 13], [6, 4], [8, 2], [9, 4], [12, 14], [16, 2], [18, 3], [24, 18], [32, 9], [36, 17], [48, 12], [64, 6], [72, 18], [96, 9], [128, 9], [144, 18], [192, 9], [256, 4], [288, 7], [384, 5], [576, 1], [768, 1]], 'representations': {'PC': {'code': '331420366141201957210312958857371708603127922506505608246599143787757433322525749627881451837157699847404164515624325936196989639890984233944029934138972240499080648705541013537616902603923019830298972851199295984746940409614305713914224486004704875530886058786649029406918289271108262633011243667224295874576055897651409990645578898138324889306225920458032399429648349687938646577485888125211836333466976574292094589127550216476727105471599068361284625685157376113888555414836834144343363812400758122105643369840591748778175008811605936719991538801893718476888286210477816926171327918724271', 'gens': [1, 3, 5, 7, 8, 10, 12, 14, 15, 16], 'pres': [16, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 32, 12109841, 49852514, 9156834, 130, 37326339, 18745747, 12904755, 13170244, 100156340, 30069636, 16593412, 228, 17445893, 113076885, 8635429, 5124149, 198688902, 108886, 4354598, 9582102, 121030, 63590, 79017991, 21012503, 4833831, 6474311, 138327, 1383, 375, 2239528, 4105800, 124504, 1256, 379468809, 20528665, 587561, 14688057, 2665993, 1870649, 4921, 473, 49268746, 8211482, 912426, 152122, 1368650, 456282, 4346, 32099339, 28491291, 33046315, 5723195, 2379, 4855771, 5915, 571, 359468, 1078332, 5068, 2965340, 5148, 1161229, 31352861, 32301, 32333, 871005, 96893, 2877, 22394894, 622110, 70917166, 11197502, 1244238, 34654, 8830, 455196687, 167215135, 11980847, 39813183, 479311, 1001567, 2211951, 553087, 184479, 15551]}, 'Perm': {'d': 21, 'gens': [5232167387746550642, 2696555690010087963]}}, 'schur_multiplier': [2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 96, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^7.A_4^2:D_4', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
