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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1192464.a', 'ambient_counter': 1, 'ambient_order': 1192464, 'ambient_tex': '\\PSL(2,13)^2', 'central': False, 'central_factor': False, 'centralizer_order': 7, 'characteristic': False, 'core_order': 1092, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1192464.a.156.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '156.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': 156, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8687014038804670111, 'subgroup_order': 7644, 'subgroup_tex': 'C_7\\times \\PSL(2,13)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1192464.a', 'aut_centralizer_order': None, 'aut_label': '156.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '170352.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['78.a1'], 'contains': ['1092.a1', '2184.b1', '12168.a1', '14196.c1', '14196.d1'], 'core': '1092.a1', 'coset_action_label': None, 'count': 156, 'diagramx': None, 'generators': [11820676383878242, 255930154616878971, 513374690911988456], 'label': '1192464.a.156.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '78.a1', 'old_label': '156.a1', 'projective_image': '1192464.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '156.a1', 'subgroup_fusion': None, 'weyl_group': '2184.o'}
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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': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 2184, 'aut_gen_orders': [12, 14], 'aut_gens': [[303179774232815129, 256247504548427444], [438333557448291090, 632560172570566100], [218442768229865545, 349656087733854374]], 'aut_group': '9539712.a', 'aut_hash': 5844502808905207782, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 9539712, 'aut_permdeg': 182, 'aut_perms': [2618933876601711035472205780229614039966456125523231304354652892511456912287091920807300589465333584930529694275234982333936097633179543439095358596249841472832169680610199459293196372918196986825417102745470568211297150059695672270886956970936728169808127952663654811637333985443971314134920713417746135497786207663421453468868009894, 4241250248575929465753763267790115832928425937143286124137946630893198298631852824215604149612879650898215429592536157875305574477745458319835236213882687844765864224644860797970722097260677240831459154205095010883536840412814217170463659049833216782984183700935267107020390404091840154671051899219020200848500164471689674337234231492], 'aut_phi_ratio': 30.333333333333332, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 91, 2, 1], [2, 8281, 1, 1], [3, 182, 2, 1], [3, 33124, 1, 1], [6, 182, 2, 1], [6, 16562, 2, 2], [6, 33124, 1, 1], [6, 33124, 2, 1], [7, 156, 2, 3], [7, 24336, 1, 3], [7, 24336, 2, 3], [13, 84, 4, 1], [13, 7056, 4, 1], [14, 14196, 2, 3], [21, 28392, 2, 3], [26, 7644, 4, 1], [39, 15288, 4, 1], [42, 28392, 2, 3], [78, 15288, 4, 1], [91, 13104, 4, 3]], 'aut_supersolvable': False, 'aut_tex': '\\PGL(2,13)\\wr C_2', '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': 2184, 'autcentquo_group': '9539712.a', 'autcentquo_hash': 5844502808905207782, 'autcentquo_nilpotent': False, 'autcentquo_order': 9539712, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,13)\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 91, 2], [2, 8281, 1], [3, 182, 2], [3, 33124, 1], [6, 182, 2], [6, 16562, 4], [6, 33124, 3], [7, 156, 6], [7, 24336, 9], [13, 84, 4], [13, 7056, 4], [14, 14196, 6], [21, 28392, 6], [26, 7644, 4], [39, 15288, 4], [42, 28392, 6], [78, 15288, 4], [91, 13104, 12]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '1192464.a', 'commutator_count': 1, 'commutator_label': '1192464.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['1092.25', '1092.25'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [['1092.25', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 91, 1, 2], [2, 8281, 1, 1], [3, 182, 1, 2], [3, 33124, 1, 1], [6, 182, 1, 2], [6, 16562, 1, 4], [6, 33124, 1, 3], [7, 156, 3, 2], [7, 24336, 3, 3], [13, 84, 2, 2], [13, 7056, 2, 2], [14, 14196, 3, 2], [21, 28392, 3, 2], [26, 7644, 2, 2], [39, 15288, 2, 2], [42, 28392, 3, 2], [78, 15288, 2, 2], [91, 13104, 6, 2]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': 122265, 'exponent': 546, 'exponents_of_order': [4, 2, 2, 2], 'factors_of_aut_order': [2, 3, 7, 13], 'factors_of_order': [2, 3, 7, 13], 'faithful_reps': [[49, 1, 4], [84, 1, 12], [91, 1, 4], [98, 1, 8], [144, 1, 9], [156, 1, 6], [168, 1, 12], [169, 1, 1], [182, 1, 4], [196, 1, 4]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1192464.a', 'hash': 6067488358697095203, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 546, 'inner_gen_orders': [91, 91], 'inner_gens': [[303179774232815129, 129013645341061956], [600326659881148986, 256247504548427444]], 'inner_hash': 6067488358697095203, 'inner_nilpotent': False, 'inner_order': 1192464, 'inner_split': True, 'inner_tex': '\\PSL(2,13)^2', 'inner_used': [1, 2], 'irrC_degree': 49, 'irrQ_degree': 98, 'irrQ_dim': 98, 'irrR_degree': 49, 'irrep_stats': [[1, 1], [7, 4], [12, 6], [13, 2], [14, 4], [49, 4], [84, 12], [91, 4], [98, 8], [144, 9], [156, 6], [168, 12], [169, 1], [182, 4], [196, 4]], 'label': '1192464.a', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'PSL(2,13)^2', '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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 36, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 81, 'number_divisions': 39, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 205, 'number_subgroup_classes': 457, 'number_subgroups': 3455202, 'old_label': None, 'order': 1192464, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 8463], [3, 33488], [6, 165984], [7, 219960], [13, 28560], [14, 85176], [21, 170352], [26, 30576], [39, 61152], [42, 170352], [78, 61152], [91, 157248]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [19841485745444196, 502652784635659385], 'outer_gens': [[23895372139103959, 124637516376406479], [103296899401514617, 1957144032441204]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [1, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': None, 'perfect': True, 'permutation_degree': 28, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [13, 2], [14, 6], [36, 2], [98, 2], [169, 1], [182, 6], [196, 8], [432, 3], [468, 2], [504, 6]], 'representations': {'Lie': [{'d': 4, 'q': 13, 'gens': [256247504548427444, 303179774232815129], 'family': 'POmegaPlus'}], 'Perm': {'d': 28, 'gens': [23021226587309801547550148098, 11743877961469217483421532144]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\PSL(2,13)^2', 'transitive_degree': 196, 'wreath_data': None, 'wreath_product': False}
