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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155870', 'ambient_counter': 155870, 'ambient_order': 1152, 'ambient_tex': 'C_3:\\OD_{16}\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 48, 'counter': 162, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155870.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1152.155870', 'aut_centralizer_order': 192, 'aut_label': '24.g1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.b1.a1', '12.bm1.a1', '12.bo1.a1'], 'contains': ['48.b1.a1', '48.r1.a1', '48.t1.a1', '72.c1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5235, 2512, 5571, 6589, 4289, 2823, 3060, 6864], 'generators': [25, 48, 96, 576, 384], 'label': '1152.155870.24.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.g1.a1', 'normal_contained_in': ['8.e1.a1', '12.b1.a1'], 'normal_contains': ['48.b1.a1', '72.c1.a1', '96.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.g1.a1', 'projective_image': '576.8344', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '48.44', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 3, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4], [3, 2, 4], [1, 2, 20], [2, 3, 4], [1, 2, 6], [1, 2, 7], [1, 26, 29], [25, 2, 30], [1, 2, 28]], 'aut_group': '384.20089', 'aut_hash': 20089, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 384, 'aut_permdeg': 10, 'aut_perms': [85945, 848929, 166680, 1961646, 1270440, 1538646, 2682390, 848928], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [3, 1, 2, 1], [4, 1, 8, 1], [6, 1, 2, 1], [6, 1, 12, 1], [12, 1, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4:S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '384.20089', 'autcent_hash': 20089, 'autcent_nilpotent': False, 'autcent_order': 384, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^4:S_4', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 7], [3, 1, 2], [4, 1, 8], [6, 1, 14], [12, 1, 16]], 'center_label': '48.44', 'center_order': 48, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 44, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['3.1', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 1, 2, 1], [4, 1, 2, 4], [6, 1, 2, 7], [12, 1, 4, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 91, 'exponent': 12, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '24.15', 'hash': 44, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 2, 4], [1, 2, 4], [1, 2, 4]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 48]], 'label': '48.44', 'linC_count': 5824, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 96, 'linQ_dim': 5, 'linQ_dim_count': 96, 'linR_count': 96, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2*C12', 'ngens': 5, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 48, 'number_divisions': 24, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 18, 'number_subgroup_classes': 54, 'number_subgroups': 54, 'old_label': None, 'order': 48, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 8], [6, 14], [12, 16]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[3, 2, 4], [1, 2, 20], [2, 3, 4], [1, 2, 6], [1, 2, 7], [1, 26, 29], [25, 2, 30], [1, 2, 28]], 'outer_group': '384.20089', 'outer_hash': 20089, 'outer_nilpotent': False, 'outer_order': 384, 'outer_permdeg': 10, 'outer_perms': [85945, 848929, 166680, 1961646, 1270440, 1538646, 2682390, 848928], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^4:S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 4]], 'representations': {'PC': {'code': 26739073, 'gens': [1, 2, 3], 'pres': [5, -2, -2, -2, -2, -3, 42, 58]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [705946296092, 141602720900, 706461794101]}, 'GLFp': {'d': 3, 'p': 13, 'gens': [10319436418, 9789111396, 6526074264, 4548416880, 6762482606]}, 'Perm': {'d': 11, 'gens': [2400, 3628800, 40320, 4, 744]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 12], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times C_{12}', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 2, 3, 4, 2, 12, 2, 3, 12, 2, 2], 'aut_gens': [[1, 2, 4, 96, 192], [49, 594, 268, 672, 864], [1, 50, 4, 96, 960], [1, 66, 4, 672, 864], [49, 82, 1052, 672, 960], [1, 674, 676, 96, 192], [1, 674, 1077, 576, 864], [1, 674, 100, 96, 192], [1, 2, 772, 96, 192], [1, 130, 908, 672, 192], [49, 2, 44, 576, 864], [49, 2, 44, 576, 480]], 'aut_group': '4608.lj', 'aut_hash': 3301011005301566777, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4608, 'aut_permdeg': 36, 'aut_perms': [318842221327561257690909875941816386406616, 31303450743034687275934959194218215276611, 248306103963959530579788426022384357112823, 7572557401267206144258658830421212443304, 93306105148693759217543321218895251109913, 291756686910626432258442951697967608255164, 172954022556206567660010165744627783, 3343623553825448687400381976689175316522, 39518024623988977774192303160082597024604, 345308436179273422841365124293065851917675, 345308436181462957899650455838677943488075], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 3, 1, 2], [2, 6, 1, 1], [2, 6, 2, 1], [2, 12, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 3, 2, 1], [4, 6, 1, 1], [4, 6, 2, 3], [4, 12, 1, 3], [6, 2, 1, 1], [6, 2, 2, 1], [6, 6, 1, 2], [6, 6, 2, 1], [6, 8, 1, 1], [6, 12, 2, 2], [6, 16, 1, 2], [6, 16, 2, 1], [8, 6, 4, 1], [8, 18, 4, 1], [8, 36, 4, 2], [12, 2, 2, 2], [12, 6, 2, 2], [12, 8, 2, 1], [12, 12, 2, 6], [12, 16, 1, 1], [12, 16, 2, 2], [24, 48, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^5.D_6^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '288.1028', 'autcentquo_hash': 1028, 'autcentquo_nilpotent': False, 'autcentquo_order': 288, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'D_6\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 3, 2], [2, 6, 3], [2, 12, 1], [3, 2, 1], [3, 8, 1], [3, 16, 1], [4, 1, 2], [4, 2, 1], [4, 3, 2], [4, 6, 7], [4, 12, 3], [6, 2, 3], [6, 6, 4], [6, 8, 1], [6, 12, 4], [6, 16, 4], [8, 6, 4], [8, 18, 4], [8, 36, 8], [12, 2, 4], [12, 6, 4], [12, 8, 2], [12, 12, 12], [12, 16, 5], [24, 48, 4]], 'center_label': '4.1', 'center_order': 4, 'central_product': True, 'central_quotient': '288.1028', 'commutator_count': 1, 'commutator_label': '72.47', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 155870, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['24.12', 1], ['48.10', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 3, 1, 2], [2, 6, 1, 3], [2, 12, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 3, 2, 1], [4, 6, 1, 3], [4, 6, 2, 2], [4, 12, 1, 3], [6, 2, 1, 1], [6, 2, 2, 1], [6, 6, 1, 2], [6, 6, 2, 1], [6, 8, 1, 1], [6, 12, 1, 2], [6, 12, 2, 1], [6, 16, 1, 2], [6, 16, 2, 1], [8, 6, 2, 2], [8, 18, 2, 2], [8, 36, 2, 4], [12, 2, 2, 2], [12, 6, 2, 2], [12, 8, 2, 1], [12, 12, 1, 2], [12, 12, 2, 5], [12, 16, 1, 1], [12, 16, 2, 2], [24, 48, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 80640, 'exponent': 24, 'exponents_of_order': [7, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 8]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '288.1028', 'hash': 155870, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 6, 2, 6], 'inner_gens': [[1, 2, 52, 96, 192], [1, 2, 68, 576, 864], [49, 34, 4, 576, 1056], [1, 674, 676, 96, 192], [1, 674, 484, 96, 192]], 'inner_hash': 1028, 'inner_nilpotent': False, 'inner_order': 288, 'inner_split': True, 'inner_tex': 'D_6\\times S_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 6, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 12, 'irrep_stats': [[1, 16], [2, 28], [3, 16], [4, 10], [6, 20]], 'label': '1152.155870', 'linC_count': 128, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 128, 'linQ_dim': 9, 'linQ_dim_count': 64, 'linR_count': 32, 'linR_degree': 7, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3:OD16*S4', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 51, 'number_characteristic_subgroups': 63, 'number_conjugacy_classes': 90, 'number_divisions': 60, 'number_normal_subgroups': 79, 'number_subgroup_autclasses': 502, 'number_subgroup_classes': 614, 'number_subgroups': 3086, 'old_label': None, 'order': 1152, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 39], [3, 26], [4, 88], [6, 150], [8, 384], [12, 272], [24, 192]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 2, 4, 96, 960], [1, 50, 4, 96, 960], [1, 2, 44, 576, 864], [1, 2, 21, 576, 864]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [3, 8], [4, 8], [6, 12], [8, 3], [12, 2], [16, 1], [24, 2]], 'representations': {'PC': {'code': '1325372148165850938277959705989126656129273064907680438904852537122075523081', 'gens': [1, 2, 3, 7, 8], 'pres': [9, -2, -2, -2, -2, -2, -3, -2, 2, -3, 1406, 929, 74, 732, 102, 1813, 130, 1742, 18159, 9096, 5325, 2310, 1374, 31120, 19033, 7810, 1339, 1996, 214, 15578]}, 'Perm': {'d': 15, 'gens': [100677830520, 193158120965, 19200746880, 288450408960, 193158120960, 3, 840, 7, 16]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3:\\OD_{16}\\times S_4', 'transitive_degree': 72, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 2, 6], 'aut_gens': [[1, 2], [13, 2], [1, 10], [9, 14]], 'aut_group': '24.14', 'aut_hash': 14, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24, 'aut_permdeg': 7, 'aut_perms': [7, 136, 856], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 2, 1], [3, 2, 1, 1], [4, 1, 2, 1], [4, 3, 2, 1], [6, 2, 1, 1], [12, 2, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 2, 1], [4, 1, 2], [4, 3, 2], [6, 2, 1], [12, 2, 2]], 'center_label': '4.1', 'center_order': 4, 'central_product': True, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['4.1', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [4, 1, 2, 1], [4, 3, 2, 1], [6, 2, 1, 1], [12, 2, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 12, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 0, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '12.4', 'hash': 5, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 10], [17, 2]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 4, 'irrep_stats': [[1, 8], [2, 4]], 'label': '24.5', 'linC_count': 2, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 5, 'linQ_dim': 4, 'linQ_dim_count': 5, 'linR_count': 5, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C4*S3', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 12, 'number_divisions': 9, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 14, 'number_subgroup_classes': 16, 'number_subgroups': 26, 'old_label': None, 'order': 24, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 8], [6, 2], [12, 4]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 14], [13, 2]], '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': 2, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [4, 1]], 'representations': {'PC': {'code': 2949342177, 'gens': [1, 2], 'pres': [4, -2, -2, -2, -3, 81, 21, 242, 34, 259]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [35931561, 26129103]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [539, 501]}, 'Perm': {'d': 7, 'gens': [127, 17, 7, 840]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4\\times S_3', 'transitive_degree': 12, 'wreath_data': None, 'wreath_product': False}
