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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.3398', 'ambient_counter': 3398, 'ambient_order': 1440, 'ambient_tex': 'C_{120}.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 72, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1440.3398.20.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1440.3398', 'aut_centralizer_order': 48, 'aut_label': '20.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.209', 'aut_weyl_index': 96, 'centralizer': '48.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '10.a1.a1', '10.b1.b1', '10.e1.a1'], 'contains': ['40.b1.a1', '40.e1.b1', '60.b1.a1', '60.k1.b1'], 'core': '20.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6405, 6472, 6339, 6807, 5057, 4882, 5570, 4693], 'generators': [541, 724, 1080, 960, 720], 'label': '1440.3398.20.c1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.c1.b1', 'normal_contained_in': ['4.c1.b1', '10.a1.a1', '10.b1.b1', '10.e1.a1'], 'normal_contains': ['40.b1.a1', '60.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.c1.b1', 'projective_image': '720.651', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.b1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
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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': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 2, 3], 'aut_gens': [[1, 6], [1, 30], [5, 6], [5, 42], [19, 42], [37, 6], [25, 6]], 'aut_group': '96.209', 'aut_hash': 209, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 96, 'aut_permdeg': 9, 'aut_perms': [5160, 120, 16, 121, 7, 45360], 'aut_phi_ratio': 4.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 2, 1, 1], [4, 6, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [12, 2, 2, 2], [12, 2, 4, 1], [12, 6, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_4\\times D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '12.4', 'autcentquo_hash': 4, 'autcentquo_nilpotent': False, 'autcentquo_order': 12, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [3, 2, 3], [4, 2, 1], [4, 6, 2], [6, 1, 2], [6, 2, 3], [12, 2, 8], [12, 6, 4]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '12.4', 'commutator_count': 1, 'commutator_label': '6.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 26, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['24.4', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 2, 1, 1], [4, 6, 1, 2], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [12, 2, 2, 2], [12, 2, 4, 1], [12, 6, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 12, 'exponents_of_order': [3, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 0, 4]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '36.12', 'hash': 26, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6], 'inner_gens': [[1, 66], [13, 6]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': True, 'inner_tex': 'D_6', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 4, 'irrep_stats': [[1, 12], [2, 15]], 'label': '72.26', 'linC_count': 4, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 16, 'linQ_dim': 6, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3^2:Q8', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 14, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 27, 'number_divisions': 16, 'number_normal_subgroups': 18, 'number_subgroup_autclasses': 23, 'number_subgroup_classes': 27, 'number_subgroups': 42, 'old_label': None, 'order': 72, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 1], [3, 8], [4, 14], [6, 8], [12, 40]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [18, 0, 0], 'outer_gens': [[19, 6], [5, 6], [1, 42]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 7], [4, 4], [8, 1]], 'representations': {'PC': {'code': 75140255264546281, 'gens': [1, 3], 'pres': [5, -2, -3, -2, -2, -3, 10, 186, 992, 42, 1203, 58, 1204]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [41715828716014388, 58415888739750341]}, 'GLFp': {'d': 2, 'p': 13, 'gens': [15381, 6592, 221]}, 'Perm': {'d': 14, 'gens': [6314119039, 12593, 13971242880, 18619, 20122058880]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:Q_8', 'transitive_degree': 24, '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': '40.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [6, 24, 6, 6, 24, 12, 4], 'aut_gens': [[1, 2, 12], [1089, 1322, 1092], [786, 69, 1408], [546, 1025, 476], [5, 1210, 372], [1026, 781, 400], [1386, 425, 472], [1266, 781, 44]], 'aut_group': None, 'aut_hash': 7047191688454449486, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 9216, 'aut_permdeg': 32, 'aut_perms': [37374757259418106542915772616655614, 54960709794644725664059169232212232, 77855397998093995797976871903302698, 199260128159523008574628039311054278, 193304368248919484402206168364361811, 23590047996388886904304534268870917, 184736766966437360933321836673688500], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 12, 2, 1], [2, 18, 1, 1], [3, 2, 2, 1], [3, 4, 1, 1], [4, 2, 1, 1], [4, 9, 2, 1], [4, 12, 2, 1], [5, 1, 4, 1], [6, 2, 2, 1], [6, 4, 1, 1], [6, 24, 2, 1], [8, 2, 2, 1], [8, 18, 2, 1], [10, 1, 4, 1], [10, 12, 8, 1], [10, 18, 4, 1], [12, 4, 2, 2], [12, 24, 2, 1], [15, 2, 8, 1], [15, 4, 4, 1], [20, 2, 4, 1], [20, 9, 8, 1], [20, 12, 8, 1], [24, 4, 4, 2], [30, 2, 8, 1], [30, 4, 4, 1], [30, 24, 8, 1], [40, 2, 8, 1], [40, 18, 8, 1], [60, 4, 8, 2], [60, 24, 8, 1], [120, 4, 16, 2]], 'aut_supersolvable': False, 'aut_tex': '(C_4^2\\times C_3:S_3).C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.45', 'autcent_hash': 45, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '288.889', 'autcentquo_hash': 889, 'autcentquo_nilpotent': False, 'autcentquo_order': 288, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'D_6\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 12, 2], [2, 18, 1], [3, 2, 2], [3, 4, 1], [4, 2, 1], [4, 9, 2], [4, 12, 2], [5, 1, 4], [6, 2, 2], [6, 4, 1], [6, 24, 2], [8, 2, 2], [8, 18, 2], [10, 1, 4], [10, 12, 8], [10, 18, 4], [12, 4, 4], [12, 24, 2], [15, 2, 8], [15, 4, 4], [20, 2, 4], [20, 9, 8], [20, 12, 8], [24, 4, 8], [30, 2, 8], [30, 4, 4], [30, 24, 8], [40, 2, 8], [40, 18, 8], [60, 4, 16], [60, 24, 8], [120, 4, 32]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '144.145', 'commutator_count': 1, 'commutator_label': '36.8', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3398, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['288.457', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 12, 1, 2], [2, 18, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [4, 2, 1, 1], [4, 9, 2, 1], [4, 12, 1, 2], [5, 1, 4, 1], [6, 2, 1, 2], [6, 4, 1, 1], [6, 24, 1, 2], [8, 2, 2, 1], [8, 18, 2, 1], [10, 1, 4, 1], [10, 12, 4, 2], [10, 18, 4, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 24, 1, 2], [15, 2, 4, 2], [15, 4, 4, 1], [20, 2, 4, 1], [20, 9, 8, 1], [20, 12, 4, 2], [24, 4, 2, 2], [24, 4, 4, 1], [30, 2, 4, 2], [30, 4, 4, 1], [30, 24, 4, 2], [40, 2, 8, 1], [40, 18, 8, 1], [60, 4, 4, 2], [60, 4, 8, 1], [60, 24, 4, 2], [120, 4, 8, 2], [120, 4, 16, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 83328, 'exponent': 120, 'exponents_of_order': [5, 2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[4, 0, 16]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '360.153', 'hash': 3398, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 6, 12], 'inner_gens': [[1, 10, 1092], [725, 2, 132], [361, 1322, 12]], 'inner_hash': 145, 'inner_nilpotent': False, 'inner_order': 144, 'inner_split': False, 'inner_tex': 'C_{12}:D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 64, 'irrQ_dim': 64, 'irrR_degree': 8, 'irrep_stats': [[1, 40], [2, 70], [4, 70]], 'label': '1440.3398', 'linC_count': 16, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 64, 'linQ_dim': 16, 'linQ_dim_count': 144, 'linR_count': 152, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C120.D6', 'ngens': 8, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 38, 'number_characteristic_subgroups': 32, 'number_conjugacy_classes': 180, 'number_divisions': 54, 'number_normal_subgroups': 76, 'number_subgroup_autclasses': 170, 'number_subgroup_classes': 270, 'number_subgroups': 1124, 'old_label': None, 'order': 1440, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 43], [3, 8], [4, 44], [5, 4], [6, 56], [8, 40], [10, 172], [12, 64], [15, 32], [20, 176], [24, 32], [30, 224], [40, 160], [60, 256], [120, 128]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [108, 0, 0, 0, 0], 'outer_gens': [[186, 1381, 980], [721, 10, 12], [1, 722, 12], [1, 2, 1212], [1, 2, 1356]], 'outer_group': '64.260', 'outer_hash': 260, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 12, 'outer_perms': [120, 39916800, 362880, 5040, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 12], [8, 14], [16, 5], [32, 4], [64, 1]], 'representations': {'PC': {'code': 2064178787203132405360448163245125668730919583640450892807, 'gens': [1, 2, 4], 'pres': [8, -2, -2, -3, -2, -2, -2, -3, -5, 161, 41, 17474, 4338, 34947, 2123, 91, 29764, 5292, 116, 12685, 141, 29582, 222]}, 'Perm': {'d': 27, 'gens': [405935366914083612327322320, 886829022618529001165239680, 1307371758981965037833472000, 33, 1648147148814358665817344000, 2130263511230305953958579200, 3991680, 5760]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{120}.D_6', 'transitive_degree': 240, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 12], 'aut_gens': [[1, 2], [10, 13], [10, 15]], 'aut_group': '24.5', 'aut_hash': 5, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24, 'aut_permdeg': 7, 'aut_perms': [127, 857], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [5, 1, 4, 1], [10, 1, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4\\times S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '24.5', 'autcent_hash': 5, 'autcent_nilpotent': False, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4\\times S_3', '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, 3], [5, 1, 4], [10, 1, 12]], 'center_label': '20.5', 'center_order': 20, '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', '5.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [5, 1, 4, 1], [10, 1, 4, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 6, 'exponent': 10, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '20.5', 'hash': 5, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 20]], 'label': '20.5', 'linC_count': 72, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 6, 'linQ_dim': 5, 'linQ_dim_count': 6, 'linR_count': 12, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C10', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 20, 'number_divisions': 8, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 10, 'number_subgroups': 10, 'old_label': None, 'order': 20, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 3], [5, 4], [10, 12]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 12], 'outer_gen_pows': [0, 0], 'outer_gens': [[10, 13], [10, 15]], 'outer_group': '24.5', 'outer_hash': 5, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [127, 857], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4\\times S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 4]], 'representations': {'PC': {'code': 2179, 'gens': [1, 2], 'pres': [3, -2, -2, -5, 16]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [141602720900, 706303489327]}, 'GLFp': {'d': 2, 'p': 11, 'gens': [13320, 4001]}, 'Perm': {'d': 9, 'gens': [40320, 720, 96]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{10}', 'transitive_degree': 20, 'wreath_data': None, 'wreath_product': False}
