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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47311', 'ambient_counter': 47311, 'ambient_order': 1728, 'ambient_tex': 'C_{12}.D_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 216, 'counter': 100, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47311.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.148', 'subgroup_hash': 148, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.S_3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.47311', 'aut_centralizer_order': None, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.j1', '4.o1', '4.u1', '4.v1'], 'contains': ['16.a1', '16.l1', '24.bv1', '24.by1', '24.cc1', '24.cg1', '24.cj1', '24.cn1', '24.cp1'], 'core': '8.k1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [159, 576, 96, 864, 24, 16], 'label': '1728.47311.8.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1', 'normal_contained_in': ['4.b1', '4.j1', '4.o1', '4.u1', '4.v1'], 'normal_contains': ['16.a1', '16.l1'], 'normalizer': '1.a1', 'old_label': '8.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1', 'subgroup_fusion': None, 'weyl_group': None}
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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': 936, 'aut_gen_orders': [13, 3, 2, 2, 3, 2, 2, 3], 'aut_gens': [[1, 4, 12, 36], [13, 160, 172, 184], [81, 4, 12, 36], [27, 16, 24, 60], [109, 4, 12, 36], [21, 4, 12, 36], [1, 4, 12, 38], [3, 4, 12, 36], [13, 4, 12, 36]], 'aut_group': '2426112.a', 'aut_hash': 8128528744486036570, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2426112, 'aut_permdeg': 31, 'aut_perms': [3547131807848858163069121388118960, 3018761843913776478593951888837760, 3247704582262163115836048556991327, 1, 2806547503682286971387065737901560, 16, 7, 1116613815263017792611182715917640], 'aut_phi_ratio': 33696.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 2, 13, 1], [4, 27, 4, 1], [6, 2, 13, 1], [6, 2, 26, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3.(D_4\\times \\GL(3,3))', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.3', 'autcent_hash': 3, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 936, 'autcentquo_group': '303264.a', 'autcentquo_hash': 8091482650397092313, 'autcentquo_nilpotent': False, 'autcentquo_order': 303264, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3:\\GL(3,3)', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 2, 13], [4, 27, 4], [6, 2, 39]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '54.14', 'commutator_count': 1, 'commutator_label': '27.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 148, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['108.34', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 13], [4, 27, 2, 2], [6, 2, 1, 39]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 420, 'exponent': 12, 'exponents_of_order': [3, 3], 'factors_of_aut_order': [2, 3, 13], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '108.44', 'hash': 148, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3, 3, 3], 'inner_gens': [[1, 8, 24, 180], [9, 4, 12, 36], [25, 4, 12, 36], [73, 4, 12, 36]], 'inner_hash': 14, 'inner_nilpotent': False, 'inner_order': 54, 'inner_split': True, 'inner_tex': 'C_3^2:S_3', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 52]], 'label': '216.148', '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': True, 'metacyclic': False, 'monomial': True, 'name': 'C6^2.S3', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 7, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 60, 'number_divisions': 58, 'number_normal_subgroups': 143, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 224, 'number_subgroups': 692, 'old_label': None, 'order': 216, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 3], [3, 26], [4, 108], [6, 78]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 312, 'outer_gen_orders': [26, 12, 12], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[111, 12, 144, 200], [109, 152, 148, 62], [109, 4, 92, 122]], 'outer_group': None, 'outer_hash': 7194555242513615633, 'outer_nilpotent': False, 'outer_order': 44928, 'outer_permdeg': 17, 'outer_perms': [234562976540046, 84264293479822, 1314515826862], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'D_4.\\SL(3,3)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 54]], 'representations': {'PC': {'code': 31849857157303432269, 'gens': [1, 3, 4, 5], 'pres': [6, -2, -2, -3, -3, -2, -3, 12, 146, 579, 5404, 88, 5189]}, 'GLZN': {'d': 2, 'p': 30, 'gens': [27301, 40966, 219472, 297011, 513019, 32773]}, 'Perm': {'d': 15, 'gens': [93884318665, 3628800, 186810624000, 45363, 45364, 80787]}}, 'schur_multiplier': [3, 3, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2.S_3', 'transitive_degree': 216, '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': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[1, 2, 4, 48, 288], [25, 2, 4, 48, 1440], [1, 26, 4, 240, 1440], [1, 2, 44, 48, 1440], [1, 2, 4, 72, 1440], [1, 2, 20, 240, 312], [13, 14, 4, 240, 288], [1, 2, 4, 1104, 288], [1, 2, 868, 912, 288], [1, 866, 868, 1104, 288], [1, 2, 20, 48, 288], [1, 2, 4, 240, 288], [1, 2, 4, 48, 1440], [17, 2, 4, 48, 288], [1, 98, 4, 48, 288], [1, 2, 4, 624, 288]], 'aut_group': '2916.kq', 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 221184, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 6, 2, 1], [2, 6, 4, 1], [2, 18, 2, 1], [2, 54, 2, 1], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [4, 2, 2, 1], [4, 6, 2, 1], [4, 6, 4, 1], [4, 18, 2, 1], [4, 18, 4, 2], [4, 54, 2, 1], [6, 2, 1, 3], [6, 2, 2, 3], [6, 4, 1, 3], [6, 4, 2, 3], [6, 6, 4, 1], [6, 8, 1, 1], [6, 8, 2, 1], [6, 12, 2, 1], [6, 12, 4, 3], [6, 24, 4, 1], [6, 36, 2, 1], [12, 4, 2, 3], [12, 4, 4, 1], [12, 6, 4, 1], [12, 8, 2, 2], [12, 8, 4, 1], [12, 12, 2, 1], [12, 12, 4, 3], [12, 18, 4, 1], [12, 24, 4, 1], [12, 36, 4, 2]], 'aut_supersolvable': None, 'aut_tex': 'C_3^4:C_6^2', 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 6], [2, 18, 2], [2, 54, 2], [3, 2, 3], [3, 4, 3], [3, 8, 1], [4, 2, 2], [4, 6, 6], [4, 18, 10], [4, 54, 2], [6, 2, 9], [6, 4, 9], [6, 6, 4], [6, 8, 3], [6, 12, 14], [6, 24, 4], [6, 36, 2], [12, 4, 10], [12, 6, 4], [12, 8, 8], [12, 12, 14], [12, 18, 4], [12, 24, 4], [12, 36, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '432.759', 'commutator_count': 1, 'commutator_label': '54.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 47311, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['864.4360', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 6], [2, 18, 1, 2], [2, 54, 1, 2], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [4, 2, 1, 2], [4, 6, 1, 6], [4, 18, 1, 10], [4, 54, 1, 2], [6, 2, 1, 9], [6, 4, 1, 9], [6, 6, 2, 2], [6, 8, 1, 3], [6, 12, 1, 10], [6, 12, 2, 2], [6, 24, 1, 4], [6, 36, 1, 2], [12, 4, 1, 6], [12, 4, 2, 2], [12, 6, 2, 2], [12, 8, 1, 4], [12, 8, 2, 2], [12, 12, 1, 10], [12, 12, 2, 2], [12, 18, 2, 2], [12, 24, 1, 4], [12, 36, 1, 8]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 19998720000, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '864.4704', 'hash': 47311, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 432, 'inner_split': None, 'inner_tex': 'C_2\\times S_3^3', 'inner_used': None, 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 48], [4, 46], [8, 12]], 'label': '1728.47311', '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': True, 'metacyclic': False, 'monomial': True, 'name': 'C12.D6^2', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 58, 'number_characteristic_subgroups': 80, 'number_conjugacy_classes': 138, 'number_divisions': 124, 'number_normal_subgroups': 652, 'number_subgroup_autclasses': 1056, 'number_subgroup_classes': 3714, 'number_subgroups': 24884, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 183], [3, 26], [4, 328], [6, 438], [12, 752]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': True, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '512.519620', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 512, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^6:D_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 48], [4, 26], [8, 14], [16, 4]], 'representations': {'PC': {'code': 6391722000760265967437605425818296741826302978840943125, 'gens': [1, 2, 3, 6, 8], 'pres': [9, 2, 2, 2, 2, 3, 2, 3, 2, 3, 216, 1190, 389, 74, 1443, 102, 1444, 7142, 158, 6063, 2212, 214, 1997]}, 'Perm': {'d': 27, 'gens': [405880137023713854056755920, 886834641045759912182839680, 1306778286713649760857369601, 24, 1617641616052166198181811200, 2083699538098702282317081600, 3991680, 5760, 3]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}.D_6^2', 'transitive_degree': 96, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 0, 'aut_exponent': 84, 'aut_gen_orders': [3, 3], 'aut_gens': [[1, 2, 4], [4, 5, 3], [2, 4, 1]], 'aut_group': '168.42', 'aut_hash': 42, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 168, 'aut_permdeg': 7, 'aut_perms': [4361, 244], 'aut_phi_ratio': 42.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 7, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PSL(2,7)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 84, 'autcent_group': '168.42', 'autcent_hash': 42, 'autcent_nilpotent': False, 'autcent_order': 168, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\PSL(2,7)', '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]], 'center_label': '8.5', 'center_order': 8, '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'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 3]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [3], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '8.5', 'hash': 5, '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, 8]], 'label': '8.5', 'linC_count': 28, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 28, 'linQ_dim': 3, 'linQ_dim_count': 28, 'linR_count': 28, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^3', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 8, 'number_divisions': 8, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 16, 'number_subgroups': 16, 'old_label': None, 'order': 8, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 7]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 84, 'outer_gen_orders': [3, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[4, 5, 3], [2, 4, 1]], 'outer_group': '168.42', 'outer_hash': 42, 'outer_nilpotent': False, 'outer_order': 168, 'outer_permdeg': 7, 'outer_perms': [4361, 244], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\PSL(2,7)', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 6, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8]], 'representations': {'PC': {'code': 0, 'gens': [1, 2, 3], 'pres': [3, -2, 2, 2]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [16482, 16322, 3362]}, 'GLFp': {'d': 3, 'p': 3, 'gens': [8156, 13286, 13933]}, 'Perm': {'d': 6, 'gens': [120, 6, 1]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3', 'transitive_degree': 8, 'wreath_data': None, 'wreath_product': False}
