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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.1242', 'ambient_counter': 1242, 'ambient_order': 1344, 'ambient_tex': 'C_2^2.(D_4\\times F_7)', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': True, 'core_order': 7, 'counter': 286, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '1344.1242.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.891', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 891, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_2^3.D_4', 'simple': True, 'solvable': True, 'special_labels': ['L3', 'C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
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gps_subgroup_data • Show schema
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{'ambient': '1344.1242', 'aut_centralizer_order': 896, 'aut_label': '192.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 896, 'centralizer': '6.b1.a1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.b1.b1', '96.c1.a1', '96.d1.a1', '96.e1.a1', '96.e1.b1'], 'contains': ['1344.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1002, 2945, 1682, 7823, 2865, 4129, 3466, 4066], 'generators': [192], 'label': '1344.1242.192.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['64.a1.a1', '96.a1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '1344.1242', 'quotient_action_image': '6.2', 'quotient_action_kernel': '32.30', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '7.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 6, 'aut_gen_orders': [6], 'aut_gens': [[1], [3]], 'aut_group': '6.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 6, 'aut_permdeg': 5, 'aut_perms': [27], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [7, 1, 6, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_6', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 6, 'autcent_group': '6.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_6', '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], [7, 1, 6]], 'center_label': '7.1', 'center_order': 7, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['7.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [7, 1, 6, 1]], 'element_repr_type': 'PC', 'elementary': 7, 'eulerian_function': 1, 'exponent': 7, 'exponents_of_order': [1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [7], 'faithful_reps': [[1, 0, 6]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '7.1', 'hash': 1, 'hyperelementary': 7, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 6, 'irrQ_dim': 6, 'irrR_degree': 2, 'irrep_stats': [[1, 7]], 'label': '7.1', 'linC_count': 6, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 1, 'linQ_dim': 6, 'linQ_dim_count': 1, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C7', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 7, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 7, 'order_factorization_type': 1, 'order_stats': [[1, 1], [7, 6]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6], 'outer_gen_pows': [0], 'outer_gens': [[3]], 'outer_group': '6.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 6, 'outer_permdeg': 5, 'outer_perms': [27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 7, 'pgroup': 7, 'primary_abelian_invariants': [7], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [6, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -7]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [74473229056828135]}, 'Lie': [{'d': 1, 'q': 7, 'gens': [873], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 7, 'gens': [351]}, 'Perm': {'d': 7, 'gens': [4320]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [7], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_7', 'transitive_degree': 7, '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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [6, 14, 4, 4, 2, 2], 'aut_gens': [[1, 2, 4, 48], [1, 2, 4, 240], [579, 2, 388, 744], [3, 2, 6, 722], [349, 698, 4, 48], [1, 2, 28, 72], [1, 26, 676, 720]], 'aut_group': '5376.db', 'aut_hash': 1775239541180599517, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5376, 'aut_permdeg': 64, 'aut_perms': [698118874010435020407788863756899447641779612470886154247950249777546928257838653, 414643143414938982412664555731743672811322066008563897414880013092382054165281544376, 1986102288367133559168647856974177505678854246134011520249479126651350889421570344847320, 1794465579488923802243331487872787935421581540348660181670356310789918929120103503165440, 4185514905693626227367405939525664125527391177024407216447337062084386102554258800634880, 85090332556846972479083097615343527514256057230769746580470244024375985475393442552319360], 'aut_phi_ratio': 14.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 2, 2, 1], [2, 4, 1, 1], [2, 28, 2, 1], [3, 7, 1, 2], [4, 4, 1, 1], [4, 4, 2, 1], [4, 8, 1, 1], [4, 28, 2, 1], [4, 56, 2, 1], [6, 7, 1, 2], [6, 14, 1, 2], [6, 14, 2, 2], [6, 28, 1, 2], [6, 28, 2, 2], [7, 6, 1, 1], [12, 28, 1, 2], [12, 28, 2, 4], [12, 56, 1, 2], [12, 56, 2, 2], [14, 6, 1, 1], [14, 6, 2, 1], [14, 12, 2, 1], [14, 24, 1, 1], [28, 12, 4, 1], [28, 24, 1, 1], [28, 24, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^4:D_4\\times F_7', '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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 84, 'autcentquo_group': '672.1093', 'autcentquo_hash': 1093, 'autcentquo_nilpotent': False, 'autcentquo_order': 672, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_4\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 3], [2, 4, 1], [2, 28, 2], [3, 7, 2], [4, 4, 3], [4, 8, 1], [4, 28, 2], [4, 56, 2], [6, 7, 2], [6, 14, 6], [6, 28, 6], [7, 6, 1], [12, 28, 10], [12, 56, 6], [14, 6, 3], [14, 12, 2], [14, 24, 1], [28, 12, 4], [28, 24, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '672.355', 'commutator_count': 1, 'commutator_label': '56.13', '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', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 1242, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [2, 4, 1, 1], [2, 28, 1, 2], [3, 7, 2, 1], [4, 4, 1, 1], [4, 4, 2, 1], [4, 8, 1, 1], [4, 28, 1, 2], [4, 56, 1, 2], [6, 7, 2, 1], [6, 14, 2, 3], [6, 28, 2, 3], [7, 6, 1, 1], [12, 28, 2, 3], [12, 28, 4, 1], [12, 56, 2, 3], [14, 6, 1, 1], [14, 6, 2, 1], [14, 12, 1, 2], [14, 24, 1, 1], [28, 12, 4, 1], [28, 24, 1, 1], [28, 24, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 139776, 'exponent': 84, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[12, 0, 4]], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '168.47', 'hash': 1242, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 2, 6, 28], 'inner_gens': [[1, 2, 6, 626], [1, 2, 4, 72], [3, 2, 4, 1104], [795, 26, 292, 48]], 'inner_hash': 355, 'inner_nilpotent': False, 'inner_order': 672, 'inner_split': True, 'inner_tex': '(D_4\\times C_{14}):C_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 12, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 24, 'irrep_stats': [[1, 24], [2, 18], [4, 6], [6, 8], [12, 6]], 'label': '1344.1242', 'linC_count': 48, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 4, 'linQ_dim': 14, 'linQ_dim_count': 4, 'linR_count': 12, 'linR_degree': 14, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2.(D4*F7)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 41, 'number_characteristic_subgroups': 36, 'number_conjugacy_classes': 62, 'number_divisions': 39, 'number_normal_subgroups': 66, 'number_subgroup_autclasses': 224, 'number_subgroup_classes': 320, 'number_subgroups': 2228, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 67], [3, 14], [4, 188], [6, 266], [7, 6], [12, 616], [14, 66], [28, 120]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [672, 0, 0], 'outer_gens': [[349, 698, 4, 48], [1, 2, 6, 50], [1, 2, 28, 48]], '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': 4, 'perfect': False, 'permutation_degree': 23, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 14], [4, 6], [6, 4], [8, 1], [12, 4], [16, 1], [48, 1]], 'representations': {'PC': {'code': '8817358988742550178008482679262375920435930044882036938886228803644637', 'gens': [1, 2, 3, 6], 'pres': [8, 2, 2, 2, 2, 3, 2, 2, 7, 146, 66, 91, 30053, 1741, 13269, 7229, 1333, 141, 71238, 12118, 7422, 3062, 166, 73735, 6167, 6175, 1575]}, 'Perm': {'d': 23, 'gens': [1139233440728548126207, 982102981412085120, 2460433413401951460480, 304, 258018158542188844800, 3695624892109688469120, 4771896497056136448000, 978]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2.(D_4\\times F_7)', 'transitive_degree': 112, '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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 3, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4, 16], [101, 106, 12, 16], [1, 2, 4, 80], [1, 2, 4, 24], [11, 2, 100, 184], [15, 106, 99, 21], [1, 10, 4, 114], [9, 10, 4, 112], [9, 2, 12, 24], [9, 2, 4, 16]], 'aut_group': '768.1089108', 'aut_hash': 1089108, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 768, 'aut_permdeg': 12, 'aut_perms': [207381007, 16, 7, 212340383, 141568680, 178981920, 94434600, 135359400, 182610840], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 3, 1], [2, 4, 3, 1], [3, 1, 2, 1], [4, 4, 2, 1], [4, 4, 3, 1], [4, 8, 3, 1], [6, 1, 2, 1], [6, 2, 6, 1], [6, 4, 6, 1], [12, 4, 4, 1], [12, 4, 6, 1], [12, 8, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^5:S_4', '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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '48.48', 'autcentquo_hash': 48, 'autcentquo_nilpotent': False, 'autcentquo_order': 48, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 3], [2, 4, 3], [3, 1, 2], [4, 4, 5], [4, 8, 3], [6, 1, 2], [6, 2, 6], [6, 4, 6], [12, 4, 10], [12, 8, 6]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '32.27', 'commutator_count': 1, 'commutator_label': '8.5', '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'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 891, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['64.139', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [2, 4, 1, 3], [3, 1, 2, 1], [4, 4, 1, 3], [4, 4, 2, 1], [4, 8, 1, 3], [6, 1, 2, 1], [6, 2, 2, 3], [6, 4, 2, 3], [12, 4, 2, 3], [12, 4, 4, 1], [12, 8, 2, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 2912, 'exponent': 12, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, 0, 4]], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '24.15', 'hash': 891, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 2, 4], 'inner_gens': [[1, 2, 4, 26], [1, 2, 12, 24], [1, 10, 4, 112], [3, 10, 100, 16]], 'inner_hash': 27, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': True, 'inner_tex': 'C_2^2\\wr C_2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 24], [2, 18], [4, 6]], 'label': '192.891', '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': 'C3*C2^3.D4', 'ngens': 7, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [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': 14, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 48, 'number_divisions': 30, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 66, 'number_subgroup_classes': 160, 'number_subgroups': 322, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 19], [3, 2], [4, 44], [6, 38], [12, 88]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 96, 0], 'outer_gens': [[1, 2, 12, 16], [101, 106, 4, 16], [101, 106, 105, 181]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [16, 127, 847], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 14], [4, 6], [8, 1], [16, 1]], 'representations': {'PC': {'code': 671362084075287509438503425, 'gens': [1, 2, 3, 5], 'pres': [7, 2, 2, 2, 2, 2, 2, 3, 135, 58, 914, 431, 998, 102, 1685, 124]}, 'Perm': {'d': 19, 'gens': [81385447377367440, 54243084178483200, 27121166408468160, 4, 13516396743550584, 13516309089926904, 6423384156578664]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times C_2^3.D_4', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
