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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1992.19', 'ambient_counter': 19, 'ambient_order': 1992, 'ambient_tex': 'S_3\\times C_{332}', 'central': True, 'central_factor': False, 'centralizer_order': 1992, 'characteristic': True, 'core_order': 332, 'counter': 9, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '1992.19.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '332.2', 'subgroup_hash': 2, 'subgroup_order': 332, 'subgroup_tex': 'C_{332}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1992.19', 'aut_centralizer_order': 12, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '164.5', 'aut_weyl_index': 12, 'centralizer': '1.a1.a1', 'complements': ['332.b1.a1', '332.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '498.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7178, 8637, 451, 8172, 9604, 9332, 7642, 9476], 'generators': [498, 24, 996], 'label': '1992.19.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.a1', '498.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '6.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '332.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 82, 'aut_gen_orders': [2, 82], 'aut_gens': [[1], [165], [207]], 'aut_group': '164.5', 'aut_hash': 5, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 164, 'aut_permdeg': 84, 'aut_perms': [240653664262646398824364291566343783056841073003064150375214511720418715778479274250420219239686814127869506093056000000000, 39690023759901851291238314391404848408565128844719606421931883881267721041837538408892844648735826359864255861227520000000000], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [83, 1, 82, 1], [166, 1, 82, 1], [332, 1, 164, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_{82}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 82, 'autcent_group': '164.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 164, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_{82}', '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, 1], [4, 1, 2], [83, 1, 82], [166, 1, 82], [332, 1, 164]], 'center_label': '332.2', 'center_order': 332, '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', '83.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['4.1', 1], ['83.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [83, 1, 82, 1], [166, 1, 82, 1], [332, 1, 164, 1]], 'element_repr_type': 'PC', 'elementary': 166, 'eulerian_function': 1, 'exponent': 332, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 41], 'factors_of_order': [2, 83], 'faithful_reps': [[1, 0, 164]], 'familial': True, 'frattini_label': '2.1', 'frattini_quotient': '166.2', 'hash': 2, 'hyperelementary': 166, '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': 164, 'irrQ_dim': 164, 'irrR_degree': 2, 'irrep_stats': [[1, 332]], 'label': '332.2', 'linC_count': 164, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 84, 'linQ_degree_count': 2, 'linQ_dim': 84, 'linQ_dim_count': 2, 'linR_count': 82, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C332', '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': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 332, 'number_divisions': 6, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 6, 'number_subgroups': 6, 'old_label': None, 'order': 332, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 1], [4, 2], [83, 82], [166, 82], [332, 164]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 82, 'outer_gen_orders': [2, 82], 'outer_gen_pows': [0, 0], 'outer_gens': [[165], [207]], 'outer_group': '164.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 164, 'outer_permdeg': 84, 'outer_perms': [240653664262646398824364291566343783056841073003064150375214511720418715778479274250420219239686814127869506093056000000000, 39690023759901851291238314391404848408565128844719606421931883881267721041837538408892844648735826359864255861227520000000000], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{82}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 87, 'pgroup': 0, 'primary_abelian_invariants': [4, 83], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [82, 2], [164, 1]], 'representations': {'PC': {'code': 7323821225, 'gens': [1], 'pres': [3, -2, -2, -83, 6, 16]}, 'GLFp': {'d': 2, 'p': 167, 'gens': [201068]}, 'Perm': {'d': 87, 'gens': [73244706973894307200686465498775901464814724925949293665326497315665606801546942697270474477608640244751532032000000000000000000000, 38979875363505302337055332973131205624792690113575452946607196594293007568261730186266584808295291703787520000000000000000000, 24230409623807297735032522591020389846572871218715623800325883342752545308873741993653594520624288182324816773120000000000000000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [332], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{332}', 'transitive_degree': 332, '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': '664.8', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 246, 'aut_gen_orders': [2, 2, 2, 246], 'aut_gens': [[1, 2], [997, 2], [1, 1330], [1, 998], [1329, 650]], 'aut_group': '1968.201', 'aut_hash': 201, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1968, 'aut_permdeg': 90, 'aut_perms': [37559651963968831432012439432445104472906923537173135968360467360373319728268396642529167447998859345361387006565961262820912, 17118985614813611913800496531900684025105494222374663833885481785579608082920602096302280509864154128215432096645120000000014, 37559651963968831432012439432445104472906923537173135968360467360373319728268396642529167447998859345361387011567909648689216, 1317434016949714657566144437387675356408774320038397197791795773243381441279426307879867601747582434341387039230660160838196636182634552280], '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], [83, 1, 82, 1], [166, 1, 82, 1], [166, 3, 164, 1], [249, 2, 82, 1], [332, 1, 164, 1], [332, 3, 164, 1], [498, 2, 82, 1], [996, 2, 164, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{246}:C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 82, 'autcent_group': '328.15', 'autcent_hash': 15, 'autcent_nilpotent': True, 'autcent_order': 328, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_{82}', '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], [83, 1, 82], [166, 1, 82], [166, 3, 164], [249, 2, 82], [332, 1, 164], [332, 3, 164], [498, 2, 82], [996, 2, 164]], 'center_label': '332.2', 'center_order': 332, 'central_product': True, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '83.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 19, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['4.1', 1], ['6.1', 1], ['83.1', 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], [83, 1, 82, 1], [166, 1, 82, 1], [166, 3, 82, 2], [249, 2, 82, 1], [332, 1, 164, 1], [332, 3, 164, 1], [498, 2, 82, 1], [996, 2, 164, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 504, 'exponent': 996, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 3, 41], 'factors_of_order': [2, 3, 83], 'faithful_reps': [[2, 0, 164]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '996.8', 'hash': 19, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 1330], [665, 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': 328, 'irrQ_dim': 328, 'irrR_degree': None, 'irrep_stats': [[1, 664], [2, 332]], 'label': '1992.19', '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': True, 'monomial': True, 'name': 'S3*C332', 'ngens': 5, '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': 16, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 996, 'number_divisions': 18, 'number_normal_subgroups': 22, 'number_subgroup_autclasses': 28, 'number_subgroup_classes': 32, 'number_subgroups': 52, 'old_label': None, 'order': 1992, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 8], [6, 2], [12, 4], [83, 82], [166, 574], [249, 164], [332, 656], [498, 164], [996, 328]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 82, 'outer_gen_orders': [2, 2, 82], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[997, 2], [1, 998], [1, 1970]], 'outer_group': '328.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 328, 'outer_permdeg': 47, 'outer_perms': [5502622159812088949850305428800254892961651752960000000000, 2658271574788448768043625811014615890319638528000000000, 1437642729082795807916967057028356205707264000000000], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{82}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 90, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 83], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [4, 1], [82, 4], [164, 4], [328, 1]], 'representations': {'PC': {'code': 263099408383646218608152895012451, 'gens': [1, 2], 'pres': [5, -2, -2, -2, -3, -83, 13301, 26, 10022, 42, 26723, 78]}, 'GLFp': {'d': 2, 'p': 997, 'gens': [686781692594, 339922252082, 995006]}, 'Perm': {'d': 90, 'gens': [120, 9, 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420934400, 16, 840]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 332], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'S_3\\times C_{332}', 'transitive_degree': 996, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 4], [1, 3], [2, 4]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [3, 2, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', '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': 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, 3, 1], [3, 2, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [3, 2, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 3, 'exponent': 6, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '6.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 3], [2, 4]], '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': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 2], [2, 1]], 'label': '6.1', 'linC_count': 1, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'S3', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 3, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 3, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 6, 'old_label': None, 'order': 6, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 3], [3, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 3, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1]], 'representations': {'PC': {'code': 25, 'gens': [1, 2], 'pres': [2, -2, -3, 17]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [28, 45]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'GL'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'SL'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'PSL'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'PGL'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'SO'}, {'d': 2, 'q': 2, 'gens': [20, 69], 'family': 'SU'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'PSO'}, {'d': 2, 'q': 2, 'gens': [20, 69], 'family': 'PSU'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'GO'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'Omega'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'PGO'}, {'d': 2, 'q': 2, 'gens': [20, 138], 'family': 'PGU'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'POmega'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'CSO'}, {'d': 2, 'q': 4, 'gens': [20, 194], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [13, 14], 'family': 'CSOMinus'}, {'d': 2, 'q': 2, 'gens': [20, 69], 'family': 'CSU'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'CO'}, {'d': 2, 'q': 2, 'gens': [13, 14], 'family': 'COMinus'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'PGammaL'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'PSigmaL'}, {'d': 2, 'q': 2, 'gens': [20, 138], 'family': 'PGammaU'}, {'d': 1, 'q': 3, 'gens': [1, 3], 'family': 'AGL'}, {'d': 1, 'q': 3, 'gens': [1, 3], 'family': 'AGammaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11, 6]}, 'Perm': {'d': 3, 'gens': [1, 4]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'S_3', 'transitive_degree': 3, 'wreath_data': None, 'wreath_product': False}
