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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 90, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.6.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.d1', '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '90.10', 'subgroup_hash': 10, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '540.76', 'aut_centralizer_order': 90, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 360, 'centralizer': '6.a1.d1', 'complements': ['90.d1.e1', '90.d1.g1', '90.d1.f1', '90.d1.a1', '90.d1.c1', '90.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.d1'], 'contains': ['12.a1.d1', '18.a1.a1', '18.b1.d1', '30.a1.d1'], 'core': '6.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [3642, 3307, 6612, 3998, 4383, 8670, 8431, 5831], 'generators': [270, 6, 108, 2], 'label': '540.76.6.a1.d1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.d1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.d1', '18.a1.a1', '30.a1.d1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.d1', 'projective_image': '90.9', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '90.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 12, 4, 4], 'aut_gens': [[1, 3], [2, 3], [1, 23], [61, 35], [30, 65]], 'aut_group': '192.951', 'aut_hash': 951, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 192, 'aut_permdeg': 12, 'aut_perms': [39928327, 262085177, 176163120, 127024560], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 8, 1], [5, 1, 4, 1], [6, 1, 8, 1], [10, 1, 4, 1], [15, 1, 32, 1], [30, 1, 32, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4\\times \\GL(2,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '192.951', 'autcent_hash': 951, 'autcent_nilpotent': False, 'autcent_order': 192, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_4\\times \\GL(2,3)', '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, 1], [3, 1, 8], [5, 1, 4], [6, 1, 8], [10, 1, 4], [15, 1, 32], [30, 1, 32]], 'center_label': '90.10', 'center_order': 90, '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', '3.1', '3.1', '5.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 10, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 2], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 4], [5, 1, 4, 1], [6, 1, 2, 4], [10, 1, 4, 1], [15, 1, 8, 4], [30, 1, 8, 4]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 18, 'exponent': 30, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '90.10', 'hash': 10, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 3], [1, 3]], '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, 90]], 'label': '90.10', 'linC_count': 1728, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 42, 'linQ_dim': 8, 'linQ_dim_count': 42, 'linR_count': 432, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3*C30', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, '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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 90, 'number_divisions': 20, 'number_normal_subgroups': 24, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 24, 'number_subgroups': 24, 'old_label': None, 'order': 90, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 1], [3, 8], [5, 4], [6, 8], [10, 4], [15, 32], [30, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [2, 12, 4, 4], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[2, 3], [1, 23], [61, 35], [30, 65]], 'outer_group': '192.951', 'outer_hash': 951, 'outer_nilpotent': False, 'outer_order': 192, 'outer_permdeg': 12, 'outer_perms': [39928327, 262085177, 176163120, 127024560], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_4\\times \\GL(2,3)', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 3, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 8], [4, 2], [8, 8]], 'representations': {'PC': {'code': 12453447, 'gens': [1, 2], 'pres': [4, -3, -2, -3, -5, 21, 46]}, 'GLFp': {'d': 2, 'p': 31, 'gens': [148980, 208564]}, 'Perm': {'d': 13, 'gens': [479001600, 7257600, 10080, 96]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 30], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times C_{30}', 'transitive_degree': 90, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 120, 'aut_gen_orders': [2, 6, 2, 4, 6, 6, 5], 'aut_gens': [[1, 2, 6, 18], [1, 2, 12, 522], [193, 8, 6, 342], [271, 2, 6, 342], [1, 2, 6, 234], [5, 2, 6, 348], [1, 366, 6, 524], [109, 2, 6, 18]], 'aut_group': '17280.fp', 'aut_hash': 7336759155281172877, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 17280, 'aut_permdeg': 90, 'aut_perms': [13357779239927666839809778456543992889412518401823662532893362271125824152719785631360555617509030751232945427097292785657760765676608309, 978613680725323270384434294457193026921394144055421984018444271912762099360789422859598132352700472478959216594635672207122762056079380869, 279004299646206441845458296556284371251574540062133696495377982428251485111916975396247019002808891086425910916239835508541725453593359823, 16139122172685439329720083305288619421418590216798701673118038559552406498722208608113309694749490966560804142448254012500870040737823139, 75863757752509316609258673884453135207185806119270676776384000385981663829215367589309020766472407799566776833970477494832762008179991989, 13702594761328959788500468831365115559273828929113376101760182677903942625737987505725434495002562825267124380807410410050676090151522869, 98130979101455530525240081550282725754448652195002864852508550686779444130136165331085921397085458917280086494666833177277615687252260217], 'aut_phi_ratio': 120.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 45, 2, 1], [3, 1, 2, 1], [3, 6, 4, 1], [5, 2, 2, 1], [6, 1, 2, 1], [6, 6, 4, 1], [6, 45, 4, 1], [10, 2, 2, 1], [15, 2, 4, 1], [15, 6, 16, 1], [30, 2, 4, 1], [30, 6, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{30}:C_{12}:\\GL(2,3)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 120, 'autcentquo_group': '8640.be', 'autcentquo_hash': 9203803121985669655, 'autcentquo_nilpotent': False, 'autcentquo_order': 8640, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\times C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 45, 2], [3, 1, 2], [3, 6, 4], [5, 2, 2], [6, 1, 2], [6, 6, 4], [6, 45, 4], [10, 2, 2], [15, 2, 4], [15, 6, 16], [30, 2, 4], [30, 6, 16]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '90.9', 'commutator_count': 2, 'commutator_label': '135.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 76, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['270.19', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 45, 1, 2], [3, 1, 2, 1], [3, 6, 1, 4], [5, 2, 2, 1], [6, 1, 2, 1], [6, 6, 1, 4], [6, 45, 2, 2], [10, 2, 2, 1], [15, 2, 4, 1], [15, 6, 4, 4], [30, 2, 4, 1], [30, 6, 4, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3402, 'exponent': 30, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[6, 0, 4]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '180.36', 'hash': 76, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 3, 1, 15], 'inner_gens': [[1, 4, 6, 534], [5, 2, 6, 24], [1, 2, 6, 18], [43, 14, 6, 18]], 'inner_hash': 9, 'inner_nilpotent': False, 'inner_order': 90, 'inner_split': False, 'inner_tex': 'C_3:D_{15}', 'inner_used': [1, 2, 4], 'irrC_degree': 6, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 12, 'irrep_stats': [[1, 4], [2, 44], [3, 8], [6, 8]], 'label': '540.76', 'linC_count': 216, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 6, 'linQ_dim': 10, 'linQ_dim_count': 6, 'linR_count': 108, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^2:D30', '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, 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': 13, 'number_conjugacy_classes': 64, 'number_divisions': 28, 'number_normal_subgroups': 31, 'number_subgroup_autclasses': 40, 'number_subgroup_classes': 110, 'number_subgroups': 850, 'old_label': None, 'order': 540, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 91], [3, 26], [5, 4], [6, 206], [10, 4], [15, 104], [30, 104]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [2, 6, 4, 2, 4], 'outer_gen_pows': [0, 0, 0, 1, 0], 'outer_gens': [[1, 4, 12, 20], [271, 192, 6, 208], [1, 364, 6, 28], [1, 188, 6, 416], [1, 192, 6, 388]], 'outer_group': '192.1480', 'outer_hash': 1480, 'outer_nilpotent': False, 'outer_order': 192, 'outer_permdeg': 18, 'outer_perms': [11913376991400, 1166514173052841, 2297134228929240, 4764534621827160, 2657282294944104], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '\\GL(2,3):C_2^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 2], [6, 4], [8, 8], [24, 2]], 'representations': {'PC': {'code': 3453579399119156924909981761863, 'gens': [1, 2, 3, 4], 'pres': [6, 2, 3, 3, 2, 3, 5, 49, 12819, 297, 69, 15304, 730, 118, 15557]}, 'Perm': {'d': 16, 'gens': [287411886847, 1, 1601792277120, 2815618619520, 966, 4292504254080]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:D_{30}', 'transitive_degree': 90, '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}
