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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5615', 'ambient_counter': 5615, 'ambient_order': 256, 'ambient_tex': 'C_4^2:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5615.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.486', 'subgroup_hash': 486, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:C_4^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '256.5615', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1024.dly', 'aut_weyl_index': 8, 'centralizer': '32.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.b1', '4.c1.d1', '4.k1.b1', '4.m1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3413, 3806, 3941, 6434, 3393, 4055, 3929, 6422], 'generators': [17, 4, 96], 'label': '256.5615.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.b1', '4.c1.d1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.21', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 4, 4, 4, 4, 4, 4, 4], 'aut_gens': [[1, 4, 8, 32], [1, 4, 24, 112], [15, 68, 88, 112], [125, 4, 24, 112], [9, 68, 88, 52], [57, 68, 72, 36], [65, 68, 88, 116], [117, 68, 24, 100], [113, 4, 88, 112]], 'aut_group': None, 'aut_hash': 208746013969629176, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 2048, 'aut_permdeg': 64, 'aut_perms': [63492976871434181051696087804067356213241161253936229947592826484776390592472264611917316, 50413057944906442574915686287997711473055995374150107274727298757038163182996550761962593, 106724733474247710076962239772688200731586978482417725751346608623997995785289595197585670, 2071433587454328297489706912393742795629056798321766529561982101512724057324497820254713, 11133790402138620685717683182980649637268908148713692842867590378070788896698331978884684, 65419762084395880404748710373788308925520114149516283712391917491967297718237195109209423, 47158429411783218131228174406424781396947923353172497794291648157280150647048025188523942, 8969495724672622674610604314616693582716417094769591542490828675944227501282472028444226], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 2, 4, 1], [2, 4, 2, 1], [4, 1, 4, 1], [4, 2, 2, 1], [4, 2, 4, 1], [4, 4, 2, 3], [4, 4, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^7.C_2^4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.2163', 'autcent_hash': 2163, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4:D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '16.11', 'autcentquo_hash': 11, 'autcentquo_nilpotent': True, 'autcentquo_order': 16, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 6], [2, 4, 2], [4, 1, 4], [4, 2, 6], [4, 4, 22]], 'center_label': '8.2', 'center_order': 8, 'central_product': True, 'central_quotient': '16.3', 'commutator_count': 1, 'commutator_label': '4.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 486, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['32.6', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 6], [2, 4, 1, 2], [4, 1, 2, 2], [4, 2, 2, 3], [4, 4, 1, 2], [4, 4, 2, 10]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 336, 'exponent': 4, 'exponents_of_order': [7], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.14', 'frattini_quotient': '8.5', 'hash': 486, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [4, 2, 1, 2], 'inner_gens': [[1, 68, 8, 36], [65, 4, 8, 32], [1, 4, 8, 32], [5, 4, 8, 32]], 'inner_hash': 3, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': False, 'inner_tex': 'C_2^2:C_4', 'inner_used': [1, 2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8], [4, 4]], 'label': '128.486', 'linC_count': 64, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 16, 'linQ_dim': 6, 'linQ_dim_count': 16, 'linR_count': 16, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^3:C4^2', 'ngens': 3, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 15, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 44, 'number_divisions': 29, 'number_normal_subgroups': 78, 'number_subgroup_autclasses': 104, 'number_subgroup_classes': 206, 'number_subgroups': 436, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 23], [4, 104]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 34, 0, 0, 0], 'outer_gens': [[115, 4, 8, 36], [3, 68, 72, 48], [115, 4, 24, 36], [105, 68, 24, 100], [19, 68, 24, 32], [19, 68, 88, 32], [17, 4, 8, 32]], 'outer_group': '128.2323', 'outer_hash': 2323, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 32, 'outer_perms': [34238660649189118735322178272171640, 105887342053408704013003036836363699, 118666548911636934360532204655795898, 203256754668398284652447079477785039, 117419860533102525379623777975960740, 227839570603080247902482808241188500, 34291711226140809702117515746626484], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4:C_2^4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 12, 'pgroup': 2, 'primary_abelian_invariants': [2, 4, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [4, 4], [8, 1]], 'representations': {'PC': {'code': 5188430517745255593, 'gens': [1, 3, 4, 6], 'pres': [7, 2, 2, 2, 2, 2, 2, 2, 14, 1430, 80, 1517, 2028, 124]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [91655879435939606, 24992892284608672, 125101739154121474]}, 'Perm': {'d': 12, 'gens': [40764970, 81098650, 139725373, 167368440, 23, 207290303, 139725360]}}, 'schur_multiplier': [2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4, 4], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3:C_4^2', 'transitive_degree': 32, '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': '32.21', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [4, 8, 4, 4, 4, 4, 8], 'aut_gens': [[1, 4, 16, 64], [15, 12, 56, 96], [115, 172, 56, 224], [255, 164, 208, 64], [161, 12, 112, 224], [247, 44, 112, 192], [155, 36, 208, 192], [119, 164, 48, 96]], 'aut_group': None, 'aut_hash': 2254421811164287685, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 8192, 'aut_permdeg': 128, 'aut_perms': [21706362463397113285493347222958587670051721849208548250332636788868186885649514504938252222267298092043478114123434481248699261751232304342474694033064821516574766107255377394700932062915587007739449602496457462735, 196913305063933514122477941732366302150850639551251554438345680912707277075142984805361893153972870552582220668235219311908767560045996468585872733776947546473126939062584508624953729789363696754262129103357003574718, 154464777670002928051039283514461239723179044175655260422761079815378204621466531340789923694012494867371305640871056482787803073223837064091303312578772295495194654825481076735173861842611587952756150588019469438140, 97926820828305315442403910411304376621701356944440129216726107869755701776827352232644856957808801752986685091452713461148023512554411802175623895389320272435077407494861555039036796431984490346830091112675375441135, 298686475243549255357751186165398686650757521577291871424975078800127216066829626770963736539161042605415974946252016217082185855081373716786568489036083881356947995932406382847671935696947668144079983517489869204516, 344968591305273020973177120377901132750276396375881330521239077666786942027181983465618882580453219512960738127294793689324364369751391463336436957859419482331934801223116618809289005211468777196979388557727280730436, 115575621596075255398541758014893477943334089710857354605428218314554489075710141570971889142707302527405645982264647332029216421257809861154526521920658248500380027286311473306704494998107839251618953851448766924005], 'aut_phi_ratio': 64.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 4, 4, 1], [4, 2, 4, 1], [4, 4, 1, 2], [4, 4, 2, 1], [4, 4, 4, 1], [4, 8, 2, 4], [4, 8, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2.C_2^6.C_2^6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '128.1755', 'autcentquo_hash': 1755, 'autcentquo_nilpotent': True, 'autcentquo_order': 128, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4:D_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 4, 4], [4, 2, 4], [4, 4, 8], [4, 8, 24]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '64.90', 'commutator_count': 1, 'commutator_label': '8.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 5615, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 4, 1, 4], [4, 2, 2, 2], [4, 4, 1, 2], [4, 4, 2, 3], [4, 8, 1, 4], [4, 8, 2, 10]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 672, 'exponent': 4, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '32.46', 'frattini_quotient': '8.5', 'hash': 5615, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [4, 2, 4, 2], 'inner_gens': [[1, 4, 112, 224], [1, 4, 144, 64], [225, 132, 16, 64], [161, 4, 16, 64]], 'inner_hash': 90, 'inner_nilpotent': True, 'inner_order': 64, 'inner_split': False, 'inner_tex': 'C_2^4:C_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8], [4, 4], [8, 2]], 'label': '256.5615', 'linC_count': 32, 'linC_degree': 9, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 16, 'linQ_dim': 10, 'linQ_dim_count': 8, 'linR_count': 8, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2:C4^2', 'ngens': 3, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 17, 'number_characteristic_subgroups': 29, 'number_conjugacy_classes': 46, 'number_divisions': 31, 'number_normal_subgroups': 81, 'number_subgroup_autclasses': 143, 'number_subgroup_classes': 282, 'number_subgroups': 847, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 23], [4, 232]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [214, 0, 0, 0, 0, 0, 0], 'outer_gens': [[189, 164, 216, 224], [9, 140, 16, 64], [3, 140, 24, 96], [5, 12, 24, 192], [1, 4, 24, 64], [9, 4, 16, 64], [9, 132, 16, 64]], 'outer_group': '128.2216', 'outer_hash': 2216, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 12, 'outer_perms': [259268407, 1498320, 5, 94525320, 41091240, 172046880, 16], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4^2:C_2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 20, 'pgroup': 2, 'primary_abelian_invariants': [2, 4, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [4, 4], [8, 3]], 'representations': {'PC': {'code': 162905529925418077669625633774677, 'gens': [1, 3, 5, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 16, 66, 4484, 3532, 1460, 116, 7685, 12550, 5390, 166]}, 'Perm': {'d': 20, 'gens': [122545679562514209, 244531241770959376, 412957221061076049, 538223386547801520, 16, 621429143522317920, 778026496640818320, 912121982650136880]}}, 'schur_multiplier': [2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4, 4], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2:C_4^2', 'transitive_degree': 64, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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]], 'center_label': '2.1', 'center_order': 2, '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': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', '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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], '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': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}
