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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '16384.ji', 'ambient_counter': 243, 'ambient_order': 16384, 'ambient_tex': 'C_2^8.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 4096, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '16384.ji.4.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6530729520262835189, 'subgroup_order': 4096, 'subgroup_tex': 'C_2^6.C_2^5.C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '16384.ji', 'aut_centralizer_order': None, 'aut_label': '4.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '4.M', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [201304147925757762695055, 32649822641266472339535, 845869342738508943, 323820677096353157197813, 954691096569542647634, 47090215146113603582, 311994407647068258916874, 353027640065206021496, 1415680673528071741, 133890265046975328580865, 182441767239810358568120, 182443246543919657534752], 'label': '16384.ji.4.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.M', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.M', 'subgroup_fusion': None, 'weyl_group': '2688.cb'}
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label None does not appear in gps_groups
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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': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[134155209864517598069833, 20636876911559975149448, 384657530991126059556, 183042200708284190200130, 201304147925757762695055, 264590996380976690940696, 311993364060125006353996, 323820677096353157197813, 33101029104532181582, 47090215146113603582, 311994407647068258916874, 353027640065206021496, 499460789914068168726136, 182441767239810358568120], [289907253441132926575868, 20636876911559975149448, 1036778075756967100072, 630481299985556970923, 201304147925757762695055, 270802348522645370296076, 331398935325149847076323, 472189473048422615612437, 194571726874309586624528, 20594774503926809879280, 195392287463929738757667, 353027640065206021496, 20287320450245090697005, 20636358675085577428336], [462816616736949567816163, 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480057143150868691903205, 317374346841700313755052], [270802348522645370296076, 317373584938140324519542, 26890248362720468575502, 955856707863374869776, 201304147925757762695055, 612550276425272552727353, 14133174274709378623204, 323820677096353157197813, 13864095318122105530933, 182401643563304147316919, 311993364060125006353996, 201601083968149947396856, 317373847435519735609594, 317374346841700313755052], [128934175661965260606045, 182441767239810358568120, 21040218258094674343805, 183042905682151517796461, 201304147925757762695055, 457146382231797743041893, 14133174274709378623204, 323820677096353157197813, 324140968640112839666771, 201345021035731059396856, 14134217861652631186082, 353027640065206021496, 174624979881047609504912, 20636876911559975149448], [400892538596774962271227, 182441767239810358568120, 201634566258188197014012, 201880784126229208997280, 201304147925757762695055, 307651011729353423476747, 6557080735981745700988, 472189473048422615612437, 5687804843161038213642, 182399786163342384791064, 467399819937031420354636, 353027640065206021496, 20287896308173451436135, 182441370292743157275208], [134500681942174595379307, 20636876911559975149448, 384657530991126059556, 954057262988691678677, 201304147925757762695055, 264885377874684802624315, 311993364060125006353996, 323820677096353157197813, 311432458493017298868572, 480098976973798064585828, 14133174274709378623204, 201601083968149947396856, 182441395546527600331678, 20636358675085577428336], [599890539181841666527389, 20636876911559975149448, 182845234166331672999941, 21189357690260235208445, 201304147925757762695055, 406566230431157718853989, 311993364060125006353996, 323820677096353157197813, 324140968640112839666771, 201561548954225104861449, 311994407647068258916874, 353027640065206021496, 174328031367364497816966, 182441767239810358568120], [612550276425272552727353, 20636876911559975149448, 20336756329373407087934, 183042200708284190200130, 201304147925757762695055, 270802348522645370296076, 311993364060125006353996, 323820677096353157197813, 472455869390799020328960, 324130392295734816561157, 311994407647068258916874, 201601083968149947396856, 174624576552535236802624, 182441767239810358568120], [548672327583409300549908, 480405554653178546287268, 167636603309621833253519, 201881937266226278769367, 201304147925757762695055, 618359051872214891184237, 6557080735981745700988, 472189473048422615612437, 466528680219819615180512, 20331580082450832094820, 467399819937031420354636, 201601083968149947396856, 317372701410579476364694, 480404914039025753479958], [140122387192439337681141, 480404914039025753479958, 499864685442488756661125, 317601272547039165907706, 201304147925757762695055, 556056216489877423133227, 195392806413256357434531, 472189473048422615612437, 472473700065550327060175, 472446118575820032157440, 195392287463929738757667, 201601083968149947396856, 499165531649301181096453, 317373584938140324519542]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 16777216, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 2048.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 1, 6], [2, 2, 4, 1], [2, 4, 1, 2], [2, 4, 2, 4], [2, 4, 4, 1], [2, 4, 8, 1], [2, 8, 1, 2], [2, 8, 2, 3], [2, 8, 4, 4], [2, 8, 8, 1], [2, 8, 32, 1], [2, 16, 1, 5], [2, 16, 2, 3], [2, 16, 4, 3], [2, 16, 16, 1], [2, 32, 1, 1], [2, 32, 2, 3], [2, 32, 8, 1], [2, 64, 1, 3], [4, 8, 4, 1], [4, 16, 1, 2], [4, 16, 2, 1], [4, 16, 4, 2], [4, 16, 16, 1], [4, 32, 1, 3], [4, 32, 2, 6], [4, 32, 4, 5], [4, 32, 8, 2], [4, 64, 1, 5], [4, 64, 2, 8], [4, 64, 4, 3], [4, 128, 1, 2], [4, 128, 2, 6], [4, 128, 8, 3], [4, 256, 1, 5], [4, 256, 4, 1], [8, 128, 2, 1], [8, 256, 1, 3], [8, 256, 4, 1], [8, 512, 2, 1]], 'aut_supersolvable': None, 'aut_tex': None, '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, 2, 10], [2, 4, 22], [2, 8, 64], [2, 16, 39], [2, 32, 15], [2, 64, 3], [4, 8, 4], [4, 16, 28], [4, 32, 51], [4, 64, 33], [4, 128, 38], [4, 256, 9], [8, 128, 2], [8, 256, 7], [8, 512, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '512.7540510', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 14, 'conjugacy_classes_known': True, 'counter': 243, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 10], [2, 4, 1, 22], [2, 8, 1, 64], [2, 16, 1, 39], [2, 32, 1, 15], [2, 64, 1, 3], [4, 8, 1, 4], [4, 16, 1, 28], [4, 32, 1, 51], [4, 64, 1, 33], [4, 128, 1, 38], [4, 256, 1, 9], [8, 128, 1, 2], [8, 256, 1, 7], [8, 512, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 2, 'eulerian_function': None, 'exponent': 8, 'exponents_of_order': [14], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '512.7540510', 'frattini_quotient': '32.51', 'hash': 3568873400067866534, 'hyperelementary': 2, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2], 'inner_gens': [[134155209864517598069833, 20636876911559975149448, 384657530991126059556, 630481299985556970923, 201304147925757762695055, 128588710320038817538499, 311993364060125006353996, 323820677096353157197813, 14106226641129112182000, 20594774503926809879280, 14133174274709378623204, 353027640065206021496, 182443246543919657534752, 20636358675085577428336], [134155209864517598069833, 20636876911559975149448, 384657530991126059556, 183042200708284190200130, 201304147925757762695055, 128588710320038817538499, 311993364060125006353996, 323820677096353157197813, 33101029104532181582, 47090215146113603582, 311994407647068258916874, 353027640065206021496, 26205151336536352706224, 182441767239810358568120], [134155209864517598069833, 20636876911559975149448, 384657530991126059556, 183042200708284190200130, 201304147925757762695055, 264590996380976690940696, 467399819937031420354636, 472189473048422615612437, 924151396542354098208, 309721983695914418208, 467401497381193429991592, 353027640065206021496, 499460789914068168726136, 182441767239810358568120], [599890539181841666527389, 20636876911559975149448, 384657530991126059556, 183042200708284190200130, 201304147925757762695055, 108648540503408023776475, 311993364060125006353996, 323820677096353157197813, 33101029104532181582, 47090215146113603582, 311994407647068258916874, 353027640065206021496, 26205151336536352706224, 182441767239810358568120], [134155209864517598069833, 20636876911559975149448, 384657530991126059556, 183042200708284190200130, 201304147925757762695055, 264590996380976690940696, 311993364060125006353996, 323820677096353157197813, 33101029104532181582, 47090215146113603582, 311994407647068258916874, 353027640065206021496, 499460789914068168726136, 182441767239810358568120], [606342120158577192142977, 182441370292743157275208, 384657530991126059556, 630993488558925817152, 201304147925757762695055, 264590996380976690940696, 14134217861652631186082, 323820677096353157197813, 311966415757015608648984, 182399786163342384791064, 311994407647068258916874, 353027640065206021496, 20636383907934254007262, 182441767239810358568120], [134155209864517598069833, 20636876911559975149448, 182845234166331672999941, 183042200708284190200130, 201304147925757762695055, 562506004090511960639359, 311993364060125006353996, 323820677096353157197813, 33101029104532181582, 47090215146113603582, 311994407647068258916874, 353027640065206021496, 174624576552535236802624, 182441767239810358568120], [134155209864517598069833, 20636876911559975149448, 201635143184496578953223, 183042200708284190200130, 201304147925757762695055, 264590996380976690940696, 311993364060125006353996, 323820677096353157197813, 33101029104532181582, 47090215146113603582, 311994407647068258916874, 353027640065206021496, 499460789914068168726136, 182441767239810358568120], [146036283964820042887792, 20636876911559975149448, 1037289909862010227976, 183042200708284190200130, 201304147925757762695055, 549553160116039539794028, 311993364060125006353996, 323820677096353157197813, 33101029104532181582, 47090215146113603582, 311994407647068258916874, 353027640065206021496, 499460789914068168726136, 182441767239810358568120], [140122387192439337681141, 20636876911559975149448, 756891888960942968594, 183042200708284190200130, 201304147925757762695055, 108648540503408023776475, 311993364060125006353996, 323820677096353157197813, 33101029104532181582, 47090215146113603582, 311994407647068258916874, 353027640065206021496, 499460789914068168726136, 182441767239810358568120], [456847006861485540650140, 20636876911559975149448, 182845752402903387679730, 183042200708284190200130, 201304147925757762695055, 264590996380976690940696, 311993364060125006353996, 323820677096353157197813, 33101029104532181582, 47090215146113603582, 311994407647068258916874, 353027640065206021496, 174624576552535236802624, 182441767239810358568120], [134155209864517598069833, 20636876911559975149448, 384657530991126059556, 183042200708284190200130, 201304147925757762695055, 264590996380976690940696, 311993364060125006353996, 323820677096353157197813, 33101029104532181582, 47090215146113603582, 311994407647068258916874, 353027640065206021496, 499460789914068168726136, 182441767239810358568120], [264590996380976690940696, 182441767239810358568120, 384657530991126059556, 21188531385141016833722, 201304147925757762695055, 134155209864517598069833, 14133174274709378623204, 323820677096353157197813, 33101029104532181582, 47090215146113603582, 14134217861652631186082, 353027640065206021496, 499460789914068168726136, 20636876911559975149448], [606342120158577192142977, 20636876911559975149448, 384657530991126059556, 183042200708284190200130, 201304147925757762695055, 264590996380976690940696, 311993364060125006353996, 323820677096353157197813, 33101029104532181582, 47090215146113603582, 311994407647068258916874, 353027640065206021496, 26205151336536352706224, 182441767239810358568120]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 4096, 'inner_split': None, 'inner_tex': None, 'inner_used': None, 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': None, 'irrep_stats': [[1, 32], [2, 56], [4, 96], [8, 120], [16, 27]], 'label': '16384.ji', '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': False, 'metacyclic': False, 'monomial': True, 'name': 'C2^8.D4^2', 'ngens': 14, 'nilpotency_class': 5, 'nilpotent': True, 'normal_counts': [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': 111, 'number_characteristic_subgroups': 437, 'number_conjugacy_classes': 331, 'number_divisions': 331, 'number_normal_subgroups': 1169, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 16384, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 1919], [4, 11392], [8, 3072]], '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': '1024.yp', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 4096, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^2.C_4^4', 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': True, 'rational_characters_known': False, 'ratrep_stats': [[1, 32], [2, 56], [4, 96], [8, 120], [16, 27]], 'representations': {'PC': {'code': '5515989096736372861960663801038985171831804243583988149218985023417373844011111559007516447315302187928461474147802520528631733235783200474459090326029601419533199320930208963940283581590140056569308132018495025029970', 'gens': [1, 2, 4, 5, 7, 9, 10, 12, 13, 14], 'pres': [14, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 169, 71, 509379, 254705, 771684, 319778, 38392, 466, 200, 185477, 92755, 219526, 109780, 83558, 664, 286, 129031, 64533, 94143, 282262, 298404, 215762, 67600, 53502, 10676, 4152, 215049, 403223, 340517, 244211, 67265, 60559, 12413, 5441, 415, 88770, 516107, 258073, 161347, 8159, 6843, 3497, 2236428, 1118234, 139844]}, 'Perm': {'d': 24, 'gens': [134155209864517598069833, 20636876911559975149448, 384657530991126059556, 183042200708284190200130, 201304147925757762695055, 264590996380976690940696, 311993364060125006353996, 323820677096353157197813, 33101029104532181582, 47090215146113603582, 311994407647068258916874, 353027640065206021496, 499460789914068168726136, 182441767239810358568120]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 5, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 4, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^8.D_4^2', 'transitive_degree': None, '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': '4.2', '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, 2], [3, 2], [2, 3]], '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, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_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, 3]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
