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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.16406', 'ambient_counter': 16406, 'ambient_order': 384, 'ambient_tex': '(C_2\\times C_{24}):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 96, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.16406.4.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1', '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.179', 'subgroup_hash': 179, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times D_8', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '384.16406', 'aut_centralizer_order': None, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '2.f1'], 'contains': ['8.c1', '8.h1', '8.z1', '12.d1'], 'core': '4.k1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 192, 96, 4, 168, 16], 'label': '384.16406.4.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': ['2.c1', '2.f1'], 'normal_contains': ['8.c1', '8.h1', '12.d1'], 'normalizer': '1.a1', 'old_label': '4.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1', 'subgroup_fusion': None, 'weyl_group': None}
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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': 8, 'aut_gen_orders': [2, 2, 2, 2, 2, 4, 4, 2, 2], 'aut_gens': [[1, 2, 4], [49, 39, 44], [1, 74, 29], [49, 74, 76], [49, 50, 52], [1, 50, 68], [1, 75, 52], [1, 26, 4], [1, 2, 52], [1, 50, 4]], 'aut_group': '512.6344767', 'aut_hash': 1379696506294818456, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 512, 'aut_permdeg': 18, 'aut_perms': [3983334399490495, 4860204239979486, 2074202046980815, 1702247685000024, 1, 1710903284472960, 2335871571282246, 1802112561054720, 1908121357121040], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 4, 4, 1], [3, 1, 2, 1], [4, 2, 1, 2], [6, 1, 2, 1], [6, 1, 4, 1], [6, 4, 8, 1], [8, 2, 4, 1], [12, 2, 2, 2], [24, 2, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^3.D_4^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '64.202', 'autcent_hash': 202, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3:D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '8.3', 'autcentquo_hash': 3, 'autcentquo_nilpotent': True, 'autcentquo_order': 8, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 4], [3, 1, 2], [4, 2, 2], [6, 1, 6], [6, 4, 8], [8, 2, 4], [12, 2, 4], [24, 2, 8]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '8.3', 'commutator_count': 1, 'commutator_label': '4.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 179, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['16.7', 1], ['2.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 4], [3, 1, 2, 1], [4, 2, 1, 2], [6, 1, 2, 3], [6, 4, 2, 4], [8, 2, 2, 2], [12, 2, 2, 2], [24, 2, 4, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 546, 'exponent': 24, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '24.15', 'hash': 179, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [1, 2, 4], 'inner_gens': [[1, 2, 4], [1, 2, 28], [1, 74, 4]], 'inner_hash': 3, 'inner_nilpotent': True, 'inner_order': 8, 'inner_split': False, 'inner_tex': 'D_4', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 18]], 'label': '96.179', 'linC_count': 128, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 8, 'linQ_dim': 6, 'linQ_dim_count': 8, 'linR_count': 16, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6*D8', 'ngens': 6, 'nilpotency_class': 3, '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': 14, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 42, 'number_divisions': 24, 'number_normal_subgroups': 44, 'number_subgroup_autclasses': 36, 'number_subgroup_classes': 76, 'number_subgroups': 140, 'old_label': None, 'order': 96, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 19], [3, 2], [4, 4], [6, 38], [8, 8], [12, 8], [24, 16]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [4, 4, 0, 0, 8], 'outer_gens': [[49, 62, 20], [1, 62, 52], [1, 2, 20], [1, 3, 52], [1, 14, 69]], 'outer_group': '64.202', 'outer_hash': 202, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [362894, 5, 368056, 367936, 1174329], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 4], [8, 2]], 'representations': {'PC': {'code': 23334473970157313, 'gens': [1, 2, 3], 'pres': [6, -2, -2, -2, -2, -2, -3, 260, 50, 681, 69, 88]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125101739150932828, 24992906222183252, 41624325029299721]}, 'GLFp': {'d': 3, 'p': 7, 'gens': [34649835, 11532102, 34603218, 34591355, 28940755, 34649828]}, 'Perm': {'d': 13, 'gens': [135001464, 498360984, 24, 4, 1086190560, 1611308160]}}, '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_6\\times D_8', 'transitive_degree': 48, '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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 24, 'aut_gen_orders': [2, 12, 12, 4, 24, 12, 2, 4], 'aut_gens': [[1, 2, 8, 48], [289, 230, 236, 340], [365, 110, 12, 336], [101, 130, 12, 240], [317, 14, 232, 148], [73, 238, 12, 244], [337, 306, 12, 336], [1, 34, 44, 52], [125, 218, 232, 52]], 'aut_group': None, 'aut_hash': 77725528710035942, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 49152, 'aut_permdeg': 80, 'aut_perms': [7228649626228252595978354100838650080340608089294001547149308580151069471886821708895796710070969705543445866610167783, 31696087746866848694205778793617254414056271253430245403326641621081418094385270245487689963366178130072256468180247833, 14553560730745893329665336942423794467840118023167424854582642762719795476510013946979042711003833579448246361259137216, 67925646864824270572580453058904072757255207388211202774604965923910197453956766061667094077432376731421562469887429167, 6365024690830757216363202941392786776021006596297515755282380627110310398883655758664879554408883938671439476885972416, 44357682613543100501001880719403808204184109335424103941709444331062890521574437707306606519059577440293737499262924038, 107516540358673870283228322027353544736454021376930880738098296945412352643531528901085260995881596645157170464344, 61654417817841427536592249978492199110050592171405259077455158499810921149520017760234208572608345058462220851881250862], 'aut_phi_ratio': 384.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [2, 8, 4, 1], [2, 24, 2, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 12, 4, 1], [4, 24, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 2, 4, 1], [6, 8, 8, 1], [8, 2, 4, 1], [8, 4, 2, 1], [8, 12, 4, 1], [12, 4, 1, 2], [12, 4, 2, 1], [24, 4, 4, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2\\times C_2^6.C_2^6.C_2)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '256.56092', 'autcent_hash': 56092, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '192.1514', 'autcentquo_hash': 1514, 'autcentquo_nilpotent': False, 'autcentquo_order': 192, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_{12}:C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 8, 4], [2, 24, 2], [3, 2, 1], [4, 2, 4], [4, 12, 4], [4, 24, 2], [6, 2, 7], [6, 8, 8], [8, 2, 4], [8, 4, 2], [8, 12, 4], [12, 4, 4], [24, 4, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '96.209', 'commutator_count': 1, 'commutator_label': '24.9', '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', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 16406, '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, 8, 1, 4], [2, 24, 1, 2], [3, 2, 1, 1], [4, 2, 1, 4], [4, 12, 1, 4], [4, 24, 1, 2], [6, 2, 1, 3], [6, 2, 2, 2], [6, 8, 2, 4], [8, 2, 2, 2], [8, 4, 1, 2], [8, 12, 1, 4], [12, 4, 1, 4], [24, 4, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 131040, 'exponent': 24, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '48.51', 'hash': 16406, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 6, 4], 'inner_gens': [[1, 6, 8, 336], [5, 2, 232, 48], [1, 210, 8, 48], [97, 2, 8, 48]], 'inner_hash': 209, 'inner_nilpotent': False, 'inner_order': 96, 'inner_split': False, 'inner_tex': 'D_4\\times D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 28], [4, 16]], 'label': '384.16406', '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': '(C2*C24):D4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 24, 'number_characteristic_subgroups': 33, 'number_conjugacy_classes': 60, 'number_divisions': 48, 'number_normal_subgroups': 149, 'number_subgroup_autclasses': 204, 'number_subgroup_classes': 596, 'number_subgroups': 2206, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 87], [3, 2], [4, 104], [6, 78], [8, 64], [12, 16], [24, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [4, 4, 4, 2, 4, 4], 'outer_gen_pows': [16, 0, 32, 136, 96, 0], 'outer_gens': [[125, 106, 12, 240], [317, 10, 44, 340], [341, 210, 8, 340], [337, 118, 200, 144], [149, 38, 44, 244], [221, 330, 236, 340]], 'outer_group': '512.554852', 'outer_hash': 342028529733335859, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 128, 'outer_perms': [252688248365968986902102941186445730196196158966346493218268818287744470222099308779725710224262448896528896541358393959708552366994418149154674595025394222594968153995230933668785250755059933617475375601155787101351, 131587946707239719478304337315035154441177798353172644184604176293073212649341287075294565896313878314506945665969453535921427699969480643035840320751121236839494909984017834424912805360218584973706667175789509597908, 217841364432524099679443188128657592043131121671198248792025066100111537545552584980031027470653177815761802434641926232940962937872632371455030541477482743415572774840070076953671710318702051863724132278968996751732, 136451214255032672373256487368041010945503291332657109049238611638491579611109574205616935464355633849879701421841068776226128881130839918656160519031536942670677014449195752931281027363937912762660601881822223317229, 61169138485614371187751976146124754125688627242733397040007148830930821009068931723838295557313380180098857443182695909535443121335642486774391677706193398331433395170722953400168930730190028469912203947337635610997, 146443295283089957866781608594903931755510759884086988809714190303225606332886172404078522295758282904301222306257712764876417213140212015166046368225997958973307544793352789459378538762991909777938157649030339248172], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4.C_2^5', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 23, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 20], [4, 8], [8, 2], [16, 2]], 'representations': {'PC': {'code': 33452352274601048746982707790670344, 'gens': [1, 2, 4, 6], 'pres': [8, -2, -2, -2, -2, -3, -2, -2, -2, 97, 41, 3723, 91, 652, 16133, 141, 16134, 166]}, 'Perm': {'d': 23, 'gens': [221899900780350696984, 1392132272082739004904, 2562738032289383828905, 17158748779407514344, 3596214738863045376000, 4871280587992724909544, 4871280587992724908800, 3]}}, 'schur_multiplier': [2, 2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times C_{24}):D_4', 'transitive_degree': 96, '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}
