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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4096.boh', 'ambient_counter': 1048, 'ambient_order': 4096, 'ambient_tex': '(C_2^2\\times D_4^2).C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1024, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4096.boh.4._.OT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.OT', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': None, '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': '1024.ddn', 'subgroup_hash': None, 'subgroup_order': 1024, 'subgroup_tex': '(C_2\\times D_4^2):D_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '4096.boh', 'aut_centralizer_order': None, 'aut_label': None, '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': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6973827033304, 6266937726, 39921847, 39921961, 368046, 5041, 12526722437046, 6893789852872, 1313941673647, 19561077418313], 'label': '4096.boh.4._.OT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '4.OT', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4._.OT', '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': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [4, 4, 8, 4, 8, 8], 'aut_gens': [[5167, 87102727, 302814840, 1313901388800, 5606321846392, 12526762728376], [4103693809943, 127387567, 19614852622078, 127387560, 12520495790657, 15316514841600], [16825370284657, 18126770083062, 1314028776367, 16825147303657, 14008840836601, 5612588778958], [19615028054278, 18126770083062, 1313941673640, 176158200, 12526762728376, 14008840836601], [4103693809943, 4103646986903, 1314164654647, 4103646992063, 9703614810942, 6920263514872], [16825370284657, 20916522950273, 2789705318416, 302814840, 8395940079943, 11212821059896], [18126857180862, 18126730524222, 5160, 16825107018817, 12520495790657, 14002613452807]], 'aut_group': '65536.z', 'aut_hash': 7116534239874182336, 'aut_nilpotency_class': 6, 'aut_nilpotent': True, 'aut_order': 65536, 'aut_permdeg': 64, 'aut_perms': [52591626948307115290803812964962180716499066940416715786308353773404458532969890448490811, 79733326356524296867543537387297126645539955715736747972024602866386158157742232478556858, 22751799738223641498436241376578862879180243805052763503992995566977967652642691723433401, 101169841853168296652318344727987780764917922908601714227056132654911963072060055399938585, 44846508443645655065913432885788396810722743632805870966401208460230441877411542988798238, 61413131909602486310467318809265549046621126430585046183456248624528609677139695243181437], 'aut_phi_ratio': 128.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 2, 2, 1], [2, 4, 2, 1], [2, 4, 4, 2], [2, 4, 8, 1], [2, 8, 2, 2], [2, 8, 4, 3], [2, 16, 2, 1], [4, 4, 2, 1], [4, 4, 4, 2], [4, 8, 1, 1], [4, 8, 2, 2], [4, 8, 4, 3], [4, 8, 8, 2], [4, 16, 2, 1], [4, 32, 2, 1], [4, 32, 8, 1], [8, 32, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^9.C_2\\wr D_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '32.51', 'autcent_hash': 51, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 8, 'autcentquo_group': None, 'autcentquo_hash': 7822646973264783822, 'autcentquo_nilpotent': True, 'autcentquo_order': 2048, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^5.D_4^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 3], [2, 4, 18], [2, 8, 16], [2, 16, 2], [4, 4, 10], [4, 8, 33], [4, 16, 2], [4, 32, 10], [8, 32, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '512.6536092', 'commutator_count': 1, 'commutator_label': '32.46', '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', '2.1', '2.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 2120, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [2, 4, 1, 18], [2, 8, 1, 16], [2, 16, 1, 2], [4, 4, 1, 10], [4, 8, 1, 33], [4, 16, 1, 2], [4, 32, 1, 10], [8, 32, 1, 4]], 'element_repr_type': 'Perm', 'elementary': 2, 'eulerian_function': 5119672320, 'exponent': 8, 'exponents_of_order': [10], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[8, 1, 8]], 'familial': False, 'frattini_label': '32.46', 'frattini_quotient': '32.51', 'hash': 7003003021026862916, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 2, 2, 4, 4], 'inner_gens': [[5167, 87102727, 263265840, 1313901388800, 5606321846392, 11212821054743], [5167, 87102727, 263265840, 1313901388800, 8395940079943, 15316514846767], [40279687, 127387567, 302814840, 1313901388800, 15310288183806, 9703614815857], [5167, 87102727, 302814840, 1313901388800, 6920263514872, 11212861334416], [5167, 2789705323576, 18126554366022, 40279680, 5606321846392, 12526722443536], [1313941668480, 2789745598096, 18126554366022, 5160, 5606362120912, 12526762728376]], 'inner_hash': 3725227854009754059, 'inner_nilpotent': True, 'inner_order': 512, 'inner_split': False, 'inner_tex': 'C_2^6:C_2^3', 'inner_used': [1, 2, 3, 4, 5, 6], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 32], [2, 56], [8, 12]], 'label': '1024.ddn', '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*D4^2):D4', 'ngens': 6, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [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': 29, 'number_characteristic_subgroups': 31, 'number_conjugacy_classes': 100, 'number_divisions': 100, 'number_normal_subgroups': 947, 'number_subgroup_autclasses': 3360, 'number_subgroup_classes': 22344, 'number_subgroups': 79669, 'old_label': None, 'order': 1024, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 239], [4, 656], [8, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 16819007022583, 0, 0, 0, 0, 0], 'outer_gens': [[4103734094783, 1314028776360, 18126594650862, 1314028776367, 6920263509719, 9703654364857], [20916435842633, 16825322735857, 4103646992063, 215717040, 6913996572238, 12520495790657], [5167, 1313988491520, 1314164654647, 1313901388800, 5612549225033, 11219087992462], [5167, 127387567, 1314164654647, 40284847, 5612549225033, 11219087992462], [2789792421136, 87102727, 20916299969273, 127387560, 6920263509719, 9703654369782], [5167, 87102727, 302814840, 40284847, 5606321846392, 12526762728376], [5167, 87102727, 1314164654647, 40284847, 5606321846392, 12526762728376]], 'outer_group': '128.1755', 'outer_hash': 1755, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 10, 'outer_perms': [126745, 1951327, 26334, 1, 2718174, 167280, 1275486], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4:D_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 56], [8, 12]], 'representations': {'PC': {'code': '31859800216577785331555308478271677616527907748749314695626699018286266766861952945339170', 'gens': [1, 2, 4, 5, 6, 8, 9], 'pres': [10, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 121, 51, 20803, 10413, 743, 29604, 2814, 3734, 5765, 2895, 755, 405, 175, 51207, 39057, 7077, 3247, 1657, 69128, 12978, 8678, 4368, 618, 268, 28819]}, 'Perm': {'d': 16, 'gens': [87102727, 1313901388800, 12526762728376, 302814840, 5167, 5606321846392]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 5, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times D_4^2):D_4', 'transitive_degree': 16, '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': '64.267', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [8, 6, 8, 4, 4, 4, 2, 4, 2, 2, 2, 2, 2, 2], 'aut_gens': [[6268112329, 13412413015, 1313901388800, 6973827033311, 12526722437046, 20862563517670], [1321087582206, 1321087224361, 19678982814, 9737014285560, 2790183150425, 19561077423238], [19554849232865, 20862523595830, 1327353718609, 8429379476527, 13995292123577, 20862564319319], [20855378493959, 20849151836153, 19554849227824, 4104045423952, 8436564495654, 20862564319312], [20868750621665, 13451967054, 1313941668487, 2790183513311, 11232460109208, 41086489], [1313902558369, 19541478269104, 1307714284800, 4104045786838, 8442791884494, 20862563517784], [6267744409, 19679350615, 1307714284800, 2790144403198, 11212861323001, 19554889149785], [1313942480214, 1321086781128, 39916801, 6973826665265, 12520535333160, 19561076611625], [1174615, 1321086781014, 39916801, 6973827033311, 11219087980800, 19561076611625], [1307675174694, 1327353350808, 40284847, 6973827033311, 11212861323001, 20862563517670], [6268112329, 1327353350808, 1313901388800, 5659885727710, 12520535333160, 20862563517670], [6268112329, 1327353350808, 40284847, 6973827033311, 12526722437046, 20862563517670], [1307675174694, 13412413015, 1313901388800, 6973827033311, 11212861323001, 19561076611625], [806695, 19678982809, 1313901756846, 6973826665265, 8442751604809, 20862563875624], [1313942480328, 19678982809, 39916801, 5659885727710, 9744239226534, 19561076253671]], 'aut_group': '1572864.de', 'aut_hash': 1112540888349540976, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1572864, 'aut_permdeg': 192, 'aut_perms': [167869481768919551271216646126200053779248059097569727642321672417118201129313294531424586709672710139844925676787815570386598636646706198483224559740564599035870226870041405595822847730165950929480995787879009714135576333517237018652925560648383396490461766723232457277464471930022204050825138572952786074943428398118806438495967698232876261193611459862356, 218618913362992416185916432005358873960001483255623259019409272963750558571757151213880494514613612443641779548949578108757578988564145626534279634801096517577392502218320641350369663645363167121922567328144827612835488744562253114957336440963996367040127873869741844834399014031976102536685498480326926964040334610244455307019485443406209189652098769579672, 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127228621255968172809149909250721747663480733143251835038339567741553624681087688590867310318026615089664165936422512077250639622957200101616603062611640197407021518652734294675848901465211071324311867801049013174090538364247036569530484213248137345202613116867145992510200500551702296271397957980111907953996814280547100932438955051385117453986418532346218, 268183799730356851542350158895690738638608196958536975442464703001842918686183552675890888215534461080846577343341980528393987775378592830581898086820075625832412356115444956023083344700623429858062166627915662326082047743788266580732428181327137934304793503842543987974738149551014364478003443191021021820288001540796552185964142210516891099021624414473482], 'aut_phi_ratio': 768.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 3, 1], [2, 4, 1, 2], [2, 8, 4, 1], [2, 8, 12, 1], [2, 16, 6, 1], [2, 16, 12, 1], [2, 32, 3, 1], [4, 8, 2, 1], [4, 8, 6, 1], [4, 16, 3, 1], [4, 16, 12, 1], [4, 32, 6, 1], [4, 32, 12, 2], [4, 64, 24, 1], [8, 64, 12, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_2^3\\times C_4^3).C_2^7:S_4', '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': 24, 'autcentquo_group': None, 'autcentquo_hash': 2753293854424490967, 'autcentquo_nilpotent': False, 'autcentquo_order': 24576, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2.C_2^6.(D_4\\times S_4)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 3], [2, 4, 2], [2, 8, 16], [2, 16, 18], [2, 32, 3], [4, 8, 8], [4, 16, 15], [4, 32, 30], [4, 64, 24], [8, 64, 12]], 'center_label': '2.1', 'center_order': 2, 'central_product': None, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '64.261', 'complements_known': False, 'complete': False, 'complex_characters_known': True, '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'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 1048, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [2, 4, 1, 2], [2, 8, 1, 16], [2, 16, 1, 18], [2, 32, 1, 3], [4, 8, 1, 8], [4, 16, 1, 15], [4, 32, 1, 30], [4, 64, 1, 24], [8, 64, 1, 12]], 'element_repr_type': 'Perm', 'elementary': 2, 'eulerian_function': None, 'exponent': 8, 'exponents_of_order': [12], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [[8, 1, 16], [32, 1, 1]], 'familial': False, 'frattini_label': '64.261', 'frattini_quotient': '64.267', 'hash': 7282668615247213970, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [4, 4, 2, 2, 4, 4], 'inner_gens': [[6268112329, 13412413015, 1313901388800, 5666112385511, 8442791516448, 19554889507625], [6268112329, 13412413015, 1307714284800, 4104045429112, 11219087980800, 19561076253785], [6268112329, 19679350615, 1313901388800, 5659885727710, 11212821043326, 19561076253671], [1313902558495, 19547665015390, 39916801, 6973827033311, 11212860965047, 20862563517670], [19554889507630, 1327313796895, 5160, 6973826665265, 12526722437046, 1307715454488], [1313942112294, 1327353718728, 39916801, 6973827033311, 8436564500695, 20862563517670]], 'inner_hash': 8643401727932920871, 'inner_nilpotent': True, 'inner_order': 2048, 'inner_split': False, 'inner_tex': 'C_2^5.C_2^6', 'inner_used': [1, 2, 3, 4, 5, 6], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 64], [4, 28], [8, 40], [32, 1]], 'label': '4096.boh', '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': '(C2^2*D4^2).C2^4', 'ngens': 6, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [1, 1, 3, 1, 7, 7, 43, 91, 651, 1395, 651, 63, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 19, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 133, 'number_divisions': 133, 'number_normal_subgroups': 2915, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 4096, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 527], [4, 2800], [8, 768]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 2, 3, 2, 2, 2, 2], 'outer_gen_pows': [15302967293502, 0, 19640234880, 1313941305727, 20862564324472, 0, 0, 0, 0], 'outer_gens': [[19541478269104, 40728654, 39916806, 12533947741129, 2790143233624, 1321126334934], [1313942480328, 1321086781014, 6227020801, 4104084534065, 8423152455721, 19554889149671], [19547704483798, 20855338572119, 19561116533470, 2790144035152, 11219087980800, 20868751423312], [6267744409, 13412413015, 1313901388800, 6973827834839, 8423152450680, 20862563875510], [19639066015, 13452768001, 5041, 11219087980926, 14008665052823, 19547665373225], [1307675174694, 13412413015, 1313901388800, 6973827033311, 12526722437046, 19561076611625], [1307675174694, 1327353350808, 1313901388800, 6973827033311, 12526722437046, 19561076611625], [6268112329, 1327353350808, 40284847, 6973827033311, 12526722437046, 19561076611625], [1307675174694, 1327353350808, 40284847, 6973827033311, 12526722437046, 19561076611625]], 'outer_group': '768.1087581', 'outer_hash': 1087581, 'outer_nilpotent': False, 'outer_order': 768, 'outer_permdeg': 12, 'outer_perms': [18596216, 83464754, 467629125, 90843196, 423456463, 83462480, 2354, 90760402, 11372474], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\wr D_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 6, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 64], [4, 28], [8, 40], [32, 1]], 'representations': {'PC': {'code': '1459710864851287011790695370180501053402241883984878105511808026157085761110164969603202754678242415935761021694531613492289142331371613', 'gens': [1, 2, 3, 5, 7, 9, 10, 11, 12], 'pres': [12, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 12672, 46514, 20822, 98, 100227, 975, 13095, 185284, 1456, 48748, 16720, 172, 26886, 56802, 50430, 22218, 2406, 5946, 246, 49183, 41480, 15572, 10400, 32876, 16472, 99861, 84513, 38445, 19257, 106690, 6418, 4643]}, 'Perm': {'d': 16, 'gens': [6268112329, 13412413015, 1313901388800, 12526722437046, 6973827033311, 20862563517670]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 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_2^2\\times D_4^2).C_2^4', 'transitive_degree': 16, '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}
