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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '15552.lm', 'ambient_counter': 299, 'ambient_order': 15552, 'ambient_tex': 'C_3^3:C_{12}:\\GL(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2592, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '15552.lm.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', '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': '2592.ov', 'subgroup_hash': 6364532303939573533, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:(C_4\\times Q_8)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '15552.lm', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1.a1', 'complements': ['2592.r1.a1', '2592.u1.a1', '2592.t1.a1', '2592.v1.a1', '2592.r2.a1', '2592.u2.a1', '2592.r1.b1', '2592.u1.b1', '2592.t1.b1', '2592.v1.b1', '2592.r2.b1', '2592.u2.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.g1.a1', '12.h1.a1', '54.f1.a1', '54.k1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7820, 6526, 7766, 6653, 7601, 5297, 7799, 5297], 'generators': [357364, 146625, 101149171200, 338677, 287404777350, 200222668800, 45507, 19203609600, 224189], 'label': '15552.lm.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '15552.lm', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '15552.lm'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [12, 24, 12, 8], 'aut_gens': [[1, 4, 24, 288, 864], [351, 1568, 620, 2016, 288], [1501, 1032, 1996, 288, 1440], [1085, 1420, 2228, 1440, 1728], [1703, 1364, 1916, 1440, 2304]], 'aut_group': None, 'aut_hash': 6992198563583357107, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 62208, 'aut_permdeg': 72, 'aut_perms': [59337954524260299147239479231456308609542877753321291861071666012360992601168804384681343198718589647974, 14344502551738426924292597637688643297065548355246542714127488255960835144724819971820216689407596634625, 21719763909055219358775850506632154880960229290500740068887400799937638998982197715359490526184569220200, 50606389757777099263840341806009131198700894585479325532481830159213537292152553338567132265629290429180], 'aut_phi_ratio': 72.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 81, 1, 1], [3, 4, 2, 1], [3, 8, 1, 1], [3, 32, 2, 1], [4, 9, 2, 1], [4, 18, 3, 1], [4, 81, 2, 1], [4, 162, 3, 1], [4, 162, 6, 1], [6, 36, 2, 1], [6, 72, 1, 1], [12, 72, 2, 1], [12, 72, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3:S_3.C_6^2.C_{12}.C_2^3', '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': 24, 'autcentquo_group': None, 'autcentquo_hash': 6992198563583357107, 'autcentquo_nilpotent': False, 'autcentquo_order': 62208, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3:S_3.C_6^2.C_{12}.C_2^3', 'cc_stats': [[1, 1, 1], [2, 9, 2], [2, 81, 1], [3, 4, 2], [3, 8, 1], [3, 32, 2], [4, 9, 2], [4, 18, 3], [4, 81, 2], [4, 162, 9], [6, 36, 2], [6, 72, 1], [12, 72, 8]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '2592.ov', 'commutator_count': 1, 'commutator_label': '162.52', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 386, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['36.9', 1], ['72.41', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 81, 1, 1], [3, 4, 1, 2], [3, 8, 1, 1], [3, 32, 1, 2], [4, 9, 2, 1], [4, 18, 1, 3], [4, 81, 2, 1], [4, 162, 1, 3], [4, 162, 2, 3], [6, 36, 1, 2], [6, 72, 1, 1], [12, 72, 1, 6], [12, 72, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 89600, 'exponent': 12, 'exponents_of_order': [5, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[32, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '2592.ov', 'hash': 6364532303939573533, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [4, 12, 12, 3, 3], 'inner_gens': [[1, 1988, 904, 2016, 2304], [1929, 4, 168, 1728, 288], [1881, 148, 24, 1440, 1152], [865, 1156, 2328, 288, 864], [2017, 1444, 600, 288, 864]], 'inner_hash': 6364532303939573533, 'inner_nilpotent': False, 'inner_order': 2592, 'inner_split': False, 'inner_tex': 'C_3^4:(C_4\\times Q_8)', 'inner_used': [1, 2, 3], 'irrC_degree': 32, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 32, 'irrep_stats': [[1, 16], [2, 4], [4, 8], [8, 6], [32, 2]], 'label': '2592.ov', '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': 'C3^4:(C4*Q8)', 'ngens': 9, '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, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 36, 'number_divisions': 30, 'number_normal_subgroups': 42, 'number_subgroup_autclasses': 130, 'number_subgroup_classes': 276, 'number_subgroups': 8384, 'old_label': None, 'order': 2592, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 99], [3, 80], [4, 1692], [6, 144], [12, 576]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [1010, 867, 0], 'outer_gens': [[1011, 100, 136, 288, 864], [577, 2436, 752, 1152, 288], [2031, 896, 1764, 576, 2016]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [7, 136, 856], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 9], [8, 4], [16, 1], [32, 2]], 'representations': {'PC': {'code': '1328119806124440603277271337533222477719567761067511596996479622963788828106892892236505465348513471928236583', 'gens': [1, 3, 5, 8, 9], 'pres': [9, 2, 2, 2, 3, 2, 2, 3, 3, 3, 18, 53678, 19721, 74, 74883, 33996, 678, 40684, 15673, 1912, 130, 119669, 53150, 158, 7062, 6063, 145159, 20752, 31129, 5218, 4363, 916, 186632, 70001, 5858, 17531, 3932, 2969]}, 'Perm': {'d': 15, 'gens': [1520637524, 224189, 45507, 338677, 63975, 219574, 87737376696, 24951986164, 355419192715]}}, 'schur_multiplier': [6, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4:(C_4\\times Q_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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [12, 8, 8, 12], 'aut_gens': [[219574, 338677, 368871149493, 267762216480, 63975, 287404882998, 130855, 45507, 19203664935, 224189, 268240896693], [219574, 24202, 25430952694, 193999634064, 26719, 268244874533, 23940, 80884, 280259558839, 5515, 361726363894], [45507, 227590, 368871234601, 19203895240, 285303, 193077793956, 238510, 184197, 267762013457, 362879, 19200066601], [184197, 349733, 19200150974, 280259627950, 152824, 25909828726, 243, 321987, 193999420205, 40892, 368871318974], [219574, 152824, 456053278993, 19203686921, 238785, 268244768800, 349453, 138690, 181062710386, 40892, 3838993]], 'aut_group': None, 'aut_hash': 6992198563583357107, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 62208, 'aut_permdeg': 432, 'aut_perms': [36789118987155964156795851712408208777047707017109154311902254194277011808920225092318399746913539513543608645615797118871048933202354385048445628019256933695023069223957878410137271862946379131718971740878508385707993992474221631751048054567586779313747206592041169464589461142205625132086234317817428772662726536396583954400545348984240676426835578623072553227222466027987178213594965535583753488612558978535452749337121136626292627308032200030013350106941775569843398715699803094194595556484120059116155130878371761841211684986814460095227066977438951062822363929607756558633500027913226670573491801153821679406062522368228924136865289568301514938497694842716167383024444071461711699434217294349549455745555230185578509242473274836281965724434697249144369444543942861926957826807112385674642071319498480802097284962587424637071117383142954804362872656912733978774817075918592346838593795319431757663101470105301244114111610889141423267040222336692431, 16897587572546628611013978840588244300697154828436257116863620648655298826118986649841330944263274369138473926019146903210979128943147814271601131346803157687143044870616382674207767915067109963078868121766175938275422643200163889098706193792299813665502905883381118500243939314230923702647577794848129208588773105512725289440469646531047964497126608125291439849903020478291225991091116524863715738071181982395509775468931551634442692005188429623222604847730124137526373568370372299879855257682840310428733029396653932717482860752153083291509461342201766116464280522525887009016908077358914647640370142301146020533967050050406932106143438714978703633338731527916612283706172883583044096811091783248901628433239214043284596589122253665079657580558036442909040752870458360777517500158118286896638699665007322710454255419544771151033391881217388475323674468263742077942078066373514360715033716897875964164269304997700469940870834284138197538047588895363420, 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32079420273679332999075543385560947527648368826506083105142696077387697284942575083659260435319993444052679212251369388730172498795470834188663855785297207331134514448715058028911003520670221749552402570359808956952003046331200037077624309728573954301003066248669413209892938791641043310800871505015483985168141054509630227898230005217367669654775123987480635602554494055874897009789500835552832827327812758975873249693057529692690906410787710531450369945019073741494365356230727268827769533194967860819330064259360827664022787947175487570028600183554705747091203820238561363083150118407458661410976308204508242781668360770374156329428629116854933735446665933236707549583156878235052485633076225393647647285628441868325506888007778240683980998312832324480654744750582491974517028516373302847657390089592782121510743758536647492161411289328519893161468781131492125972039188660947791499714813916134165360512283232705206615976660428332095659366177739325741], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 81, 1, 1], [2, 216, 2, 1], [3, 4, 2, 1], [3, 8, 1, 1], [3, 24, 1, 1], [3, 32, 2, 1], [3, 48, 1, 1], [3, 96, 2, 1], [3, 192, 2, 1], [4, 18, 1, 1], [4, 54, 1, 1], [4, 162, 1, 1], [4, 486, 1, 1], [4, 972, 1, 1], [6, 36, 2, 1], [6, 72, 1, 2], [6, 216, 1, 1], [6, 288, 2, 1], [6, 432, 1, 1], [6, 432, 2, 2], [6, 648, 1, 1], [6, 864, 2, 1], [8, 324, 2, 2], [12, 144, 1, 1], [12, 216, 2, 2], [12, 432, 2, 1], [12, 648, 2, 1], [24, 648, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3:S_3.C_6^2.D_{12}.C_2^2', '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': 24, 'autcentquo_group': None, 'autcentquo_hash': 6992198563583357107, 'autcentquo_nilpotent': False, 'autcentquo_order': 62208, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3:S_3.C_6^2.C_{12}.C_2^3', 'cc_stats': [[1, 1, 1], [2, 9, 2], [2, 81, 1], [2, 216, 2], [3, 4, 2], [3, 8, 1], [3, 24, 1], [3, 32, 2], [3, 48, 1], [3, 96, 2], [3, 192, 2], [4, 18, 1], [4, 54, 1], [4, 162, 1], [4, 486, 1], [4, 972, 1], [6, 36, 2], [6, 72, 2], [6, 216, 1], [6, 288, 2], [6, 432, 5], [6, 648, 1], [6, 864, 2], [8, 324, 4], [12, 144, 1], [12, 216, 4], [12, 432, 2], [12, 648, 2], [24, 648, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '15552.lm', 'commutator_count': 1, 'commutator_label': '3888.kp', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 11, 'conjugacy_classes_known': True, 'counter': 299, 'cyclic': False, 'derived_length': 5, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 81, 1, 1], [2, 216, 1, 2], [3, 4, 1, 2], [3, 8, 1, 1], [3, 24, 1, 1], [3, 32, 1, 2], [3, 48, 1, 1], [3, 96, 1, 2], [3, 192, 1, 2], [4, 18, 1, 1], [4, 54, 1, 1], [4, 162, 1, 1], [4, 486, 1, 1], [4, 972, 1, 1], [6, 36, 1, 2], [6, 72, 1, 2], [6, 216, 1, 1], [6, 288, 1, 2], [6, 432, 1, 5], [6, 648, 1, 1], [6, 864, 1, 2], [8, 324, 2, 2], [12, 144, 1, 1], [12, 216, 1, 2], [12, 216, 2, 1], [12, 432, 2, 1], [12, 648, 2, 1], [24, 648, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 576, 'exponent': 24, 'exponents_of_order': [6, 5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[32, 1, 4], [64, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '15552.lm', 'hash': 7470095568335943882, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [3, 4, 2, 3, 4, 4, 3, 3, 6, 2, 2], 'inner_gens': [[219574, 33770, 368871471094, 267762171028, 20073, 287404839096, 33383, 45507, 19203708873, 5515, 268241218294], [45507, 338677, 368871234506, 267762060374, 166153, 287404931606, 349453, 321987, 19203715186, 224189, 268240981706], [321987, 157572, 368871149493, 25427221074, 72949, 19679198654, 329656, 45507, 181062682039, 317372, 19199981493], [138690, 257573, 448908099840, 267762216480, 285303, 25909789572, 27170, 45507, 19203899079, 362879, 479139840], [138690, 254325, 368871279233, 267761967800, 63975, 287404741624, 37525, 184197, 19203673026, 224189, 268241026433], [138690, 285303, 448908225403, 181062820883, 227590, 287404882998, 299453, 184197, 25427252056, 362879, 268241159803], [357364, 146625, 368871318974, 267762162779, 254325, 287404746372, 130855, 321987, 19203797686, 224189, 268241066174], [219574, 108554, 368871149493, 267762216480, 294198, 287404785526, 263606, 45507, 19203864102, 178682, 268240896693], [184197, 336160, 448908131774, 267761962999, 55180, 281174127750, 33383, 219574, 19203664935, 143305, 268241066174], [321987, 338677, 368871471094, 267762078690, 63975, 287404785526, 130855, 80884, 19203633879, 224189, 268241218294], [321987, 157572, 88698759093, 181062824274, 72949, 287404805054, 329656, 45507, 19203686839, 317372, 268240896693]], 'inner_hash': 7470095568335943882, 'inner_nilpotent': False, 'inner_order': 15552, 'inner_split': False, 'inner_tex': 'C_3^3:C_{12}:\\GL(2,3)', 'inner_used': [1, 2, 3, 4, 6, 11], 'irrC_degree': 32, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 32, 'irrep_stats': [[1, 4], [2, 9], [3, 4], [4, 9], [6, 1], [8, 10], [12, 4], [16, 7], [32, 4], [64, 2]], 'label': '15552.lm', 'linC_count': 16, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 16, 'linQ_dim': 12, 'linQ_dim_count': 16, 'linR_count': 16, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C3^3:C12:GL(2,3)', 'ngens': 11, '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, 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': 36, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 54, 'number_divisions': 47, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 615, 'number_subgroup_classes': 1014, 'number_subgroups': 97276, 'old_label': None, 'order': 15552, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 531], [3, 728], [4, 1692], [6, 5544], [8, 1296], [12, 3168], [24, 2592]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [281173939200, 0], 'outer_gens': [[219574, 338677, 268240896693, 280259803680, 63975, 180587526198, 130855, 45507, 286482928935, 224189, 368871149493], [321987, 157572, 368871149493, 267762113874, 72949, 287404805054, 329656, 45507, 19203686839, 317372, 268240896693]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [3, 4], [4, 10], [6, 1], [8, 7], [12, 4], [16, 7], [32, 5], [64, 2]], 'representations': {'PC': {'code': '551568676365381902309845844145946523115508878897172026572603232375637337628148736192678720191502557695133350390703219689565189994041910147983341936473955339686744441736011720320021253705624432807', 'gens': [1, 2, 5, 7, 10, 11], 'pres': [11, 2, 2, 2, 3, 2, 3, 2, 2, 3, 3, 3, 152549, 56, 114710, 90, 304835, 92404, 376875, 149186, 86332, 158, 41189, 248704, 158427, 57458, 1248, 94254, 248573, 48538, 64488, 3284, 226, 126727, 371730, 221789, 79240, 260, 114056, 16651, 28542, 760329, 665300, 190111, 166362, 47573, 7984, 6675, 1406, 1254538, 8766, 26201, 5884, 4443]}, 'Perm': {'d': 15, 'gens': [219574, 338677, 368871149493, 267762216480, 63975, 287404882998, 130855, 45507, 19203664935, 224189, 268240896693]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^3:C_{12}:\\GL(2,3)', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
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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}
