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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3072.qo', 'ambient_counter': 431, 'ambient_order': 3072, 'ambient_tex': '(C_2\\times C_4^2).\\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1536, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3072.qo.2.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408633421', 'subgroup_hash': 1463032256093085800, 'subgroup_order': 1536, 'subgroup_tex': '(C_2^2\\times C_4^2).S_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '3072.qo', 'aut_centralizer_order': 2, 'aut_label': '2.B', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '1536.A', 'complements': ['1536.E', '1536.H', '1536.J'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.A', '4.F', '6.H', '8.F', '8.G'], 'core': '2.B', 'coset_action_label': None, 'count': 2, 'diagramx': [108, 1383, 294, 1233], 'generators': [134021272931346744110039, 458433780559861017541985, 187973685956283861726862, 25903229681844523013167, 5167, 51091299166812272040, 108169377830641999883662, 25903229683158464676480, 51212588579832556921, 512330114468178570400703], 'label': '3072.qo.2.B', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.B', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.A'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '1536.408633531', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.B', 'subgroup_fusion': None, 'weyl_group': '1536.408633531'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [4, 8, 4, 4, 2, 4], 'aut_gens': [[1, 4, 24, 48, 96, 384], [1071, 1060, 984, 1008, 96, 384], [289, 1204, 888, 432, 96, 576], [1071, 1444, 888, 1392, 96, 384], [971, 980, 1512, 1392, 1440, 384], [975, 916, 216, 48, 96, 576], [161, 1124, 1200, 312, 384, 96]], 'aut_group': None, 'aut_hash': 7539401700553807780, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12288, 'aut_permdeg': 192, 'aut_perms': [304764125840648489058603819846386562574854920944601298644882065920706607937725388849831011703550972866195940433380573325244764496132837995677998118312433045058948346423004973274108640082679473044687972031260029416847060093377966991633716231872837177906037174997333848861385216681115766747823173089926947431016594600048729478641029887442111865036103890932316, 347762334431852150580986845534742062874699299010239207802469751966202096854591394296638718249431631919562451257227399350570846660474277743248339236533101326901601969976144273366752856351284047610479033837018811322621603423423064391752556599036501539254127836141517248302231187986290268907029978437713031569082147105725738641393592503941968730606868809606422, 304764161052316172512450949255061461068927259098114053404946408678769638835710444493896869267687579074369850963515224852053925381564023048159134350330147919667022781559124104904727724959302074648151550831064449436815657655793902997689077344105025267835231619624621327710969436076195753477105609719439595088042213280326556851018191361608754976135867350194120, 247900630471920894918343043546513085593254197523274852731933836065909537569369091033130753784443478516475585153971368846120736722527022678252920216757671001640236851299620111496896688184030319740047997603935756878668830371815143399645353227665527856427710644858743144890827747960534151142553359317484159687415408481208704575330954766788722526117716303117531, 197496711170946312865317281569246610446614577576773636047285664304953611215320468249337608410564990451662773811044633488214472160760865499574861966722403734672043243827924648378247998328316275623355598503314677628077991876471798847991340012816621733517442429847458086295938384810166137891221107352961020416253119664701245380880355986315828058714150397584465, 317646045200246187145663098391091687815378772371636122620888260530774699893226795184139455704643664156355185896565811725351517960420104978686867179755715069852170346543305598184030970145522021905143902515720656811586199016802957137115320638600615702184007326707821195296827584288842511057707305550333397242687460309833021485581873406001468226186129799813934], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 4, 1, 2], [2, 12, 2, 2], [2, 24, 1, 2], [3, 128, 1, 1], [4, 6, 1, 4], [4, 12, 1, 2], [4, 12, 2, 2], [4, 24, 1, 2], [4, 48, 4, 1], [6, 128, 1, 3], [8, 24, 8, 1], [8, 48, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4^2:A_4.D_4.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': None, 'autcentquo_hash': 2330610246365708940, 'autcentquo_nilpotent': False, 'autcentquo_order': 6144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_4^2:A_4.C_4.C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 4, 2], [2, 12, 4], [2, 24, 2], [3, 128, 1], [4, 6, 4], [4, 12, 6], [4, 24, 2], [4, 48, 4], [6, 128, 3], [8, 24, 8], [8, 48, 8]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '768.1088655', 'commutator_count': 1, 'commutator_label': '192.1023', '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', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 408633421, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['768.1088655', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 4, 1, 2], [2, 12, 1, 4], [2, 24, 1, 2], [3, 128, 1, 1], [4, 6, 1, 4], [4, 12, 1, 6], [4, 24, 1, 2], [4, 48, 2, 2], [6, 128, 1, 3], [8, 24, 2, 4], [8, 48, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 18, 'exponent': 24, 'exponents_of_order': [9, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 2], [12, 1, 2]], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '192.1538', 'hash': 408633421, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [4, 6, 4, 4, 4, 4], 'inner_gens': [[1, 20, 120, 1320, 96, 1248], [9, 4, 1032, 984, 480, 864], [289, 244, 24, 48, 288, 1344], [1273, 844, 24, 48, 1056, 1152], [1, 1156, 216, 1008, 96, 384], [1057, 1444, 984, 816, 96, 384]], 'inner_hash': 1088655, 'inner_nilpotent': False, 'inner_order': 768, 'inner_split': False, 'inner_tex': '(C_2\\times C_4^2).S_4', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 4], [3, 24], [6, 4], [12, 8]], 'label': '1536.408633421', 'linC_count': 4, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 2, 'linQ_dim': 12, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': '(C2^2*C4^2).S4', 'ngens': 10, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 48, 'number_divisions': 38, 'number_normal_subgroups': 35, 'number_subgroup_autclasses': 822, 'number_subgroup_classes': 1379, 'number_subgroups': 12760, 'old_label': None, 'order': 1536, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 111], [3, 128], [4, 336], [6, 384], [8, 576]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 12, 12, 12], 'outer_gens': [[961, 916, 216, 48, 96, 576], [1, 4, 312, 624, 96, 384], [3, 4, 888, 432, 96, 384], [13, 4, 888, 432, 96, 384]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [3, 12], [6, 10], [12, 4], [24, 2]], 'representations': {'PC': {'code': '4706275195275271533981582862510438787961577877349281837249388121535142135363719763600830149558427801819001771072', 'gens': [1, 3, 5, 6, 7, 9], 'pres': [10, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 20, 602, 82, 643, 6004, 5414, 12924, 6334, 444, 79205, 24495, 14785, 2015, 1015, 8426, 11796, 886, 1596, 206, 19227, 7717, 112328, 19468, 7598, 5088, 2218, 268, 96009, 4829, 12039]}, 'Perm': {'d': 24, 'gens': [25852394491454237016262, 432474715758828847104000, 25903229683158464681647, 54003382327446436696462, 25903107683852745438857, 108118165251765908747536, 53952291033879632521552, 122000787877207687, 25903229681844523013167, 1313941673647]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_2^2\\times C_4^2).S_4', 'transitive_degree': 24, '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': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [8, 6, 4, 12, 6], 'aut_gens': [[108169256548142928628553, 486640968089256833126695, 566496110689622789725128], [187973563956797432597176, 566282149412710332706871, 324192775155664486574158], [162121547572292249601857, 270240740206860860237088, 458326854152504522437990], [133970303632967768771273, 486691937387635808465689, 512279023883002003336336], [108118287245465432829377, 216237357882210482904529, 594596384619065371071048], [134021272924432795075342, 242140465564568616326688, 566495988691644296824903]], 'aut_group': None, 'aut_hash': 3931087640067296130, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 49152, 'aut_permdeg': 384, 'aut_perms': [119595349405362648765413340210785537267018040479246755390956712825580025999966459269339095363728934433713935285662671077807824370091143899200405599591462475317127851683430376670658294028988758459522417309823826579352902044799811701490821666554270799055609118675114759173879320008877865563703231566253808661706918895764261008747848705478719614818246120517871519532545137524979064262851797195507473228853930891093513546461186091776069436053764607981529503969417565573055730518340655416587205272407873007355519379461513821115878806367798442508639897987908847826711652799445536389016301846443090795445089462710454786173715532713950778889170798675688736474780282771922026165915449667795481568080554089027825524274605043950754973292386610658422402739058323243615760344139280768416005905023020829270282264827816599595099308288635070927, 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99629556586582439972181665004688511853963463684599089455523346661679452783346816525998430912810163319512993118598685449428870775974081389152724755974129922320141709013466168980624337882926483132843474136213895397821258335943388320024419663647409811555981640373710570129538989454048758344259781679995142782459975315333141996177019517716753556128656853091039256188552034893239423133652902156285103154786308949105481978580793916614932779776030774621629857878564163699263791655775182581271154885135488081985763610850944770712787580801700007082953061332350435986825136132363706489078891439140239306576981334258109730493791339052932189820951539029637479425070273519146177705368458398486719125217529801759338966973020707921642397373298383532043393440759450305354319312955853049892029625843037825564477931717866212140615053834932353317, 181818685045527751679337676206498372072903573627555736058614204846839483588671757939752568707578659349899700901816720258530909930019803621944655161024600488948413406439091429778727723356381775587751822637397654523738009094261031445201859283033651755093080972895327531856320955556000863775523664356840142831586666749209204063675970618828134067348018801368313149118072856843597206676354249017115504019757112781418197677469045576771301148399562421574441863877316835925682476536825999873093542978119534154331692584174650800353737787857168103225185624732960326942803967916974741098309302327607073133666320835572554118252256238963651937590497930391620233304708566705920373891538329871752289400114745961538318358788296151264374592924343530924289335247275490183753666733561916829071425557936365494534501559992745178926711870250872622472], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 4, 2, 1], [2, 8, 2, 1], [2, 12, 2, 2], [2, 12, 4, 1], [2, 24, 2, 2], [3, 128, 1, 1], [4, 6, 2, 2], [4, 12, 1, 2], [4, 12, 4, 1], [4, 24, 1, 2], [4, 24, 2, 1], [4, 24, 4, 1], [4, 96, 4, 1], [6, 128, 1, 1], [6, 128, 2, 1], [6, 128, 4, 1], [8, 48, 8, 1], [8, 96, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4^2:A_4.C_2^5.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '12288.bnm', 'autcentquo_hash': 6874179144975630292, 'autcentquo_nilpotent': False, 'autcentquo_order': 12288, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '(C_2\\times C_4^3).\\GL(2,\\mathbb{Z}/4)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 4, 2], [2, 8, 2], [2, 12, 8], [2, 24, 4], [3, 128, 1], [4, 6, 4], [4, 12, 6], [4, 24, 8], [4, 96, 4], [6, 128, 7], [8, 48, 8], [8, 96, 8]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1536.408633531', 'commutator_count': 2, 'commutator_label': '384.18231', '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', '3.1'], 'composition_length': 11, 'conjugacy_classes_known': True, 'counter': 431, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 4, 1, 2], [2, 8, 1, 2], [2, 12, 1, 8], [2, 24, 1, 4], [3, 128, 1, 1], [4, 6, 1, 4], [4, 12, 1, 6], [4, 24, 1, 8], [4, 96, 2, 2], [6, 128, 1, 3], [6, 128, 2, 2], [8, 48, 2, 4], [8, 96, 2, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 18, 'exponent': 24, 'exponents_of_order': [10, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 4], [12, 1, 4]], 'familial': False, 'frattini_label': '16.14', 'frattini_quotient': '192.1538', 'hash': 4761554211639909038, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [4, 8, 6], 'inner_gens': [[108169256548142928628553, 620290262737323972881142, 620448401715139445829696], [187973563956797432597176, 486640968089256833126695, 404103996165445564625280], [79804308132555731044537, 158260292450946206641, 566496110689622789725128]], 'inner_hash': 3421805042093585749, 'inner_nilpotent': False, 'inner_order': 1536, 'inner_split': True, 'inner_tex': 'C_2^3.C_2^5.S_3', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 10], [3, 24], [6, 14], [12, 8], [24, 2]], 'label': '3072.qo', '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': None, 'name': '(C2*C4^2).GL(2,Z/4)', 'ngens': 3, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 66, 'number_divisions': 54, 'number_normal_subgroups': 53, 'number_subgroup_autclasses': 2250, 'number_subgroup_classes': 8594, 'number_subgroups': 92550, 'old_label': None, 'order': 3072, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 223], [3, 128], [4, 672], [6, 896], [8, 1152]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [162070456280039306531152, 0, 0, 0], 'outer_gens': [[54003382328928594648246, 540379163733755425228504, 324192775159775277923903], [133970303632967768771273, 566282149414024274375351, 540592881007778266711975], [108169256548142928633478, 540379163732441483560024, 566496110690936650834248], [108169256548142928628553, 566231180116946706834790, 566496110689622789725128]], 'outer_group': '32.27', 'outer_hash': 27, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [288, 126, 35152, 16577], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\wr C_2', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [3, 12], [4, 2], [6, 20], [12, 4], [24, 4]], 'representations': {'PC': {'code': '299936510141222886588327620902629367009139672213027843623406818507918421826500250988277071166187340909321098643050643767294466727229568', 'gens': [1, 3, 5, 6, 7, 9, 10], 'pres': [11, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 22, 19020, 56102, 13147, 90, 39779, 54046, 109564, 48195, 6296, 1687, 3591, 18056, 55446, 70241, 24052, 25911, 974, 2987, 226, 135175, 38045, 16936, 139929, 137300, 60751, 33042, 11493, 5344, 328, 23242, 5840, 26179]}, 'Perm': {'d': 24, 'gens': [566496110689622789725128, 108169256548142928628553, 486640968089256833126695]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times C_4^2).\\GL(2,\\mathbb{Z}/4)', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}
