-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1984.311', 'ambient_counter': 311, 'ambient_order': 1984, 'ambient_tex': 'C_{124}.C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 496, 'characteristic': True, 'core_order': 124, 'counter': 45, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1984.311.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '124.2', 'subgroup_hash': 2, 'subgroup_order': 124, 'subgroup_tex': 'C_{124}', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '1984.311', 'aut_centralizer_order': 3968, 'aut_label': '16.k1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '60.13', 'aut_weyl_index': 3968, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.d1.a1', '8.g1.a1'], 'contains': ['32.f1.a1', '496.k1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2692, 2236, 4681, 3396, 6912, 5644, 7120, 4356], 'generators': [1018, 64, 16], 'label': '1984.311.16.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': ['8.d1.a1', '8.c1.a1', '8.g1.a1'], 'normal_contains': ['32.f1.a1', '496.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.k1.a1', 'projective_image': '992.37', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '124.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 30, 'aut_gen_orders': [2, 30], 'aut_gens': [[1], [63], [65]], 'aut_group': '60.13', 'aut_hash': 13, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 60, 'aut_permdeg': 12, 'aut_perms': [39916800, 368673], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [31, 1, 30, 1], [62, 1, 30, 1], [124, 1, 60, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_{30}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 30, 'autcent_group': '60.13', 'autcent_hash': 13, 'autcent_nilpotent': True, 'autcent_order': 60, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_{30}', '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], [4, 1, 2], [31, 1, 30], [62, 1, 30], [124, 1, 60]], 'center_label': '124.2', 'center_order': 124, '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', '31.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['31.1', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [31, 1, 30, 1], [62, 1, 30, 1], [124, 1, 60, 1]], 'element_repr_type': 'PC', 'elementary': 62, 'eulerian_function': 1, 'exponent': 124, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 31], 'faithful_reps': [[1, 0, 60]], 'familial': True, 'frattini_label': '2.1', 'frattini_quotient': '62.2', 'hash': 2, 'hyperelementary': 62, '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': 60, 'irrQ_dim': 60, 'irrR_degree': 2, 'irrep_stats': [[1, 124]], 'label': '124.2', 'linC_count': 60, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 32, 'linQ_degree_count': 2, 'linQ_dim': 32, 'linQ_dim_count': 2, 'linR_count': 30, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C124', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 124, 'number_divisions': 6, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 6, 'number_subgroups': 6, 'old_label': None, 'order': 124, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 1], [4, 2], [31, 30], [62, 30], [124, 60]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 30], 'outer_gen_pows': [0, 0], 'outer_gens': [[63], [65]], 'outer_group': '60.13', 'outer_hash': 13, 'outer_nilpotent': True, 'outer_order': 60, 'outer_permdeg': 12, 'outer_perms': [39916800, 368673], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{30}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [4, 31], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [30, 2], [60, 1]], 'representations': {'PC': {'code': 134001029, 'gens': [1], 'pres': [3, -2, -2, -31, 6, 16]}, 'GLFp': {'d': 2, 'p': 61, 'gens': [11891453]}, 'Perm': {'d': 35, 'gens': [903065032356436195533892217733120000000, 7957585794365731759089254400000000, 295495929876537834377785827655680000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [124], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{124}', 'transitive_degree': 124, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 1860, 'aut_gen_orders': [30, 60, 30, 30, 10, 60, 30, 30, 10], 'aut_gens': [[1, 4, 32], [1003, 60, 416], [27, 772, 416], [993, 750, 1568], [19, 300, 1888], [1019, 14, 864], [1003, 1748, 1888], [1009, 726, 416], [1019, 76, 608], [1001, 1836, 864]], 'aut_group': None, 'aut_hash': 7455719972580001064, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 238080, 'aut_permdeg': 512, 'aut_perms': [74376746842624169664390713326047546930812112631551754144784331144923639378153404116423946872553240241984358309874313054384383907244058102012739529574263907704491146008244095515795262090276184834554119011913409654334503919302929589557654707415348373135344737183824778686305896769786079769265584853118887378280909588827731242512997667563610208023879304667978514673114892026306846161784997127731917990497246298583852453974108664593636027510206444885442900972521863507162475483238575344950827226389064496953602362356384982025520292639788364451503740187466039409502951224340181946828062620038554791283657710219497366748497358331201510711378436586440773229258033975102680191723997658081866772315345818934257748054985151245656250853358162840613571230471343436201367532641901275647675326872465106641351410091618018807669236675889410771102990415268298424500683378906891460519237710099862581841457855495334502405550322471552448054833806202280536177975315794910196803172481704163497955059953527509588263915333657792922969847750629523281103392266700719535444667591394348169019442158226167023074053817769479066860573213599661653905777878992433535027794663050386840064159699727055, 7287355842868307935557223493521874873338621197057881099865621349712975726325372879382846340052093896295466943269752667978165958376731630929963926734435069791579343644004572458378845749705622604367209493849400189446836759120292505288363675382799574204679334952114119242488787783210524174108607241769210298315419012896694357608338905846901341676338231453004569093739522672990163368636929031262348864598708989728205511081258258757690398828305260868932331032868262559437311613747073002675354158514486390056532068951608446650619106131713981355461694461204575548908926204883823525129368762485321084604098671080471759541635358445855544918042547696978254456297836354959160761749640299857448221157009677985843839340710096028619281436706577019715035720406017608791389984819904556932780295238099298718827249532620123147144951315024849563231049145782396047347772631569211339987568612982768757682086020997631190088360631588243241549075068397643098311536506223836818259927042279375636567928345768599329313407882581034983343772978263041580801998405907267062492399412104844170033577150664087054675849943945979775731266955953615307056111314513887863002547446193463913393363588759344, 70420061552854538686773082690017099682633048582853490242658968577456203218545395198907652695521560207483768411138954291242330843980189629562752697263411782833432566626295300856893066383575668522520222250451672739247997643788485428039713874252373358846990150877334290904371080718761058432979395531968100516694696414095894522618996533624665308942974875660493988884465889118810822557694527783585052515876331663343282479929677536837569058742626015793782509901494342022106307933878274181652628125355759709788326584074964591008890880859954809973503519683410029372801138621132287172102789951498315690915122449027000004944496094284691913184078423310278862619945303107046346144530308718531952184399314488823738421049098762674240775863898095036084479740022972099973044392492740977713200912872888383083568881721605040137474467075366811731748970156992827323832130599248628216248571861535583951459641214435902039790904621595166854284485729818823606159419072693767237479541181564049563290356375897145277175619128254871469247720553593321574469872018260662066256342666143991338441393602790453741802694014719591806475744291996369480471112447070795552926691943068779091587853781538576, 55712448504842582501326493020400365388552632776618704412012174607577909198286491789590403308085456389481137279287121532550483647609541355087782565289612621634678053358366308342591307017570992665294721467213584077954153039501092345380076354030772556915102321260395753340540923613409038154906076025121658912019391183992061394254762297728382369301826478673937562338934388528443735174614885733944260989085587142331935053303580352153744935027312057267051539622050194885747814502099332070529718517413964492074950655796773399725596831834005654176980522229001145763714946117877320968319847293122575113852070224327698154702156589531770409701596593484257689399227961981843951121759994761416206053115766932918881230272169582779794105785038977366376406582931522503129528471455860162142265616971532852482358214964485871766667320785663246289545710944042073006378592570151997441997861513373983763544996774815670875251069162996376163427327800575549485173001188474824649040042923119187014832740860347953218198331528887021211387346323930154615235861846269387708635148842873851042413357741761745116075395440283644596953984389384556315387273084111552119462038999223615096078863325950720, 75821450267782602575494085586277007307807906862872912770812179846102321852107736737531436449015994163647737542820991641303263211442475114008593702534589387139383829349795355567804532204530979808811145572565036199185580611406033518498216398626138133220139333851035587828208165312457403052527403368981141766839836103842194630419809171670220544890743180545033877009450806685597282148915903703027483585612215466835568345838329880265919695164317194621855640540211839493836226007136299692821588971144420927872619494331738012855510461488133289052385608821917415184163926330915802561523107985270451347485209512054025128809580136532236521497964825076942184911491801267582392940826925913181692953279756335848244168357777522019878513613616901104285284303721589230567401354695722028077690640290517749504176118251089546404800039811506389855549866725175721752278183416946311172217828171184242510694608709837340513591275602154925548789667445826835021301601161417928094559358720564873123182355532645478848466191060752238536201842349354997277623557458276783553738119527787705616499039569809930089636657869529970215871761631887173334491518567545598026526218288891450174336773647962192, 75556964398525534861690934317320881541009317279257779684118591031219840429221525700332987688102728025644409052743461024419326183227316802483934086250784346390712235032722780013939668666171860111460953528871455143267904311607956212180161414975011777548907760319002242643012494472244423290447917025272240615130550052255556075278989192999725685353708390572886136720215051143447706501207796607878616424819411644451742681082608691231199222912143674067800227442001864569633583796761388451241251893014016204266758292915333647514863081047766613868217382236433709935281512227197973451900041829716689695814169457290574641757145801626429564716278949240330666049840393130281754122680473589903868620225749577900833220514497142896820321515072758452864962984076454982574235222265312802451379501408002349197860589598866122800353918753196162618498396637461795113426847890274232082382018260920627760561883831442329112967088723155259919269045324012793246665064002977610583315909293300640256651400140032549340831536158755985686074392653701859856429057933918432990476170304966809136254486133904448742748536972027327056954373450922379760303003962153100486846620267979575562262989675624655, 70109057186798169192696891401064306675252182162180749184273335518424092500871309511540140256373291595139980327275029237078742535356279823500116250321386024645239913317764049099643012954520962758622495899167462095574458836523673469249906356451899800261452303721187582515935098420537402237282566661426913050933875411814494098941637980822296009111552977846635184406153653926549688030549842449662114172283908652733098788985209420103355558020136655371869433556787624540544893960716564025206444029706430621366386939996395834161077951888395092113794235963935058310398255994774902423824234141579156021393873320068432350169931479966555771800924802445752554775150297887847327615469508846351562691249964301723183025336577842942817496192105131408977943530201473195279310237015946672251781040702677438104534315178463941756996989670375543229303648170363813159605767033911734603305966812098710243258034576493739969620339413738986319146601652826680007688976361510079489327841742744819360585114847450942234914078586260144943693862205182864951798407649273136468190301285176212841882867059109294608364836714466142932407960031044930618474953143491863992836507135795932102743711881089967, 75590189082473838576435040916156944239420285732666797927775904888352845783655817194704081165989882409158011653984686208735581457523434173185908406119796725145159334789086085478640623937247664924913048745857565954370179237891621169709023229428549622447858567501714476634171879927942308125913738206383682523698739779827086169284582096874285900430911706062432434775867653157544494632221174681160615921028465858068969827590305011105258980530236747193115736607247160885160000516426973298115174056033856010927752743954292457684877722362899513817218865556043623590163448237353346374959481274474868577623579952688600405983787396085141801439029720350980887115625052879366230483673509098297420052307196170569541598684257563459372740393647945740542409210481929439460176613229248651768357697176187706842772902953681407736786620661984457513174901278263764505081886255164999472890268368709525328277592686168457410380661438259767497946065084568623923734977310890371742208123144658973227279505666567903903385522157107929545440516191510802037449478525674580627725605489344353394983965820478342386634584995835657601059458872421846167276899509769531023409808060431213300381665520525104, 18793217359678997462691427834296942317180097039687229745765230755419030002314210556721074245810080913445959181855802231298494239834586500518259778214297801147490355097785076122593720785402787811763100337586145803194156187464122655557349591583814358361489266894107249528753516072608475897066221537820663873144787376998457891893936156244994173008512920420061544137675279744189607107099982918889238843776069455257921744672274137948840324987091384659213546367809432183337151881315523835074891842559759875596408389073452469361069443003095416515727587256637114145567540279822561386582880496595123122289316959964620016359822238411778720872498603680423982677472576244509083997432265987648869281232249373781404300877336378294858557758114695638223898975777882232922307655099764360297288837287569073366870401290256638635648904659829303094444050695697974037213797249233425673285712618415051858353744182230452164011690088749423843764876869073393026503889872217935511616624890006785931175074458409066395439591327155515637751776848373352318223842595210026254169862380517489127691983481998887186076612564328396811780397962651243121055839579220797463705236279310172741982657053000976], 'aut_phi_ratio': 248.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [4, 2, 1, 4], [4, 4, 4, 1], [4, 124, 4, 1], [8, 62, 8, 1], [31, 2, 15, 1], [62, 2, 15, 7], [124, 4, 15, 4], [124, 4, 120, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{62}.C_{30}.C_2^6.C_2', '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': 930, 'autcentquo_group': '3720.h', 'autcentquo_hash': 2260278060070233462, 'autcentquo_nilpotent': False, 'autcentquo_order': 3720, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times F_{31}', 'cc_stats': [[1, 1, 1], [2, 1, 7], [4, 2, 4], [4, 4, 4], [4, 124, 4], [8, 62, 8], [31, 2, 15], [62, 2, 105], [124, 4, 180]], 'center_label': '8.5', 'center_order': 8, 'central_product': False, 'central_quotient': '248.7', 'commutator_count': 1, 'commutator_label': '124.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '31.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 311, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [4, 2, 1, 4], [4, 4, 2, 2], [4, 124, 2, 2], [8, 62, 4, 2], [31, 2, 15, 1], [62, 2, 15, 7], [124, 4, 15, 4], [124, 4, 60, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 248, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3, 5, 31], 'factors_of_order': [2, 31], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '124.3', 'hash': 311, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 124, 'inner_gen_orders': [2, 4, 31], 'inner_gens': [[1, 1020, 32], [1001, 4, 1952], [1, 68, 32]], 'inner_hash': 7, 'inner_nilpotent': False, 'inner_order': 248, 'inner_split': True, 'inner_tex': 'C_{31}:D_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 252], [4, 60]], 'label': '1984.311', 'linC_count': 11520, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 36, 'linQ_degree_count': 48, 'linQ_dim': 38, 'linQ_dim_count': 126, 'linR_count': 300, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C124.C4^2', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 28, 'number_characteristic_subgroups': 59, 'number_conjugacy_classes': 328, 'number_divisions': 32, 'number_normal_subgroups': 67, 'number_subgroup_autclasses': 98, 'number_subgroup_classes': 114, 'number_subgroups': 1356, 'old_label': None, 'order': 1984, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [4, 520], [8, 496], [31, 30], [62, 210], [124, 720]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 2, 2, 2, 2, 30], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[17, 4, 1952], [1, 20, 1952], [3, 4, 1952], [993, 4, 1952], [1, 6, 1952], [17, 996, 96]], 'outer_group': '960.11394', 'outer_hash': 11394, 'outer_nilpotent': True, 'outer_order': 960, 'outer_permdeg': 20, 'outer_perms': [362880, 121645100408832000, 355687428096000, 1307674368000, 6227020800, 39922593], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5\\times C_{30}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 47, 'pgroup': 0, 'primary_abelian_invariants': [4, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [4, 4], [30, 4], [60, 10]], 'representations': {'PC': {'code': 10305639880323941853191225144827128150000029, 'gens': [1, 3, 6], 'pres': [7, -2, -2, -2, -2, -2, -2, -31, 14, 21422, 58, 675, 80, 20515, 124, 23540]}, 'Perm': {'d': 47, 'gens': [241904185216962617015726114934982849673036782632960000000, 5505283242215565738953730471621640507183805133344192681647, 11244488761356226400912673774128185958124139787059200000000, 4282739321768215207580113554110012329033728000000000, 4282740409880303344173649914852084397847347200000000, 1625611723770265439147580131274978754560000000, 282958192612797845278006145363293]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{124}.C_4^2', 'transitive_degree': 1984, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'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': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 4], 'aut_gens': [[1, 4], [1, 6], [1, 12], [3, 4], [5, 4]], 'aut_group': '32.27', 'aut_hash': 27, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 32, 'aut_permdeg': 8, 'aut_perms': [10880, 16328, 12316, 6781], 'aut_phi_ratio': 4.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 2, 2, 1], [4, 2, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\wr C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [4, 2, 6]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 2, 1, 2], [4, 2, 2, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 3, 'exponent': 4, 'exponents_of_order': [4], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '4.2', 'hash': 4, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2], 'inner_gens': [[1, 12], [9, 4]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': True, 'inner_tex': 'C_2^2', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 2]], 'label': '16.4', 'linC_count': 8, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 5, 'linQ_dim': 4, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C4:C4', 'ngens': 2, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 10, 'number_divisions': 8, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 10, 'number_subgroup_classes': 13, 'number_subgroups': 15, 'old_label': None, 'order': 16, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 3], [4, 12]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [4, 0], 'outer_gens': [[5, 4], [7, 6]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [7, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 8, 'pgroup': 2, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4]], 'representations': {'PC': {'code': 141333, 'gens': [1, 3], 'pres': [4, 2, 2, 2, 2, 8, 146, 34]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [7233580, 26129426]}, 'GLFp': {'d': 3, 'p': 5, 'gens': [1816751, 1282502, 438254, 1565004]}, 'Perm': {'d': 8, 'gens': [1569, 5896, 11520, 16]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 3, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4:C_4', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
