-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96800.c', 'ambient_counter': 3, 'ambient_order': 96800, 'ambient_tex': 'C_{11}^2:C_8:C_{10}^2', 'central': True, 'central_factor': False, 'centralizer_order': 96800, 'characteristic': True, 'core_order': 10, 'counter': 339, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '96800.c.9680.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9680.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9680.ba', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7887305892697447099, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 9680, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times D_{11}^2:C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U1', 'Z', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '96800.c', 'aut_centralizer_order': None, 'aut_label': '9680.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['880.a1', '880.b1', '880.c1', '880.d1', '1936.a1', '4840.a1', '4840.b1', '4840.d1', '4840.g1', '4840.i1'], 'contains': ['19360.a1', '48400.a1'], 'core': '9680.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5928, 9708, 3816, 9915], 'generators': [48400, 19360], 'label': '96800.c.9680.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '9680.a1', 'normal_contained_in': ['80.a1', '4840.a1'], 'normal_contains': ['19360.a1', '48400.a1'], 'normalizer': '1.a1', 'old_label': '9680.a1', 'projective_image': '9680.ba', 'quotient_action_image': '1.1', 'quotient_action_kernel': '9680.ba', 'quotient_action_kernel_order': 9680, 'quotient_fusion': None, 'short_label': '9680.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '10.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [4], 'aut_gens': [[1], [7]], 'aut_group': '4.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [9], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [5, 1, 4, 1], [10, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4', '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], [5, 1, 4], [10, 1, 4]], 'center_label': '10.2', 'center_order': 10, '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', '5.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [5, 1, 4, 1], [10, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 10, 'eulerian_function': 1, 'exponent': 10, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 5], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '10.2', 'hash': 2, 'hyperelementary': 10, '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': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 10]], 'label': '10.2', 'linC_count': 4, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 1, 'linQ_dim': 4, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C10', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 10, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 10, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [5, 4], [10, 4]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4], 'outer_gen_pows': [0], 'outer_gens': [[7]], 'outer_group': '4.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 2]], 'representations': {'PC': {'code': 83, 'gens': [1], 'pres': [2, -2, -5, 4]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [16717348]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [131, 504]}, 'Perm': {'d': 7, 'gens': [720, 96]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{10}', 'transitive_degree': 10, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '200.52', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [20, 20, 20, 2, 4, 2, 20], 'aut_gens': [[1, 10, 40, 440], [93541, 24370, 35520, 20880], [3801, 2590, 8880, 91080], [29741, 37550, 280, 93840], [64521, 33050, 400, 96360], [4841, 24230, 52840, 86680], [4801, 72890, 400, 96360], [48161, 55430, 88360, 54120]], 'aut_group': None, 'aut_hash': 5634752407501600181, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3097600, 'aut_permdeg': 781, 'aut_perms': [57209118836984706037929584647529393927966445960084826151464701120656472687585918075905065679133771640609607344860931655718080720994195612343090247028393131022788654967519683556030698050794773809716778478648853885678581852885189324508029733160389036858162346736262763905033882422880784901006114156849500156530056343674872999690166338692097527029671101071429390602664778387164671915197436709980069575564601723440721371832565580029494929058919389165670420114014757869814291809140844979779050509917072391605584556335843670599186221527911052991952192083382338598913736646799727587626966752677292060508818113270509339934425745543487915120585020512675995600181432914552399606659801843519161446226350877606738252751366320048392676409953640010183580267976839662383475470732498465556851154448957144901838329334822316181642957729026961153432661658640646263825693157863340808874853441870749545110666354507480552562229939650211057658928345549411382012788838385283498497511746000661967063034584933158491644975736945908396166491270590236268235646713891843795420069297618417941020765996090927989014461706722573818178553900262127713058084011030562013025013779388547457294331270931360439975637752778886247297518391313835444429454117669230515334072957588911518542233778756493746275747062260289194399474709149440898981381448786285493263582750001643114218604241576996910353366096509240662123570665017469407362796204786589422098821428837781782635031155542542491188552987488413165710433026056576810932409812624259082608467335993089816425170859932715008922369826481596673934053100779284286098336982275627554114875279859960657496756761337676502626369941213101665817749518818721846624596323514495642362096891051492685530380554246631998829713261838576625349911600390575103793027009752209394373962025234912877165575672844067548255673222088973944136772889573590620167802127178861204745086790794440311106396599222384425028912611990463953195594177511447, 18416670030357918900291609396181886547006815334586557473252150544096174946730568165467735193478732690976764112328773576477092162283402376846429826242901760321066047950637320287453417040403542503859409666357552906497495144242219352864733924227887431988237343474266604731051129958452124999436712712450714377251600135858693541778419951190664622279236161644876109994090778373774705860776398475829109582234698900566246506023540174584196914164606585826802664615623787194833472391852434846011652260464393679564097446529125304737650619864865506203933615961519233149930159217000428270711243585422425741803172572441769684894454748508803057320246088273508274035774012365471417693325408871350987457568718739650077649606855632288074878963737249119828469495873316359185709300362357308292648212128454009382539363153314706906185032439461457036055916750210872060267415375352840055489257679999308434324485059149673224436301925215550464680031208162894377811632720664922663038081690927724745962925335408488084398718318621951572117189679355295082348645929075480458206160061079559800808263918357652123570850999392571216929969858011609076557815563781065826993805329178754882134945292205943006830781440353060503111030329310641247901365709403520241038020064712116660910013964847961011078748664435628831854719615650581893889941645638625957862904697762690581237584919399498935339088138726346293024018488049229865377636412334551095047720526919767111613342725822208477146809613348194969535078544936716767664315723908946042591026783100073087644349936923300606666108271907813050020566558820829052284432604916866917060078125308814368896403110058228388653738347231349201374603442348291304478208234703768622778434179216700272641538977934690878125110496949294192042729118158041206121166528164243544527679435489903739748872660859101721763228616278140580265041392372179079341642279089888452737068340259024791794062861383208188722873380473758982786850419386007, 40562582231799197742045056511566565655505097180082519855265805944933620301104913843252584059889057983632171445363156330567804565873756190162493425000999242929132230681666937472635277461230873112636769298088057910207704413134949917865770416514185258656540048831988787040827102580777152911242531807795625251759525528553336150568563765072165775036313817477863820261075227324190808997195095675118908989822345365169136375839309354058131381052947951530837775963874977944994416568440524349872498763709698750021208707974018160711700443502542538596799634492086653935322021072055187402890528910345720588306556906435913460549121839164000367059518794254726875672316477517646139257974511767033118426127585663163271360469343261515195813490409204953760809897015668744857126396990449838919681904679647806191088576930308462990754259535520604218821979140193132111639999905733127058981199649687225444767329680884901062833750065974046716873242281779071848604993961473261753939149907572983055605517956381974901493542666757940855620765049607958365341230290515309777192194369877388105223648492636130546680229066328315796216013098911033349226459149035905314849994331483551426742268534995358906651556611159529900796935496035802892259214428100406444273980085759915968764279977879500286389494117509000108166181064355005345163180993553350825683265228761844253083683726211307655362268495853884849419438256869506303853571644863755751682691967335708142615227976157571106863194725710145898707227355451603054272093883652663830899735186743372200943968671518365071220917557716776928750310034380189623234439414424719208621298179501395759149964072153934502332048851441941162565226396987607577999517682020320856540361983534124141564859485094440390076308305199114829792655019519389007167147713651094914005017888979554236703720902252307081533508807138029230524304365900650087057665031303739872156370475418496655290739977027948150879160373179164639778371603174172, 17709843805288047563660347030959506971979811658153486597736415382324914976099076151352781129917214595649080347911308299206021655162029128810949443980331738021609046667598206204443631219371424690748551556191269603650487587171170188683049598729954015429702393836021122868537097617265748244800632965212204399584478984723703556349416261994175610056768665240839384172669260372620724520261654084003366659442462842090054815804153556837026278677330069227974792903692244002667800312527897725081728147203648399641928045410563600968125531075435789814986880471613688305200646656035690452725256197727541939960137120949973819456163077492450874361582136205687463989129090403283424150067881939999138488816473062484853487003848662452649393345971905952627503495955365417410384286598683584961415823653452597352443736361753565884702292685687060289782843286493408027181049849271785594947723325029665985224332520490777888906978119923775088248046669680141351685905055425328964844365675588332681515032508494317439829737318832220134054957023004268554441558397388683731557651246098833268241668650960114031312119682781525363904248122068670430222663496649827712734570954913903814327971992950381234177886101149478340488192737344795046390042837496305388848213140174007845614387733688479515964671662467676977494462622123672847844348284298091019538736505013530252324098741821978447920504410662013202802764744487382755819876679654756197824969730606381653977118665328029717434709560920073205415770317200455942000867737752721095588617330309346727476580311939131154881821715731521863667894149946176782213628718294152918184345483563507151514091197176568610835620086421840009267684429249204044754392884836993705323643776974497366422737312610913221046988414797775626819390274058839355378193770762043276701261763002649280201380973845338845046246123966710832496463614023633529501731263753003706488278307901627584864054938048589760853397797780966043212075031308798, 24844719071899369860092900537430425538620790918540044845322948758859334050798394354753728501416240932875308932887085925726342136117262563811453108294444118057156698558787940815094074656082031100958329547660907888319475234329167875724809501843991781750346580617781720936987831651643435289774164578657789458815063270963473445679171171141899546176724551314360360545834627952550254630675409537248725026117119956708930411130056351733028765449595455339791891876928762394896769358047875945663751365736897024472489638054603125126234842742547556700932427517672938631863873876023309902728033461343987797656080897628388545750258434008964793384060528364752494969911901131391565194813989643129877464318276334418397887415835361641111471735470305518448318822093603992102708487896412906812459877928039495205892346051530589478664877837669552655965886247202865407971543672635407903628621938021734035202848978224370349206116205005872857094137926905562379693577694097490918200547481287403886600239672748734098792622162514313168489788007576199057807362446325337075023248994291670281130805471939696185353017281424771966229490754778026632952836116490822406412346925778182659305196934668664986263392538337185694888604837508101902599767777307895137648980993540577685784690010978493002966001548968412627427090791198996873061773992045759846980057503037082078389662644997710741615265397873927349386155325066422121163533205427955118146041880520108517691666938336700962484964499221801325257677157061525179745805284217838822132293406673856422094673342024732356021324238420435504114794532442363629965430327119884780940408209541428706152546292090461523481191670329942120106746219371894005198295642669768359158117604750982359742061266613584054473798712177715587589000666776070415080626143498348462622662417420098190066140730908875150548116494940817002058333984793080154489678973758747535571808047439403202599665904451602007588802310210477894499751532033467, 18393604534287818318809107597770416421039894977193612336549570790948970920530313124258558909455719315336242354419414660368189602218809526215316321877509229667236413273494592095656069723037506808355829408293247802848241510799329290633367713270438799162300239333245891895696235574416429407150547812844840502953589357889127906494191244258384724881598351524994671988730910332412871224075589932997020725234213221911772201638411257577483335978937699200217814271311679842193127942666505214072788643532050537042854180531022359785271016803541551226045607550671822155373731753576878279171613514660007022524239023878619724318027153513252191870223591313876291579499169381220418596556861575259062420414982132082145809863819357143065413722734432501075697102189345649911439002164316355580322590349878834589147065209243893391079888012349692934987897456194220744388087350909431767362915653598301652475753416009396288374566238927112639955937964569706676606193655533650108643191044502152555913652814676486539001356526509839336927435207696881108389782091352330585502755278964589470280209613906510652046001562252449597375324799351433121370629611518581684931399597975795441230275028543569846888977969992041057440759547144324585712805525960714290285517372257762860550160104148758058586023494802578602208537527938879607981872253533383084475912938008017510156426858738712344359333968515942691597382934291829722747331767209998322153245655891848068089490811897930758772739177221212692171343407925779420612050221737003612847339589699716854832402586019672952450979738094287037256906695418759573548073800248988131137782029719763919725380353672106706181368469374519682211605320120316057616579109177066337820497077985327972691075324330397970703323259927619971120727296435017982428749228643017473824390327692822900605115436721936527175456243052444154944592845521711943548008459398759555920524276030835500681031563796001133500801720195991637540399602080487, 25085998006417713777020481178824401314390000959667325092884971266469930408720154391357013263463100009013168899439022511471261369605239828972175739455932155267539907796006548632800729127394585294278547977127952410868161726952141068342718682066028196397166573641021210504287564530615546093368054128957408283725263819748010477947500831373140806844407154394493068833238675342913024395498914611629463853711868433461610337816183410392868572371412845487655787447380978549190460958639290726287118631072417566235441721745680699065465659768303232070738239560526268776538820089604613954167464503510630095062913596850431134416448551762700189832561430006426217930928841632025685646691529128416927409491830129130115152806249031475802661782752157552458181604765374493444706505693985603928006987124132122654476639580255289607105048484578727011550734742672948845082036525296866496958311410137012877890548306280150913235265606505462175001073781921618190679423351082510148700906827410645720292534480252130060616133242689128654194583672538674985000542269466363311692648181264872598482417105544849164606685222020916168624588660114338941587008743765807289436716397701233679089044874232845484139281996526196693402681057240846085596682821127775865901605394264248156402645420857610081154227356843483151130194501165941983121081596584123984599043034946378170769102281664721075673459783222748181706757095041549739641595725861535783911777663865009150075865334879815858811264122935100713868069556119864257780842964924407213487721087979329611753301051247866754184409879678734416964300142431210260488897998759487731191589677472811499207492282184840607845368424222352266819857268865523997653936688642761118872346408634280753544690512422969860352797799481050984041349904835654853875333173620465702729995147126578934980068782947333789724852089719396313875658176121116049842314204308746848589500614107220869730262545904126407285240946171512579605202735527601], 'aut_phi_ratio': 88.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 44, 2, 1], [2, 121, 2, 1], [4, 2, 1, 1], [4, 44, 2, 1], [4, 242, 1, 1], [5, 1, 4, 1], [5, 121, 5, 4], [8, 242, 4, 1], [10, 1, 4, 1], [10, 44, 8, 1], [10, 121, 5, 4], [10, 121, 8, 1], [10, 121, 10, 4], [10, 484, 10, 4], [11, 20, 1, 2], [11, 40, 1, 2], [20, 2, 4, 1], [20, 44, 8, 1], [20, 242, 4, 1], [20, 242, 5, 8], [20, 484, 10, 4], [22, 20, 1, 2], [22, 40, 1, 2], [22, 440, 2, 1], [40, 242, 16, 1], [40, 242, 20, 4], [44, 40, 1, 2], [44, 40, 2, 2], [44, 440, 2, 1], [55, 20, 4, 2], [55, 40, 4, 2], [110, 20, 4, 2], [110, 40, 4, 2], [110, 440, 8, 1], [220, 40, 4, 2], [220, 40, 8, 2], [220, 440, 8, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_{11}\\times C_{55}).C_2^3.C_{10}.C_2^6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '160.236', 'autcent_hash': 236, 'autcent_nilpotent': False, 'autcent_order': 160, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times F_5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 220, 'autcentquo_group': None, 'autcentquo_hash': 5713448921273139074, 'autcentquo_nilpotent': False, 'autcentquo_order': 19360, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_{11}^2.C_{10}.C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 44, 2], [2, 121, 2], [4, 2, 1], [4, 44, 2], [4, 242, 1], [5, 1, 4], [5, 121, 20], [8, 242, 4], [10, 1, 4], [10, 44, 8], [10, 121, 68], [10, 484, 40], [11, 20, 2], [11, 40, 2], [20, 2, 4], [20, 44, 8], [20, 242, 44], [20, 484, 40], [22, 20, 2], [22, 40, 2], [22, 440, 2], [40, 242, 96], [44, 40, 6], [44, 440, 2], [55, 20, 8], [55, 40, 8], [110, 20, 8], [110, 40, 8], [110, 440, 8], [220, 40, 24], [220, 440, 8]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '9680.ba', 'commutator_count': 1, 'commutator_label': '484.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1', '11.1', '11.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['19360.h', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 44, 1, 2], [2, 121, 1, 2], [4, 2, 1, 1], [4, 44, 1, 2], [4, 242, 1, 1], [5, 1, 4, 1], [5, 121, 4, 5], [8, 242, 2, 2], [10, 1, 4, 1], [10, 44, 4, 2], [10, 121, 4, 17], [10, 484, 4, 10], [11, 20, 1, 2], [11, 40, 1, 2], [20, 2, 4, 1], [20, 44, 4, 2], [20, 242, 4, 11], [20, 484, 4, 10], [22, 20, 1, 2], [22, 40, 1, 2], [22, 440, 1, 2], [40, 242, 8, 12], [44, 40, 1, 2], [44, 40, 2, 2], [44, 440, 1, 2], [55, 20, 4, 2], [55, 40, 4, 2], [110, 20, 4, 2], [110, 40, 4, 2], [110, 440, 4, 2], [220, 40, 4, 2], [220, 40, 8, 2], [220, 440, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 91494144, 'exponent': 440, 'exponents_of_order': [5, 2, 2], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[40, 0, 24]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': None, 'hash': 6433433583729693702, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 220, 'inner_gen_orders': [10, 4, 11, 22], 'inner_gens': [[1, 270, 35520, 40040], [48661, 10, 44400, 800], [61761, 52890, 40, 440], [57201, 90, 40, 440]], 'inner_hash': 7887305892697447099, 'inner_nilpotent': False, 'inner_order': 9680, 'inner_split': True, 'inner_tex': 'C_2\\times D_{11}^2:C_{10}', 'inner_used': [1, 2, 4], 'irrC_degree': 40, 'irrQ_degree': 160, 'irrQ_dim': 160, 'irrR_degree': 80, 'irrep_stats': [[1, 200], [2, 150], [20, 40], [40, 50]], 'label': '96800.c', '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': 'C11^2:C8:C10^2', '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, 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': 76, 'number_characteristic_subgroups': 36, 'number_conjugacy_classes': 440, 'number_divisions': 116, 'number_normal_subgroups': 182, 'number_subgroup_autclasses': 364, 'number_subgroup_classes': 1040, 'number_subgroups': 61600, 'old_label': None, 'order': 96800, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 331], [4, 332], [5, 2424], [8, 968], [10, 27944], [11, 120], [20, 30368], [22, 1000], [40, 23232], [44, 1120], [55, 480], [110, 4000], [220, 4480]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 20, 'outer_gen_orders': [2, 4, 4, 10], 'outer_gen_pows': [0, 0, 0, 24200], 'outer_gens': [[61601, 61850, 400, 57640], [80961, 61850, 400, 67320], [85801, 86050, 400, 9240], [43561, 48410, 40, 440]], 'outer_group': '320.1595', 'outer_hash': 1595, 'outer_nilpotent': False, 'outer_order': 320, 'outer_permdeg': 11, 'outer_perms': [120, 408367, 294, 8028847], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_{10}.C_2^4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 50], [8, 12], [16, 12], [20, 8], [40, 6], [80, 10], [160, 6], [320, 2]], 'representations': {'PC': {'code': '616523555900916148759214399820771422033509000207498056946533638685762878504933970343989389853466986743154747993519041718250963045280961828666240375868102803181030090039', 'gens': [1, 3, 5, 6], 'pres': [9, 2, 5, 2, 2, 11, 2, 2, 5, 11, 18, 7292, 599546, 74, 2694963, 798852, 87150, 1598404, 8113, 199822, 931, 2162165, 1675094, 4343, 24980, 158, 5045046, 859335, 7332, 58245, 186, 4561927, 1964176, 13561, 133090, 430, 2138408, 3207617, 72602, 356435]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [5063783017457019, 3352440040187918, 16265167320216339, 30551766872799773, 16267516240797404, 44332910602637236, 10522401710269773, 12531822321003912, 33418192856010432]}, 'Perm': {'d': 35, 'gens': [46, 44026240096457147966622872325797491983, 348477377634661013568323939255620250223, 1611308206, 636293381657302016344704923522698291263, 947025426155669667810891924109032960077, 627610133555545546619982789537505887437, 1250408348587825395092330134279121971263, 1557046041894326188638190842187955000477]}}, 'schur_multiplier': [2, 10], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10, 10], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}^2:C_8:C_{10}^2', 'transitive_degree': 440, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '40.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 440, 'aut_gen_orders': [10, 40, 40, 40], 'aut_gens': [[1, 10, 40, 440], [7041, 590, 3840, 1320], [1711, 6850, 2680, 5240], [8551, 1490, 1040, 5120], [7031, 2890, 4760, 4920]], 'aut_group': None, 'aut_hash': 1837177274347552641, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 38720, 'aut_permdeg': 209, 'aut_perms': [395635247047606812764238377487059817317764806624905854877526175855876719122207078853848128053772909132234588486885413521024682743122517267141453891004514463280019051352865195818112205968551411100802760997558697178111367349530866453830107985177724491279413836115665365669165167655954516053711418461578130902908925591511821064945219819053416867022450931718193463756268673667805956383841324889665958, 328454809201550730717100953496871666678070507420076999450030088665398768350362655238405927632111162370216445743282164383504098115649928176918011825928013295811987719307134163726118718000267447148656102188409404796257401914473840039432920531203772330981127463023713572328253124258090529912615040747849711529667096586132361415727126091895020863980414298095781439037176982872120724218955108621294160, 199119777475434917939163306589835338456688372300990599402193010523807501206623106409727854136786517485412432779555189281947400650479818742401989115082524679819773905185074793381090133598937174850152503920628664716849529616972961399280424392610387678082059176234812184540789847342202990753905363482022961893909092874097078479494617485238926802214481230424042242026712986068935149387397473710840373, 329017820536853016862108065503725190080043737836906290663008975614199189765030876641895744966059879461069573767945006272300105852874019112817735894863000915575510333729034423786460345619336092323997403925368119769461646507191407130865229372445093558093232419940351990173546064055964154487579006884446034706493176655139849109321676839737638162891701180434272047846257421998942045063199797532573023], 'aut_phi_ratio': 11.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 22, 4, 1], [2, 121, 1, 2], [4, 242, 2, 1], [5, 121, 1, 4], [10, 121, 1, 12], [10, 242, 4, 4], [11, 20, 2, 1], [11, 40, 2, 1], [20, 242, 2, 4], [22, 20, 2, 1], [22, 40, 2, 1], [22, 220, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.(C_2\\times C_{20}).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': 440, 'autcentquo_group': '9680.bb', 'autcentquo_hash': 4086966246574240694, 'autcentquo_nilpotent': False, 'autcentquo_order': 9680, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_{11}^2:(C_5\\times \\SD_{16})', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 22, 4], [2, 121, 2], [4, 242, 2], [5, 121, 4], [10, 121, 12], [10, 242, 16], [11, 20, 2], [11, 40, 2], [20, 242, 8], [22, 20, 2], [22, 40, 2], [22, 220, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '4840.bt', 'commutator_count': 1, 'commutator_label': '242.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '5.1', '11.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 27, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['4840.bt', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 22, 1, 4], [2, 121, 1, 2], [4, 242, 1, 2], [5, 121, 4, 1], [10, 121, 4, 3], [10, 242, 4, 4], [11, 20, 1, 2], [11, 40, 1, 2], [20, 242, 4, 2], [22, 20, 1, 2], [22, 40, 1, 2], [22, 220, 1, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 7624512, 'exponent': 220, 'exponents_of_order': [4, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[20, 1, 4], [40, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '9680.ba', 'hash': 7887305892697447099, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 220, 'inner_gen_orders': [10, 4, 11, 11], 'inner_gens': [[1, 310, 9160, 5720], [301, 10, 4800, 520], [1001, 5370, 40, 440], [4401, 370, 40, 440]], 'inner_hash': 876640736845914585, 'inner_nilpotent': False, 'inner_order': 4840, 'inner_split': False, 'inner_tex': 'D_{11}^2:C_{10}', 'inner_used': [1, 2], 'irrC_degree': 20, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 20, 'irrep_stats': [[1, 40], [2, 10], [20, 8], [40, 4]], 'label': '9680.ba', '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*D11^2:C10', 'ngens': 7, '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': 35, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 62, 'number_divisions': 32, 'number_normal_subgroups': 40, 'number_subgroup_autclasses': 90, 'number_subgroup_classes': 192, 'number_subgroups': 8908, 'old_label': None, 'order': 9680, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 331], [4, 484], [5, 484], [10, 5324], [11, 120], [20, 1936], [22, 1000]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [8832, 4784], 'outer_gens': [[8851, 10, 6160, 2400], [4371, 4850, 3520, 7720]], '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': 4, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 8], [8, 2], [20, 8], [40, 4]], 'representations': {'PC': {'code': '6727578487317897194034193755965688885035921082267707572778976143823527160576736370300909', 'gens': [1, 3, 5, 6], 'pres': [7, 2, 5, 2, 2, 11, 2, 11, 14, 6512, 20274, 58, 225683, 29410, 320604, 2811, 16818, 725, 240245, 138612, 2203, 19430, 124, 86246, 86253, 5116, 21587]}, 'Perm': {'d': 24, 'gens': [29392299989550486480487, 56473374501715940301606, 83494798612057273536390]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 10], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times D_{11}^2:C_{10}', 'transitive_degree': 44, 'wreath_data': None, 'wreath_product': False}
