Formats: - HTML - YAML - JSON - 2026-07-20T14:06:18.556395
  • gps_subgroup_search • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '22674816.mj', 'ambient_counter': 322, 'ambient_order': 22674816, 'ambient_tex': 'C_3^6.(C_3\\times S_3\\wr D_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 3779136, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '22674816.mj.6.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3779136.op', 'subgroup_hash': 2776966184764586600, 'subgroup_order': 3779136, 'subgroup_tex': 'C_3^6.S_3\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • gps_subgroup_data • Show schema
    {'ambient': '22674816.mj', 'aut_centralizer_order': None, 'aut_label': '6.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.B', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [148311879831258572617263545887398359486134, 271353676394454377792702129150099764, 10872818880982496732313752133, 109900955613340922550081068540160, 8222838669689168581034339899808375, 116402028746988687111275838076948006921413, 10628380765426167900161457350544321177603, 418802671169936714973312003, 191469869419146555635461657520918225014892, 6790244583891749623177323607624408918, 51704034189144853017744, 17683942790150574557177061504243, 8223143542522567700438361122524824, 8222838654177955983155394012802560, 10333156189529703288896251288337297841869, 2554547282942135043], 'label': '22674816.mj.6.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.B', 'subgroup_fusion': None, 'weyl_group': None}
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 72, 'aut_gen_orders': [18, 18, 36], 'aut_gens': [[1, 2, 12, 72, 1296, 23328, 419904], [2435762, 192781, 2909132, 59508, 1322316, 1470672, 1679616], [3405173, 2600062, 3608940, 2035620, 3773736, 1309788, 144], [1006622, 670477, 2953484, 495828, 3539736, 2629584, 233280]], 'aut_group': '22674816.mj', 'aut_hash': 8826279076269810851, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 22674816, 'aut_permdeg': 1980, 'aut_perms': [176849937370903947423203585691203675312819833873269393733610320037746006834942562570280001303568052833303016603999797269633118371631957941413429224500059173646406077120385143985762678879814751616193259420518631260766200063191910375331217553414663461312784821868312606142306590737699293680545492644399639248168570814933100731465786197170924477259339862819453704947194109804813137001496832938697673894661949815286623683669132224114459786210049386763872975980930563228978693505769406386765288180794932299694176153766571165316288859710906865803114806955464975329238718309208975849830073622478907735233276965056803542180081199318169824003379413584088897593220479983620996094515478442514118728449633896419630777697192026592351780603397319403669374603874382735452404602426184809510171682885312570383261812058948184880088801042224688314626452103979531180162538459447692508411226107018623630668940352837110753367804915098056166586602493158425356152500547083433287135955332230947062908367333502978151630226970388299183311588146850236016572705288130348650002611371113859565112788470232248747452884694552800261444035840559050941411185089364276703377536477423757801786964402723160208601394824771099680063288607702161667429661061660607986683678784955097424879867942232598731468283646975402123321639987015759054945506695195867278409715935323028087585648450377971029326084817991860770920050787274258385777062591639195682817908638106982756545490043140258577110368407757351932685502291323406215668691096480166646797995817633787639486700854637922740629148598699317325363627963894197877197412988786509866567552922838226134286050798948974856339086856094882316650287893834029030876579128094355525426337737338849659845261585778332375412557791132659119210626484645206104981456851698711164349113775828385871993541780905145649407788503872670301737302655259146209068511801592554781429783145154472630526239100432109288313125240778328147454987433854823373673829987790599061021601001498330513563740458585548330695567456482499662713926394132625758648761116025572969895226103920242518989400606298205502701677949872942823470853449383089666060354604584682893677498652633014422969980316370232638215683742728010413391995791065763938791714525029553396135197912713185663721202320118908469349160582160573724788511047371351726929278168938441602278055532531318846605718921337683395607122693107165203557013555262066546245905991000571880309004290594259304493695198455667570088868430724254536545103524607209420638521055587930018612359118892668077717843961676908670337971558546336843933340177248711760056784213999962530646009359171325111766502825069598086004893657080913511303369058247379005159893794998502183738433634393285603377653286223821330018816024885004377371600756802713777177229179982109561210919748537594139067850060554945363882179474817761234126328291950389101639825837340069950882989019228624861483870311813372656913346792851028651471962488094454826591317165906944024558481937181044214285110580364408848771660254803837460572406438707791449228649220320029033141311654786027914474972502781768700260567177026537663020050121848074539458719674033841862981564220552129850432296816392139973616464843082862516084867211785511070981317719916581651271146527582449521512583639522116071722597413517264094213341099197751515280374992306369651731059061699748199687034585705259970777830407701050409227566700398637588500002279771563630366175904309948999475317326094329159434115966525045539406578897924099886960642762222454224540010292931273451020313366044114657827115999852629409057091772585507068538311957513905405180675225348063999547946284962764696997272523280878871838071666034730161659725211041576808750584878508198026646057717650981973547391070979911535439408406227972779411528341652200785174496028411249963533381995843893333670258140235798091096354499815718396782466535776152905603798624643974545393243066378345398520158818407146189840280637797380819863028945556803710533182710294878574928594893270486321462294264634036008417685175507414148449393232749030309176053366681372666500658518819091515814645807060432402642735425658500590111021562073611416803211574827233514849018925819464099510531703161362939077288249937713513403094218555691931779520762333420909593843672596337483240486768196876105036553270708909488165153181563083533626205683473089086982376309488849878428069332466489663698392057356532719057678282328904054726293358278556030680257994300759617604426551005638254275017070332653868056387678928990318457083450242856284746802384455358388876644950504931813004380543677272906301433416178192367943452491505000113267795001582423948398578434836982662436907647753002170013032647796672469962103314331903549940102208650037660495149600803552864751855618806451579341118297716942146994985400605148443714775825236182704425297814606027006423561563490554484626357226849802909006210698533820301953425310971164819364721771034139490699167436577339556455572656540768795324357063657148774939920977882953023931307595877638315988619756280201326921879440421178136251056559162511072646943807775707573260057519450855312789180160649826682200196468593791134909646711184680439354874692156583787770537359343404073509779551607219293608623918449398107208474224065113314233198590783835874025582308550835108369114242136800150771740984515852461140214339203256618806416244363337528463028533239958247654927705946601459104652317020678263984673968367443698437876395789173011594845533795157156340712240947499343980317412813869502995320757827505499611945057145002730543205007298863208206249151104691567271405791859272152237846316559504643232483351864923403176762829429943948704242060161371014968339267777258634030754691290428316370275838154827551, 169042728884141592063068193389141435790659026775317592713891775944429224237516598067807487176868279968117935809236718267144528592735707094691681515112597202926370758675510620796599167957519211981363952461347668778051157874469328090251940230367948044333561867852540342160394887196695036286685606125504013175329408849896083510026908248006331668846360719115607119326602308864832285944426196438699419395060982284551817989875706199336607740296888169685086211464177475936126014296545504363465106381918690318098833325023018903872320462465009179804594329748848906872410886022656784265027110253145905241411606758459553347718696683784437742147321266296229329209099154018038818987594320197123119760205454696066755964627959897051746482883178388314668645667307902377932336507640643305997914955572560798942028539569590846710622697485229353015146476056506056455801925465183635794317787006380707797802233225338184135651700825140092256755037572046017745221533416144400381546829430782253603811616164272961808343270659361358443837891743714121397242615242157572023742888245182712136673138273044767341288086688512222984946299806237692039285349230245469753499666495665216144339572658534611951126350113828421831627824087430662847938268231133400325449289350141238125035088691400375043362793322676902608867088712240198006146222091774356130658693055746517018450374989951227633873828803210943788421692213767716176148420697656947029337887743707230080466567194639659911046755293351091109718554919211742059763838189429542021057872915547231220413418400239085936613347259882594526365340057266161178151784029714952142048673361144811482641991259912682815207643228406433286677905179017921270535216161907328371936245967964553518405041606364404541227217390716054211934293770263785171732803258698414509156481839371742403456076590419749151341810581328897972698431911730639402848445675896950784604170194141803766236869354265218968855526494299196567466640312885582686607327342426796024288194071555622142506160738133022267060563980250297558384476485477180232165964153018679893248091676445720310370072478724446964521509987616553912109206422802453997680736136439682509794967568917503841408314322660402017938428264893862276918769784634339635519147340029757897063721249501100636245382683270955364170243057189874278546931205512028135484278218444060364182144652329783292695965884934197337188962586640369965115087506500445262353823827262966801847912738676837433417623568148231786788209810393247014157943056667531270226738277831662420465618352121666387679862649740696838046225673994234431789282893358335845031875207958893093829786568438628123295308579787760990611547314944255909202213021444342788245873391059975306883961206979508981309555091163990005112733226702276606717463132505225709039884633417850348403856507070740927548845373849776882406395982933695033680350455985609352669666186203616226599805506296221125146424802000929365041591638287880690869496392850256962118368814474112089578008690442820501676929391142625542506624199259807916901211312274236863372449222465354830148198273375403443735153834575144441099126058560794101479920616952134601377436813072509013871631888436116646278036343513742950652169252409371288876702686612858516484231833065266859160855044852364334624517551271757717791117839663610687544261544611751756401304299187525205106107118042386969189140984481839143482127249980176659673328261785811972549712147508934963191277723021563455050488741591546745176159397344752952528317922175701559032310074289544614408142595266137630361189584582188453617923712179909446611652477191036343059926635100356054503735847839999922346041807879205016764057935258882567069195401238725470193638613165154796480682247166963857494466598271940273513326685090757269389175237042397216345833293093514514446387372867211287791658584170379435069193850862136373604282768630628472662287068541332347941981708113670602321594157415599811571308326102817995121228763768206343414584508399667626644563141164796580172439450654858140231575624098781017104376534823033112888788023117667220404393150070929241654805522649260545536447633245581687703536471009533847494539926791470867999315716238332202710474107825178390456559522075018233255558847210415805380794514222930348894748531354375681154638303814294284779236660959155253151551472811165927640687882643356760036617049158353545375122491231229434267718141712256645176126866920340852486178859003962741221602102745784075914826609156222737180211208349229724723245258950482474391813451212214576109858739476196239091161747059676890055131372635672912463810711053594729493963346138291600938162924036421430228753765034628601791619884916495163014865655347588241142351629770352663627941050707103398572108703728899548209940773625376835105037617332609099988674155722088576170031365268839406836461200791940482954304466398361763513057502947534666470041275948337936319818231396838880938702052555612461252001581213766643077471326437817898781447911923221772965328699638748615240663887506583300765471034490247586536619797303136803365046144938952032816095003520724503043611508529753302949171244528851943901694382430390812190841862046489130220619332497322962222546145425088025546131323423446794431389113515600671944867762912853082684662534078406383481788877204876791427794601698543486014900508578233473609746804562087059516408129937969201759113331097800909708576535955568940275040219537191873476704163006484401263956911965365358772074559323844465249228138156878664504183902495144572554746375192219246134830817809066455092611734158664551755151597531516294440947181566073636248101795397410154377605366298720387338496405760886435497301145238791054779444864051561173574716503976635714083011991198906255114730763218361172, 234514722860042683058867593934666246949365025598502680102123458422679288424282933947410898912096175192000020351067494442568834305370915393622302525320501241097117458345742102779322089578156232632479911153062473917614292107873922311985080588956063109051410171434048361080268489187870381908307223015879124319562406185297427074862879558104221341766517951804287579107980874417757944466855293825532918800926569839346321301420667602411538021554393357710641985787990812043295517285958136989866322933036839255160520045230755574170721698440410941888306796324876001032090783741249401213233812388831569639336851667686289817155448322679841018584029163142775754945796521069467438049433576204888786117016342893016733601954359857601062289288838396962137464946557852097090256563131157152867955445833550983460269766257218279679026602896384097942873610288841004122308714292330849466144002533777139236030366615036476586932377108167797030112170493250366407193456340320863950159978885514980463484119527415995019865287735854346726124179327346128142147450973449692325091748223438750801658477524671887458648190688889611872961555251978359455148092052410033420067157522129223626137058854734560121223871809592548682385192116620116454583970242092359456337275140967097811341566126736839535274078393501120596451542326158880513617466807365577526110397966233522315768264043365273941662674655824997512703268620348510731436319376917722689209831205507328515100625821286281755420858612887256459563917139234930443698579575149038530623167494180507473368697224402171830170856763643754125149737135085043390461490225600451111904174521030812451182425876393120977402855557356365948537824415244352226422615795730866536971229127521577678309376770658841098747152269324666994728730635896786542340631584549390356132714574038432650320673528094294159499881437712107915287548037509170924398504291704306815145183615744296178585554237390262694500346262483787836257630881553352232316120834674406597377909980104296013978594208092279877685403276498582894771440444953953050957123143128019527444544891848709510987664281521926130846674866189797219406830192324650469345903661998594780812615327862090181736076241598395951890146478093098582846016568715551891275824090659812109605156443110616895362398751427696204540407008123549288288864440212300590418238614349070699146290675495861355504610399690828619334876072394103071466443333249174381807367287238095868189246340988555321752578550274182771740863022877080195167690566485619176990492697585345331019314371776431804033978100226337206026338910505008285216645961294576185323625980809010770535451631154847032679323454115815333116719180005700925745616401125948474033643961755739494089158541000295426086741688969638600916088313422173310970936379970320049187058408109175801451731417677355919189122930689746397323340732421291535818388575804552868065613202745388205230638474914701169481921341730012116837455738571796624583769512845473085516487836631429476220632329632102402109283068622976141832494009934227789376041336484972162642051259505173611187804621146222428736914403027897321989119760767696340434700675733309562585407393350236734356050174512200248374504310202772458388556133236484951455927887589839637137069957072113208335964145536958211313046088372000341227896541243031462598096930537178624289830815610570966743794205853611060572730096424223326324884535136341593083602668301355753561231300386526524453247990885021157784406182464350408395474292105785227675200326306441806219438252050635105480781816596548138250888763183375208517517295381544315235392259946134176698894980223241664237326021942032089126499858754759630697617240928020208389143838859927179720749694948439950381282038797986835763259617505565166290343224744547296966710606909671089990738626281266181007569953527701690056087550358878299327234805341757763211903588953374391780032805588713998490735586396214474879757253363130933967786516115139369759728247401194023483813103547517567560631774671048251420080132019665584737837954835557788932780748557295245539987000842502834414939946709043828661070091037410802593209166454198147918534625557743066811083980836712988734199183504988220492626464495630644028698082320728739601162868347143972135928779499907969257511199176519702850668726446169636731959320041544074545021450177443565083583633775809538640092727609974831089235839132490606057230818229853027399239667586691180822998257997307976503443497498370386823407255382546036117069571213808039816873988458195718224939523985456462223433203460717291211864632334565779198211203372477389763731084282528997039365143983818902526236042602194308055366266868208097104707160451081951373515277783084843254254713436507730301362490239028087193765016279701429008197883594820962599376253708798251144420307208129071577555459342486594244174679314576565013699675305939032866168815439905706481754556330909125544572643579439809826768827836246002629163517099814646424408149581833993339043769039256095323129040051795259264050901704163261286683808434823661577000742802975949642149169068221481435948985958926064706051281457161070553449950746375182317983609974644126997442846493207795748446967572549767862658571857308851777810818226334219893024094309883731849578399745617304560832751721363975148412836184716721553443019131891171636067012375238174648743966330700850391265771892775846855503111984284965015059615977644211348795685288236031633861610061714739453054006293461683902083075368745104281826303337769124138928142670634437501408045174518278581200346348815804415297498668545228544689557676435073269629389229496266059595891157996192583255921079593730935694330275595627337643794783067516527687135541798291329459171172779015818722482765978265373566420163459746], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 36, 1, 1], [2, 162, 1, 1], [2, 162, 2, 1], [2, 972, 2, 1], [2, 2916, 1, 2], [2, 6561, 1, 1], [3, 8, 1, 2], [3, 8, 2, 1], [3, 16, 1, 1], [3, 32, 1, 1], [3, 36, 1, 1], [3, 72, 2, 1], [3, 144, 1, 1], [3, 162, 2, 1], [4, 17496, 2, 1], [4, 52488, 1, 1], [4, 78732, 2, 1], [4, 236196, 1, 1], [6, 72, 1, 1], [6, 72, 2, 1], [6, 108, 1, 2], [6, 144, 1, 1], [6, 144, 2, 1], [6, 216, 2, 2], [6, 288, 1, 1], [6, 324, 1, 1], [6, 324, 2, 1], [6, 432, 1, 2], [6, 648, 1, 2], [6, 648, 2, 4], [6, 972, 2, 4], [6, 1296, 1, 1], [6, 1458, 2, 2], [6, 1944, 2, 2], [6, 2916, 1, 1], [6, 2916, 2, 3], [6, 3888, 2, 2], [6, 5832, 1, 1], [6, 5832, 2, 1], [6, 8748, 1, 2], [6, 8748, 2, 2], [6, 11664, 1, 2], [6, 13122, 2, 1], [6, 17496, 2, 1], [6, 26244, 1, 1], [9, 24, 1, 1], [9, 24, 3, 1], [9, 48, 1, 1], [9, 48, 2, 1], [9, 72, 1, 2], [9, 72, 2, 1], [9, 96, 1, 1], [9, 96, 2, 1], [9, 96, 3, 2], [9, 144, 1, 1], [9, 144, 2, 2], [9, 144, 3, 1], [9, 192, 1, 1], [9, 216, 2, 1], [9, 288, 1, 2], [9, 288, 2, 3], [9, 288, 3, 2], [9, 432, 2, 3], [9, 432, 3, 1], [9, 576, 1, 1], [9, 576, 3, 1], [9, 648, 2, 4], [9, 864, 2, 3], [9, 864, 3, 2], [9, 1296, 2, 2], [9, 1728, 2, 1], [9, 1728, 3, 1], [9, 2592, 2, 3], [12, 34992, 2, 1], [12, 52488, 2, 2], [12, 104976, 1, 1], [12, 157464, 2, 1], [18, 216, 1, 3], [18, 216, 2, 1], [18, 432, 2, 5], [18, 432, 3, 1], [18, 648, 2, 4], [18, 864, 1, 3], [18, 864, 2, 1], [18, 864, 3, 1], [18, 1296, 2, 8], [18, 1296, 3, 2], [18, 1944, 1, 1], [18, 1944, 2, 11], [18, 1944, 3, 1], [18, 2592, 2, 4], [18, 2592, 3, 3], [18, 3888, 1, 1], [18, 3888, 2, 12], [18, 3888, 3, 1], [18, 5832, 1, 2], [18, 5832, 2, 11], [18, 7776, 2, 3], [18, 11664, 1, 1], [18, 11664, 2, 5], [18, 11664, 3, 2], [18, 11664, 6, 1], [18, 17496, 1, 3], [18, 17496, 2, 3], [18, 23328, 2, 1], [18, 23328, 3, 2], [18, 34992, 2, 2], [18, 69984, 2, 1], [36, 104976, 2, 3], [36, 104976, 3, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^6.(C_3\\times S_3\\wr D_4)', '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': 72, 'autcentquo_group': '22674816.mj', 'autcentquo_hash': 8826279076269810851, 'autcentquo_nilpotent': False, 'autcentquo_order': 22674816, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^6.(C_3\\times S_3\\wr D_4)', 'cc_stats': [[1, 1, 1], [2, 36, 1], [2, 162, 3], [2, 972, 2], [2, 2916, 2], [2, 6561, 1], [3, 8, 4], [3, 16, 1], [3, 32, 1], [3, 36, 1], [3, 72, 2], [3, 144, 1], [3, 162, 2], [4, 17496, 2], [4, 52488, 1], [4, 78732, 2], [4, 236196, 1], [6, 72, 3], [6, 108, 2], [6, 144, 3], [6, 216, 4], [6, 288, 1], [6, 324, 3], [6, 432, 2], [6, 648, 10], [6, 972, 8], [6, 1296, 1], [6, 1458, 4], [6, 1944, 4], [6, 2916, 7], [6, 3888, 4], [6, 5832, 3], [6, 8748, 6], [6, 11664, 2], [6, 13122, 2], [6, 17496, 2], [6, 26244, 1], [9, 24, 4], [9, 48, 3], [9, 72, 4], [9, 96, 9], [9, 144, 8], [9, 192, 1], [9, 216, 2], [9, 288, 14], [9, 432, 9], [9, 576, 4], [9, 648, 8], [9, 864, 12], [9, 1296, 4], [9, 1728, 5], [9, 2592, 6], [12, 34992, 2], [12, 52488, 4], [12, 104976, 1], [12, 157464, 2], [18, 216, 5], [18, 432, 13], [18, 648, 8], [18, 864, 8], [18, 1296, 22], [18, 1944, 26], [18, 2592, 17], [18, 3888, 28], [18, 5832, 24], [18, 7776, 6], [18, 11664, 23], [18, 17496, 9], [18, 23328, 8], [18, 34992, 4], [18, 69984, 2], [36, 104976, 9]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '3779136.op', 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 16, 'conjugacy_classes_known': True, 'counter': 380, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 36, 1, 1], [2, 162, 1, 3], [2, 972, 1, 2], [2, 2916, 1, 2], [2, 6561, 1, 1], [3, 8, 1, 4], [3, 16, 1, 1], [3, 32, 1, 1], [3, 36, 1, 1], [3, 72, 2, 1], [3, 144, 1, 1], [3, 162, 1, 2], [4, 17496, 1, 2], [4, 52488, 1, 1], [4, 78732, 1, 2], [4, 236196, 1, 1], [6, 72, 1, 3], [6, 108, 2, 1], [6, 144, 1, 3], [6, 216, 2, 2], [6, 288, 1, 1], [6, 324, 1, 1], [6, 324, 2, 1], [6, 432, 2, 1], [6, 648, 1, 6], [6, 648, 2, 2], [6, 972, 2, 4], [6, 1296, 1, 1], [6, 1458, 2, 2], [6, 1944, 2, 2], [6, 2916, 1, 5], [6, 2916, 2, 1], [6, 3888, 1, 4], [6, 5832, 1, 1], [6, 5832, 2, 1], [6, 8748, 2, 3], [6, 11664, 1, 2], [6, 13122, 1, 2], [6, 17496, 1, 2], [6, 26244, 1, 1], [9, 24, 1, 1], [9, 24, 3, 1], [9, 48, 1, 3], [9, 72, 1, 2], [9, 72, 2, 1], [9, 96, 1, 3], [9, 96, 3, 2], [9, 144, 1, 1], [9, 144, 2, 2], [9, 144, 3, 1], [9, 192, 1, 1], [9, 216, 2, 1], [9, 288, 1, 4], [9, 288, 2, 2], [9, 288, 3, 2], [9, 432, 2, 3], [9, 432, 3, 1], [9, 576, 1, 1], [9, 576, 3, 1], [9, 648, 2, 4], [9, 864, 2, 3], [9, 864, 6, 1], [9, 1296, 1, 4], [9, 1728, 2, 1], [9, 1728, 3, 1], [9, 2592, 1, 2], [9, 2592, 2, 2], [12, 34992, 1, 2], [12, 52488, 2, 2], [12, 104976, 1, 1], [12, 157464, 1, 2], [18, 216, 1, 3], [18, 216, 2, 1], [18, 432, 1, 6], [18, 432, 2, 2], [18, 432, 3, 1], [18, 648, 2, 4], [18, 864, 1, 3], [18, 864, 2, 1], [18, 864, 3, 1], [18, 1296, 1, 2], [18, 1296, 2, 7], [18, 1296, 6, 1], [18, 1944, 1, 3], [18, 1944, 2, 10], [18, 1944, 3, 1], [18, 2592, 1, 2], [18, 2592, 2, 3], [18, 2592, 3, 1], [18, 2592, 6, 1], [18, 3888, 1, 3], [18, 3888, 2, 11], [18, 3888, 3, 1], [18, 5832, 1, 2], [18, 5832, 2, 11], [18, 7776, 2, 3], [18, 11664, 1, 7], [18, 11664, 2, 2], [18, 11664, 3, 4], [18, 17496, 1, 1], [18, 17496, 2, 4], [18, 23328, 1, 2], [18, 23328, 3, 2], [18, 34992, 2, 2], [18, 69984, 1, 2], [36, 104976, 1, 2], [36, 104976, 2, 2], [36, 104976, 3, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [10, 6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 0, 16], [24, 1, 20], [48, 0, 30], [48, 1, 21], [72, 1, 8], [96, 0, 24], [96, 1, 18], [144, 1, 14], [192, 0, 2], [192, 1, 4], [288, 1, 20], [576, 1, 3]], 'familial': False, 'frattini_label': '81.15', 'frattini_quotient': '46656.z', 'hash': 2776966184764586600, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [18, 36, 6, 18, 18, 18, 9], 'inner_gens': [[1, 2592142, 3745740, 3028644, 1259496, 1317420, 1008], [1031561, 2, 249612, 1679436, 3709440, 1971216, 326592], [477937, 334538, 12, 1635912, 294192, 3195936, 2099520], [2035981, 1894646, 2587836, 72, 208656, 816480, 3359232], [3569401, 2451746, 150348, 235944, 1296, 2916000, 419904], [78445, 1994546, 1026444, 3405960, 1307664, 23328, 3359232], [420193, 513218, 2099532, 839880, 1296, 863136, 419904]], 'inner_hash': 2776966184764586600, 'inner_nilpotent': False, 'inner_order': 3779136, 'inner_split': True, 'inner_tex': 'C_3^6.S_3\\wr C_2^2', 'inner_used': [1, 2, 4], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 8], [2, 22], [4, 30], [8, 100], [16, 51], [24, 36], [32, 22], [48, 51], [64, 1], [72, 8], [96, 42], [144, 14], [192, 6], [288, 20], [576, 3]], 'label': '3779136.op', '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': 'C3^6.S3wrC2^2', 'ngens': 16, '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, 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': 221, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 414, 'number_divisions': 252, 'number_normal_subgroups': 63, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 3779136, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 14859], [3, 728], [4, 481140], [6, 249768], [9, 58320], [12, 699840], [18, 1329696], [36, 944784]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [6], 'outer_gen_pows': [0], 'outer_gens': [[1571186, 3569905, 3082652, 1740708, 2582316, 3570192, 2099520]], 'outer_group': '6.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 6, 'outer_permdeg': 5, 'outer_perms': [28], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 14], [4, 14], [8, 30], [16, 59], [24, 8], [32, 22], [48, 20], [64, 9], [72, 12], [96, 18], [144, 5], [192, 7], [288, 13], [384, 1], [432, 4], [576, 3], [864, 4], [1728, 1]], 'representations': {'PC': {'code': '167619343545358213226370812599431131594483053895977702116269305423618597768000143731492727666560798840828238101128660687771150733945385236135684570873851161976131506213551665838733061807505171696543002894678972657199036294551898240519638320814716294628958688777899133618771327925711360788331663715086912506066778850463072485784254362710071560924034830601051707575127725401118910624038802981754702139708626440524465633609878159976688742116589699023069775879640319856354709421497100241677555571241328335971757242012546232977376350424439781169275206350547648302437214113687768345455', 'gens': [1, 2, 4, 6, 9, 12, 15], 'pres': [16, 2, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 39783552, 82948545, 81, 126636866, 38589730, 239727363, 7987603, 12792035, 179, 124452484, 5635220, 56307396, 290749829, 80612949, 41950693, 13087349, 1152933, 277, 47029254, 70689046, 16166, 6774, 4774, 438, 161243143, 497687, 9271, 181367432, 267079704, 59393128, 3530360, 101160, 417400, 424, 29998089, 22440985, 101191721, 69177, 69193, 46169, 633, 24634378, 38042, 228154, 38106, 252944651, 189236763, 52628011, 51135035, 22581579, 2177371, 432139, 95195, 571, 262559244, 349360156, 4852268, 1617468, 1617484, 1078364, 60044, 828, 1741837, 282175517, 15676461, 5225533, 871005, 48525, 241934, 39191070, 50388526, 41990462, 29393358, 11197534, 34750, 958, 110607, 17915935, 161243183, 53747775, 8958047, 27839]}, 'Perm': {'d': 36, 'gens': [180521012690507743354076296377936576419014, 148317592244206145496673191542834728129946, 201808721575339296262234372780445702880269]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 108, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6.S_3\\wr C_2^2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 72, 'aut_gen_orders': [18, 18, 36], 'aut_gens': [[10341559710233054493134541928070270514932, 116402028737842036772929287354544384054773, 297539038794244101560037845226962645183757], [10341559710237248103881856892595945932535, 42247319343021719307074191646154195549813, 244048435616148696543643428893473878692668], [191468494787246195873979803215743350179345, 95735732914962282284234659076128213673970, 95733848183496167046094071919977363471504], [339786086637375768470520602767931290460163, 159556232855746276054893328282476031099587, 159557591096606382292863491650499145519507]], 'aut_group': '22674816.mj', 'aut_hash': 8826279076269810851, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 22674816, 'aut_permdeg': 2124, 'aut_perms': [272367466177602902946883201264413555770732514828579643914594765910408400448137910140527353209046036912674061318728283380410429396268728152692813441157398790692599073724492817728588925422385724158343884993576695513298774248237384739687989529476218235096406988189230469283640588050431030859767445991491386683177560353529396999527668149179331465442107621196151822553574655760173175679185494677074311728855243514501823784702904295080373782434888832788023337879587205637364728429905565393311333095746357779898505739357779564129663231197096961186953834955435768283530674215136709651468493374247946134862459387274734660821757327555217779165470051564959573196650571280811826781179056265201184729038397808784682319940695900731066170567970670570612177852244435748361460896160695730441860010359609223328218204075814900408807581765587377909935941516535842294255667301914155847558331641923337290870911859024274155982683385684523170825391341948332525075548924943723197592204786709023893899489043665632840477865244015193995702690432202814704225884529599291263661610057260338074892076179491406333291672860855871133554989011501430464824541609141167669741736374764423827849329228090875795464286927325796931495035245121938439627990266529130342736884844594593421457156462911580864245566387115179227495065687299421804841648697621649514016668565764239662264107260967564702047314300678573590101016046931617279619111880595107389210475556939893036202039691803683176458024897236132245696734405834481248529035724952331486108942839977114809845898676239636405863421813897797797057329483879731824456575654901495654680977222521078937047011487947922146386301510778816670249267411365865313962150082673102867207595549882715716641597149701049616476308755283630637184353322806834662595432723024509634070700670920492244926589427456458614186761258762732077580571358813263245782932411976246155352801504944978623723704838841544610404901242672420739513126702858522184158115428735162234199324515630514386254075347530367406495626106826583835459666870201477971496930178302288798794284009612261269776463281397236927805841884805419709108852062196031913597667295034755785715678862689617830165200239437657792968167164932614274897295374520696676680861126927163519467923879795973736237718709861703069943791074033127984775990873260194178815683100894363828672241128966265318503251064368479403391016053177772644678523658387228809759370131597619142908551439179885197510768432551232330719229668949348616568262332993227489117713289711679868823127035851949409545501084401132721291530061191990677112019503788014133909349088284064290370468530823800699389721030367419624575897873929808954877641692757074884256129794128430658173876450212724575989041198280314213604591829314377731096775397626445681654972448551192133826884219979640262816338018943456579841838481706828664532432117628757201955417736829230709564335341123398270695836071770581181599489838866777274929076698529453309486229705806246579683640598829941609520363098086928579680256177244800200390526121805061424075002043822065443659337611478888098595591210154892447679863014959851980755910863556291127264032664602419177119542986815664707866634406818055534221106109824505215987566722557962262883468186463381632114586599319755170196801314219499973752952224027702692038067944655075077533385755437563735577867634096962364389680498948966362168446487707977364470343306271665411155157704721849629322184412921823150760277473288700982474087396556763547403785663316178414723638853622867993939477755897979450753216679585066253508951425136346290252960013241955373210534112878656849878706238500667686553268636785865071355197800838683621163852171671428051989100784346842821561658335652277189041319940876242576433850893280444133563474136698210392772430175451801651879118078142501935393003968266300086301499902016942491282219669549391259781664448258826958481399334930744772048925945809577569665088444928784357312245417370744986075377808248969463554041437399357622967176778935019242917617043467672016301085051959877282074571531266829172469549486178304665761900222260136184964991208468784503116557141880425432259163504596337967933345282448690239268639721230965503125254914814727341398964947532574967773276730088723685109981908800303895913499940904131827419205798191496279997107300759486188667908503546312346593824847822181461952602865179284878849588474008487120104674108491892018736703133558594780427254982298298333469381626223852504359038655001451450176374476577724306176451822913601486282910211141145866666566971949400446036810780244082794753895302588873637110056969106530417967393449281634830516644214915033045990424745490026819631299090527532365950875271992240235655866770053223231365758392612656692869704886022942188254247796240746474116944799990782738180132335457272937038540969656028246633338836241426414831903793726087484448103355135449565152134806519572351112667719212748012073900044058937730172511071551059495135389504499151728481772353920307047119555415981152863780849934973148694509326881490894640703575954515974056405878514004515690356602158754098355701236276501761380115570202757727378027110437937960385031762690970652649367880931768618343360279078490573855027553390022320508188293971446544181309534824166749388833921266872171789616381251692081098551666973332694569591124479102249270026565829306601069753478255944249827597306599061890702690210505391657482869070034190618671661178445723653556434676090373613000429771975717154195959078213711842657679210209490608939001526309356712999881004106386018336412522511715983936765951647468398991842051630782887571120668044837929046373660071628483968504429495334602367079792185769900490935098541306750998768291812208993486559968703309242588602312836762634815559565669886735733219553180484572605888871169283043536061396546355819839205815452696816556084822922519186937499022214337163343797773022707298220685582878754522916590344685889693310045490397465178543462716016498412764399714488071837482057282663106140232437229820878774242837011433811274682369648716278064639352705730242758363877470448832870541528685058947486875197187949261847866215198021433081822285880952319808744724597482851537315672137707577495903507534243, 89507669969572423949631147892308442453233817974626563531380273310321897396333069376454939640138417167791413343838733677678686677512749906630715067144573118274134920818485058367910145510185132895313424465007180333261563291130916750573676779869473830659222993826282751287390391765139148595305199336087554738711268133294167083178534472707194865960306846151488607887924355458433037583125619556106931828057813634608907622070199217714543500899648660582848983655601383154422255756514730880783250849624492462095431420513378567969077639251484117454206378400324553143321235869878584091155234424836937754417217857749026151142613094445570346478425803863075346193378346141835134393207961358879337326110030455635898812551345455919763997823846503604238177885278377067975958228750721253599676032539522349135287254085195181686399232231097291431592128855080307632029888322526551866646713607266612801445324022831670793857129039347339493453129095836354615198079785376994892638902994297557666907771532449772058020418573777922467213991585712042964208711298767596497568465260507303266889908447364563454667507978290411566795891419943281917704101465589357346248613865030860570259641768360110558061986181848994658069321327638987959586895291280090244160785906299994440708893218925282751585933981176893686153832874310498077269723949553239461821697512975501035570192964674293801724164656965866736998729843201464330013408017892724586087793761670882911225886170104803588498820124264916869877856736656233116819487690261141677574604404341089286066679117551183867333603647361715649512462063559845516116906260038740933423330138534039158156437945060423349144340854101708986168535930758797844177110989818861105456058456701407467474093364448893893559528589565972315265319453132246115006102972199735934649931522426581802011101944852206042491832521293039860140040332966318308675106912612013516270073839471565094833881606338792170584876238343979384959916689226345491830553274896608301687756664085588305383891573179212130678632569270884974503235441754219096908776688719680962318939938311137547680051166357761482821298363914817361905024476579519177283195453943781701166349861714803398502346075402560989498976251678014299397464764347292185277860177249676206628140701343800770350928024515448181251284515205017378891603430054631049719445811093627289276192852154238155589864005687076443848757180378098946264765573228833317837823568313548156967830258010617237469567783399628368954105601787719546614853306900406198842941398727469857415183496936034323122961073100079375150901116408563242728270421351696132334433625110224128904671534626697201625063228914110503474159972480601166678642698671428565270847834056624384133647715126519657117943799190888570738878733168597000015060978484616989177145848125675465596217288365289734733404059205533426871363218263280149222983140933981650606862091871795404410238514444258760681380638528283671849501754267404142274853226559865969079000755670929504099833958622175131746237156936403671367022733298271922387408947935690435987212186830348804883668963501035235204483417051819930634378795277568904468887197342556957485588058482343715003520689277170201986144071125681643713521491606092596655068063211297238563872664137881139492019729263682443845818620953488805996921517510213963197286959609940000067340189053519406907394659307113362766860986350867437026931260438434377850851680674100194958735387364355274567235433712218146463298415057878916208233371185697539459438863892442879446562033309244194106442515657363628689975346216436941755160412610944405192051594179513934684529596534485492341794817497664871014501357175853816115516258299714330222575160525937348124855902159187019957878134453144169582966393169245903510524998144988273701343872683429511119599550183731436450615714562263946263879699957605767387262129477119900152265510208848558240898769418352910111764962271137105414112935984362239631101754529113296735173174520484503017344763097682650310330933303619770632213509836919767681363475797475561925292692779807162236377438156182291236458494203781462331161194749890837006998160563645138353041482553750118587003404796041573868463666922604849435449486176398084656538990000155178210867188753999378603460480989117366629501734790449579576380302436905498271136207947990934779792835540407650290285956762477317456396900848634437468341689858195875255340987888570960488553290860302569572414285644466042243206713719034750657452660673273733334750879313658728634403895025734438770030352770379960603315763657558643455492440214328208999492879250755953502169036938456588603798542143976672343226843424888102171506882134509474202510192043521126774272956761914540845699827644568649368882740367858147050512465361309797062978891149904462385324995098098686441016592080151198929496789683240740638097715576143781119144817552043726152886862877530383294206830292704906255576694962590599844321086529422822641585991494740097409270774467579562420979512404910588069464772737965582766410201540336115939291123429236035337451130457634465339692630249053624888932893111987355823587308906610603986753467235131318870404495814490895798099089847685785154646167821717723043361071844749891343882407493152623509469415397949725256549847393099064501335338475227275945853906288516837483415951154232362527272098422629625092466681076851785441545271332053989282374240025410905870245047858627198608023171438076920331749025934196214373406834805551418713242915636416018310183627923753776974444633302074414015038474438962783139914341870791073878752739120555525687641932461144270630504112304576437424245800959071997371696162880908651569844513358242372945523402485152892510456335974792642405012650605555660316023481727515971844439543837956276422161579250195308818383931130135486602508585976297860732642776065191657747030368182862994150252558710439558971101584698312256070938591216821408183998796731077131338823577495583736477468412413364365019131572128607276604969731985063233181884123194868220086242888053407693619071377085333741644727223323587257860968755500895761425788165828911016618988543876683314845081653947427233312977571840530932194295505133399888747436111386828125830004510912396437926557124110055846582232294, 42485687302247790959593368148036873307475731861940672362343019760729051662775459953060380870200955866757424490279871751475393915976792688476067216253247424280879006164693276631961520826702474086009458136193114203169625930622838887545444551596012591691825532699119092291175549930623461305561665349241085101103308473247509496634190418388202976778198461366307648433626783426976109463756788486085131480722591918432978482183477360168779910422657674361818131179692576435120754890174334092335772360359371426278014492099573938002496980437039978721780084135881140172986059239177824111810569232659116313559843739753753438845041895461949166245159826577186206204345899572516426420863406128045414977013215885254691856131330734151900094473833597009076595893397333463484545555790661753325742671339993142011582489290578618839044900803210695576841686869479171115704925884696040404393671036206616966559943506636364384495859981239091628548011901257989523511668020790767733845754858679801959110150984989707016124906375156839663158711416493446271832567026015874107640735838561014429193088300726107868875073568182193960252971543288048544094198488324003645601653097406338437109252741893308554505253309557917890330397593103944237961182619289432486911387098618870095513606891108642075854668687674382976008372689660577203882471706164189680584033011462941747318815250673552121556571771222647846346131531816958294502028006424220548092369575802137558542950578265801391678053861650519764736073206721411754767708965061467790592406432867606971258330027911747358435122551485239374472048933942158337794592310638472412831815125713376055248276115126284432503161829793231363229996305804955505988246765357216246898493726430310874582645919519124579139127646852990142692074450880866797318347293616762769584791786675531828011045156099970198482009170512618565954895544517831185973118649621039357424087908527898530430808573139324878368887830920803835628113650286134585263925748411501306008826849204299584383238067589350433935946289798996509666378447667770118296313827977510454884475592933131620953248130223182290045147159578626140985726898171426134671700074355571986747154616935998593557549220398315766226940111073769120942170324651789612780764933474374249272754700893789887866443936335060017951356163995671556126118815127888191102367811607043737558596842080241786806622643249699677648388636516851774781828215089803841337904674391852711536247658291882578307342907818952075636408564792291645065233508075320279083310565090158514085108425213850141654265716060929156076366701381990850339766316983832606105078062181284367255513403716468584352449063602320698305958552693075053570061747537337194882721095163571906677981081844380930108260890594815525710743033554584963226386595914218071902088476662005867766300059760852370979900667470295539984241614302494770525725988922208209710240811779154028235061664418901823989724006081039069627192302222129018671824415695317680232785969209516936501645923554405030605457646302845447762162049728290004818552546771069580089644227466873193664220631260368837933180422431903803883623929815875808331520522212849769600372083334246390607189604085786896107320274120475213773879977149446194253781150840552176817559286284088010349422086426366846995663359159472096760864646443749767975220407343569174140473882722394556228358046051133113590362646120083261003064292364788480651516511499320833468222461369294336951735799739092002316483264968454536263957671545807097586798117240588117302881081041719982458164245632780512008340348679401271131358489770314512562317427285208444404708587997458952907049312363524719440704776056332152723038044593267646672725099820694791355706573579343027495378607296057613846826614434716222243864680959361506617915381701647002579075360490552864177136195712329823495519372248995444246433069291623272452091023362534010370294509273445429861261877686285857598117654654453440560250206685774184305037550980198947701512494905492818658182358907266175955774925664658462325376798574076748492448765721891570114050454988564288492558485125836946802074462752798181944677480928230384566910442930500842128905000563609674978178811781691623114113186016581974149165660312691167078394181969941245320116798524490108346045184550840548537756150606818580554844489670227529612471715698663680218927169344550099038761382312253073613971704110473204569500492471718866058589702497147880655205216007704207681168666554194980366534774617960560085233478084893626566087226874017801874476539919857672039579669648852214814428875111895155627284324836696294981870713622528604835729255332388896006565630880853666011632254876990918261127656677987836071030571027089257426929007146179256945658207614947543943768151413918748728978079846259869743782918088954061673898032667441894991554884110660668154087438764079528239305020046985698301185875084448454189093688870010797588594375544234944439845690976058630646860949751706653189529592715941145532952578358120727836293906881101902673441196399850979171107338077275514204312489146577124668105798559074025940724805413019588836853327105361410714678024316762247637697104772514869693362630737578548347248109654709375920850773445361247064178409831056439887912147036968493675710881814453438031406291665408447762018644897926189500527578703640371571760118307063337192655593930034124332045994702451917960452415860236283658516369361765239152643173487358637070108398290563106973236763272712190001090630500502761941094917792367000867563727052758459599618494981455378514418169661458821701797760404355598809680960025440328998932144846161059386402999047569993389236949361987270293805131122927402362797240681375388742182894702745964164598929153737625004987134258670488864629187895858152242326807561757549171486145972785007170689285734029605604565192220058682656307723425871122179136574978942340384058520668391603550196111036221738779917850606699979606050014045029585024867826663569175010756545119853417887304156633511867491286587984017553268622488685165431578586780621245587704136014611786506242982409459311774305392909243078825496198439972812384209120193805781590252958304592565906058758559325871919670426163546102563427718211834610539267408501253219366661225802], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 36, 1, 1], [2, 108, 1, 1], [2, 162, 1, 1], [2, 324, 1, 1], [2, 1944, 1, 2], [2, 2916, 1, 2], [2, 6561, 1, 1], [2, 8748, 1, 1], [3, 8, 1, 2], [3, 16, 1, 2], [3, 32, 1, 1], [3, 36, 1, 3], [3, 81, 1, 2], [3, 108, 1, 2], [3, 144, 1, 6], [3, 216, 1, 2], [3, 324, 1, 1], [4, 972, 1, 1], [4, 17496, 1, 1], [4, 34992, 1, 1], [4, 52488, 1, 1], [4, 78732, 1, 1], [4, 104976, 1, 1], [4, 157464, 1, 1], [4, 236196, 1, 1], [6, 72, 1, 1], [6, 108, 1, 2], [6, 144, 1, 2], [6, 216, 1, 3], [6, 288, 1, 2], [6, 324, 1, 5], [6, 432, 1, 10], [6, 648, 1, 9], [6, 864, 1, 4], [6, 972, 1, 6], [6, 1296, 1, 13], [6, 1458, 1, 2], [6, 1944, 1, 15], [6, 2916, 1, 13], [6, 3888, 1, 13], [6, 5832, 1, 14], [6, 6561, 1, 2], [6, 7776, 1, 3], [6, 8748, 1, 6], [6, 11664, 1, 11], [6, 17496, 1, 14], [6, 23328, 1, 2], [6, 26244, 1, 10], [6, 34992, 1, 2], [6, 52488, 1, 2], [8, 944784, 1, 1], [9, 24, 1, 1], [9, 48, 1, 1], [9, 72, 1, 3], [9, 96, 1, 2], [9, 144, 1, 6], [9, 192, 1, 2], [9, 216, 1, 2], [9, 288, 1, 10], [9, 432, 1, 10], [9, 576, 1, 10], [9, 648, 1, 6], [9, 864, 1, 19], [9, 1296, 1, 13], [9, 1728, 1, 14], [9, 2592, 1, 10], [9, 3456, 1, 3], [9, 5184, 1, 12], [12, 3888, 1, 2], [12, 5832, 1, 2], [12, 8748, 1, 2], [12, 11664, 1, 2], [12, 17496, 1, 3], [12, 34992, 1, 5], [12, 52488, 1, 6], [12, 69984, 1, 3], [12, 78732, 1, 2], [12, 104976, 1, 7], [12, 157464, 1, 7], [12, 209952, 1, 1], [12, 236196, 1, 2], [12, 314928, 1, 5], [18, 216, 1, 3], [18, 432, 1, 3], [18, 648, 1, 1], [18, 864, 1, 12], [18, 1296, 1, 22], [18, 1728, 1, 3], [18, 1944, 1, 9], [18, 2592, 1, 37], [18, 3888, 1, 43], [18, 5184, 1, 13], [18, 5832, 1, 11], [18, 7776, 1, 59], [18, 11664, 1, 52], [18, 15552, 1, 13], [18, 17496, 1, 9], [18, 23328, 1, 31], [18, 34992, 1, 23], [18, 46656, 1, 6], [18, 52488, 1, 3], [18, 69984, 1, 20], [18, 104976, 1, 7], [18, 139968, 1, 3], [24, 944784, 1, 2], [36, 11664, 1, 3], [36, 23328, 1, 3], [36, 34992, 1, 9], [36, 69984, 1, 3], [36, 104976, 1, 9], [36, 209952, 1, 9], [36, 314928, 1, 3], [36, 629856, 1, 3]], 'aut_supersolvable': False, 'aut_tex': 'C_3^6.(C_3\\times S_3\\wr D_4)', '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': 72, 'autcentquo_group': '22674816.mj', 'autcentquo_hash': 8826279076269810851, 'autcentquo_nilpotent': False, 'autcentquo_order': 22674816, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^6.(C_3\\times S_3\\wr D_4)', 'cc_stats': [[1, 1, 1], [2, 36, 1], [2, 108, 1], [2, 162, 1], [2, 324, 1], [2, 1944, 2], [2, 2916, 2], [2, 6561, 1], [2, 8748, 1], [3, 8, 2], [3, 16, 2], [3, 32, 1], [3, 36, 3], [3, 81, 2], [3, 108, 2], [3, 144, 6], [3, 216, 2], [3, 324, 1], [4, 972, 1], [4, 17496, 1], [4, 34992, 1], [4, 52488, 1], [4, 78732, 1], [4, 104976, 1], [4, 157464, 1], [4, 236196, 1], [6, 72, 1], [6, 108, 2], [6, 144, 2], [6, 216, 3], [6, 288, 2], [6, 324, 5], [6, 432, 10], [6, 648, 9], [6, 864, 4], [6, 972, 6], [6, 1296, 13], [6, 1458, 2], [6, 1944, 15], [6, 2916, 13], [6, 3888, 13], [6, 5832, 14], [6, 6561, 2], [6, 7776, 3], [6, 8748, 6], [6, 11664, 11], [6, 17496, 14], [6, 23328, 2], [6, 26244, 10], [6, 34992, 2], [6, 52488, 2], [8, 944784, 1], [9, 24, 1], [9, 48, 1], [9, 72, 3], [9, 96, 2], [9, 144, 6], [9, 192, 2], [9, 216, 2], [9, 288, 10], [9, 432, 10], [9, 576, 10], [9, 648, 6], [9, 864, 19], [9, 1296, 13], [9, 1728, 14], [9, 2592, 10], [9, 3456, 3], [9, 5184, 12], [12, 3888, 2], [12, 5832, 2], [12, 8748, 2], [12, 11664, 2], [12, 17496, 3], [12, 34992, 5], [12, 52488, 6], [12, 69984, 3], [12, 78732, 2], [12, 104976, 7], [12, 157464, 7], [12, 209952, 1], [12, 236196, 2], [12, 314928, 5], [18, 216, 3], [18, 432, 3], [18, 648, 1], [18, 864, 12], [18, 1296, 22], [18, 1728, 3], [18, 1944, 9], [18, 2592, 37], [18, 3888, 43], [18, 5184, 13], [18, 5832, 11], [18, 7776, 59], [18, 11664, 52], [18, 15552, 13], [18, 17496, 9], [18, 23328, 31], [18, 34992, 23], [18, 46656, 6], [18, 52488, 3], [18, 69984, 20], [18, 104976, 7], [18, 139968, 3], [24, 944784, 2], [36, 11664, 3], [36, 23328, 3], [36, 34992, 9], [36, 69984, 3], [36, 104976, 9], [36, 209952, 9], [36, 314928, 3], [36, 629856, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '22674816.mj', 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': True, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 18, 'conjugacy_classes_known': True, 'counter': 322, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 36, 1, 1], [2, 108, 1, 1], [2, 162, 1, 1], [2, 324, 1, 1], [2, 1944, 1, 2], [2, 2916, 1, 2], [2, 6561, 1, 1], [2, 8748, 1, 1], [3, 8, 1, 2], [3, 16, 1, 2], [3, 32, 1, 1], [3, 36, 1, 1], [3, 36, 2, 1], [3, 81, 2, 1], [3, 108, 2, 1], [3, 144, 1, 2], [3, 144, 2, 2], [3, 216, 2, 1], [3, 324, 1, 1], [4, 972, 1, 1], [4, 17496, 1, 1], [4, 34992, 1, 1], [4, 52488, 1, 1], [4, 78732, 1, 1], [4, 104976, 1, 1], [4, 157464, 1, 1], [4, 236196, 1, 1], [6, 72, 1, 1], [6, 108, 2, 1], [6, 144, 1, 2], [6, 216, 1, 1], [6, 216, 2, 1], [6, 288, 1, 2], [6, 324, 1, 1], [6, 324, 2, 2], [6, 432, 1, 2], [6, 432, 2, 4], [6, 648, 1, 3], [6, 648, 2, 3], [6, 864, 1, 2], [6, 864, 2, 1], [6, 972, 2, 3], [6, 1296, 1, 5], [6, 1296, 2, 4], [6, 1458, 2, 1], [6, 1944, 1, 1], [6, 1944, 2, 7], [6, 2916, 1, 1], [6, 2916, 2, 6], [6, 3888, 1, 3], [6, 3888, 2, 5], [6, 5832, 1, 4], [6, 5832, 2, 5], [6, 6561, 2, 1], [6, 7776, 1, 3], [6, 8748, 2, 3], [6, 11664, 1, 3], [6, 11664, 2, 4], [6, 17496, 1, 2], [6, 17496, 2, 6], [6, 23328, 2, 1], [6, 26244, 1, 2], [6, 26244, 2, 4], [6, 34992, 1, 2], [6, 52488, 2, 1], [8, 944784, 1, 1], [9, 24, 1, 1], [9, 48, 1, 1], [9, 72, 1, 1], [9, 72, 2, 1], [9, 96, 1, 2], [9, 144, 1, 2], [9, 144, 2, 2], [9, 192, 1, 2], [9, 216, 2, 1], [9, 288, 1, 2], [9, 288, 2, 4], [9, 432, 1, 2], [9, 432, 2, 4], [9, 576, 1, 4], [9, 576, 2, 3], [9, 648, 2, 3], [9, 864, 1, 3], [9, 864, 2, 8], [9, 1296, 1, 1], [9, 1296, 2, 6], [9, 1728, 1, 2], [9, 1728, 2, 6], [9, 2592, 1, 2], [9, 2592, 2, 4], [9, 3456, 1, 1], [9, 3456, 2, 1], [9, 5184, 1, 2], [9, 5184, 2, 5], [12, 3888, 1, 2], [12, 5832, 2, 1], [12, 8748, 2, 1], [12, 11664, 2, 1], [12, 17496, 1, 1], [12, 17496, 2, 1], [12, 34992, 1, 1], [12, 34992, 2, 2], [12, 52488, 2, 3], [12, 69984, 1, 1], [12, 69984, 2, 1], [12, 78732, 2, 1], [12, 104976, 1, 1], [12, 104976, 2, 3], [12, 157464, 1, 1], [12, 157464, 2, 3], [12, 209952, 1, 1], [12, 236196, 2, 1], [12, 314928, 1, 1], [12, 314928, 2, 2], [18, 216, 1, 1], [18, 216, 2, 1], [18, 432, 1, 1], [18, 432, 2, 1], [18, 648, 1, 1], [18, 864, 1, 4], [18, 864, 2, 4], [18, 1296, 1, 2], [18, 1296, 2, 10], [18, 1728, 1, 1], [18, 1728, 2, 1], [18, 1944, 1, 1], [18, 1944, 2, 4], [18, 2592, 1, 7], [18, 2592, 2, 15], [18, 3888, 1, 5], [18, 3888, 2, 19], [18, 5184, 1, 3], [18, 5184, 2, 5], [18, 5832, 1, 1], [18, 5832, 2, 5], [18, 7776, 1, 9], [18, 7776, 2, 25], [18, 11664, 1, 6], [18, 11664, 2, 23], [18, 15552, 1, 3], [18, 15552, 2, 5], [18, 17496, 1, 1], [18, 17496, 2, 4], [18, 23328, 1, 5], [18, 23328, 2, 13], [18, 34992, 1, 3], [18, 34992, 2, 10], [18, 46656, 1, 2], [18, 46656, 2, 2], [18, 52488, 1, 1], [18, 52488, 2, 1], [18, 69984, 1, 4], [18, 69984, 2, 8], [18, 104976, 1, 1], [18, 104976, 2, 3], [18, 139968, 1, 1], [18, 139968, 2, 1], [24, 944784, 2, 1], [36, 11664, 1, 1], [36, 11664, 2, 1], [36, 23328, 1, 1], [36, 23328, 2, 1], [36, 34992, 1, 1], [36, 34992, 2, 4], [36, 69984, 1, 1], [36, 69984, 2, 1], [36, 104976, 1, 1], [36, 104976, 2, 4], [36, 209952, 1, 1], [36, 209952, 2, 4], [36, 314928, 1, 1], [36, 314928, 2, 1], [36, 629856, 1, 1], [36, 629856, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 72, 'exponents_of_order': [11, 7], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 0, 16], [24, 1, 8], [48, 0, 32], [48, 1, 10], [72, 1, 8], [96, 0, 52], [96, 1, 11], [144, 0, 12], [144, 1, 10], [192, 0, 24], [192, 1, 6], [288, 0, 10], [288, 1, 9], [384, 0, 2], [384, 1, 1], [432, 1, 4], [576, 0, 8], [576, 1, 6], [864, 1, 9], [1728, 1, 2]], 'familial': False, 'frattini_label': '81.15', 'frattini_quotient': '279936.u', 'hash': 8826279076269810851, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 72, 'inner_gen_orders': [18, 18, 36], 'inner_gens': [[10341559710233054493134541928070270514932, 42542017731129522868572191379389885566655, 96031254153417223945134656449944120505411], [201801116326817428051637866875376806869615, 116402028737842036772929287354544384054773, 116402851945042948313084818602476764612295], [329449408073640901719775972431899375328028, 297534141504575641997075264153031179734796, 297539038794244101560037845226962645183757]], 'inner_hash': 8826279076269810851, 'inner_nilpotent': False, 'inner_order': 22674816, 'inner_split': True, 'inner_tex': 'C_3^6.(C_3\\times S_3\\wr D_4)', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 24], [2, 18], [4, 90], [8, 126], [16, 180], [24, 24], [32, 99], [48, 42], [64, 30], [72, 8], [96, 63], [144, 22], [192, 30], [288, 19], [384, 3], [432, 4], [576, 14], [864, 9], [1728, 2]], 'label': '22674816.mj', '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': 'C3^6.(C3*S3wrD4)', '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, 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, 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': 807, 'number_characteristic_subgroups': 71, 'number_conjugacy_classes': 807, 'number_divisions': 492, 'number_normal_subgroups': 71, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 22674816, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 25659], [3, 2186], [4, 683316], [6, 1188126], [8, 944784], [9, 174960], [12, 5064120], [18, 6403536], [24, 1889568], [36, 6298560]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, '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': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 14], [4, 24], [8, 56], [16, 77], [24, 8], [32, 89], [48, 18], [64, 50], [72, 8], [96, 27], [128, 12], [144, 10], [192, 32], [288, 15], [384, 13], [432, 4], [576, 11], [768, 1], [864, 9], [1152, 4], [1728, 2]], 'representations': {'PC': {'code': '204753924464296186969946519059962375052652655475942633568214243427490136073407930074016560457401090758537159028231590404130482766329098938130388729837530391094828875584511118200227703157844612941215182329908480334752322883765913875948411016494417544765931299291642024743845676310532080892374929434764549838331695343823269578187068826408567792155284713829628961499749037323627366548038341873190493293365599438982450894799256332546048845508911613530946071784879863941886876707819948508685463361930474072589461315775216445223007363038598937475536066547926401390585134985878227548532034793956994513598410894989156133140369601191232459037995320970281916461416661527939855296155230678890617507301750322135724738672420720413495878018377795647746822981001316894306571013552751651583865453982375687948007991113346077794474868874988118590632861002409256968891022415042539068708390634273870401527472460447232081372665331661649351332922367', 'gens': [1, 3, 5, 7, 8, 10, 12, 13, 15, 16, 17, 18], 'pres': [18, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 36, 1679635, 555220334, 292450358, 146, 814548963, 552531909, 109755705, 540771124, 140746702, 291605440, 78564118, 256, 1427264069, 992655671, 31362377, 137729003, 28942367, 1298977350, 968460216, 421241226, 80104812, 52837926, 34423548, 1351842, 2239411975, 228690457, 178789291, 177591229, 5941519, 1824289, 1584403, 421, 3346168328, 445969178, 205213868, 357758, 37332656, 18478466, 13082588, 1338596, 3280988169, 725787, 613993005, 307008063, 153530001, 34659, 9990117, 8775, 711, 1053119242, 3079342, 87760000, 43880050, 28612, 14374, 7264, 2302193675, 2208135197, 82991, 192596033, 559955, 886565, 46236215, 23013209, 221825, 2518304268, 25474206, 798490416, 211476162, 104828340, 99773958, 26535720, 13002582, 930, 223388977, 429141955, 214571029, 490009, 2218026254, 1360488992, 394865330, 5326646, 75096824, 7105442, 11547500, 7086038, 9932, 87710, 5455392783, 3063619617, 340402227, 515082309, 271019607, 114794601, 2820219, 29958477, 15959103, 979953, 28725, 197223, 2512705552, 2013019810, 947199796, 7314694, 5948728, 65479210, 914452, 16656334, 10484638, 77326, 129670, 6622166033, 1103881013, 5132231, 2612825, 86920235, 51018461, 30705623]}, 'Perm': {'d': 36, 'gens': [10341559710233054493134541928070270514932, 297539038794244101560037845226962645183757, 116402028737842036772929287354544384054773]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 64, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6.(C_3\\times S_3\\wr D_4)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • gps_groups • Show schema
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [5]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', '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': 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], [3, 1, 2], [6, 1, 2]], 'center_label': '6.2', 'center_order': 6, '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', '3.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 6, 'eulerian_function': 1, 'exponent': 6, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '6.2', 'hash': 2, 'hyperelementary': 6, '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': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 6]], 'label': '6.2', 'linC_count': 2, 'linC_degree': 1, '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': 'C6', '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': 6, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 6, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [3, 2], [6, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[5]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 5, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2]], 'representations': {'PC': {'code': 21, 'gens': [1], 'pres': [2, -2, -3, 4]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [73]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [31, 56]}, 'Perm': {'d': 5, 'gens': [24, 4]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6', 'transitive_degree': 6, 'wreath_data': None, 'wreath_product': False}