-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 180, 'aut_gen_orders': [30, 12, 2, 30, 30, 15], 'aut_gens': [[1, 4, 12, 24, 720, 10800], [39469, 24812, 32940, 84420, 720, 672], [105893, 111280, 133560, 155124, 528, 10080], [54001, 161404, 140892, 141096, 720, 151200], [70177, 34972, 151260, 161304, 10080, 10800], [18781, 90424, 108, 6456, 720, 10800], [86929, 9892, 348, 24, 720, 10800]], 'aut_group': '648000.v', 'aut_hash': 2811864275658790406, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 648000, 'aut_permdeg': 2250, 'aut_perms': [556875787937177997626731530726808535837249674884317946351785877097585586406305660915163329443330672029986345271458963003690145146613237810272923907108110310713879884403078766856964752883815844835893471927306300562557705581162907843785426489594581133757579786628672968721345688022967280037606866401386868950748831600605016244409203051320438751361006677068533904890420767137682038916865563590269114331275449310792135828566769133915235749256479143008999282408055899598021286938033010846468544068607093407981784118164814195555395649818109198215964550854579548731919769368671699414370249183182254374131513402285154735228675190592415280702273540524368600662974274257294407782571522707541539644683016298377966181900986700437984103606506002874613163940436638035745719641345766519823750651768054334826276599283852257155228481336343321374822469444643148407960858375849513633551157497952083390950512976139175994836532203657495667807794279026018123900092809107771215343825233460015776091351154166631880319682506513059058963911519186260788628299028817441756869308098906422517361404616192761235738882917965841641175871424114518742695504494501439430724181192758501195255347160293505073244071033009872382926711509080504568221313771779570531475216124131607305691623834770859045712271533713661380292046396461007849057534368795625224942030736342720406890387269747938534359600735421246759678047701522492334532130572310492355078023460918837781546032899994650608095513446260759866909127047192670129736923460482437132064115294781955628664009662150071564003026434854556383531288285018123169697481905002176257304175996022615434387819174389237167448154787441012716271217219162130565741236466356681560707286311250885888300243872123249703502966275554415922940486950908621176477719485504107475497808348847155974516525768056699167353064018958959240612582769625163107848434057305606423491194903032282900288199001473924498700936921552741622134465023939485508841942064254184295827741473448938509897373997973520735181920284957155758034991327323592620667094932746058825204817375401938634719355082058841233278852763830727416091067795989018846862314421894424778007065743532653411553455353886072878723102322278098095915376452050924374391531822111787415440813486432032947186590312592379177350485931706182237408407446956441024389817790452828399310984456087663989688939228850782169243901954554012186084477259585901987313076644796728877425862054456208041084964910369248237747528351272646386349928956215763939321773850645478110136501205633766096778648707340313596197338883557006873061282257343285216154244057988929800369355411365889133496472046514747534356993073591476747245071966204529099914552906603960925068886973663486957316085555862382454524864386421981312914348764893293592303501374794634052226175023484327288462768138511075951116208539099127615485943455984419493918885003516552696511058647339930144454282288976681462140590640036958043077619067102996040471347626433512913045103160637948333938928808888262091175286083088772874030581863613035634120693909854291874821874470752643569558686187916272130489759059394299579866906353286580196848197882587757190935488255528113867265379374489097724824027343588475550448905003426765962285280866389592320192749684086559176743257157953604027602440089604872996893356568735145588656518649360132552348583181135847984311092290749412468582462769029199439765746182415986626786579696216019563098495186962887489103505646917217290257774066284342295236381731325707656891371920682503082499101967965097367264630743080682081456514303920475154246532306862333692663896755843418046899901488479333859801020324759167011157514570947292794717936674614159714102734036817861298120871482055614794504640902485217789825431034154161425926239916239808971549032450788251801425542632849681090284834771218839459759909775227827727382185111520791519531351649233016984899766364900633014196285942186617553418837806538953418555615191969988249104249910537449455500619104520404434516385941838063527547902188769096739976552588592495162210002424929789190410487363356928059424655950336430308437812051898752873629917077392607586376866251388056721638119864988381968303671559841039151755227731569107756740779214361039527185950113762513917789486649136604083742499945477461072456703787333866523940420011265205067905038195937287732020197484806019816042632047220069957954132120539934988964569285260634531049079459939537584560754792242901775164409887386281049550315617258796894198248465900014843854394597988971467253323314851002912823666476515161540172537851749722392368180420910506956957153745794004630074935686539323018381340844489782164719972812718323510584683181134232753736423306497882548234004700785397719832808258996530518236574405335683768233811447968933618029842757286120671731402479712483884013175603237695890222113994429761991637022911587858971789035391615293815235337259986884940858320238997182060508065192709605006540324897961367541542675512252320186406463358252563412219495911894071632559275654367343347214932528126819449902959028985904540999796408682694535033695346399123295889175677715521677070136072681039858713904957827917388150367482962167497537125649029698546246516586035308536343250074437085325182566011698572775477773708959416986272049168215156558814129168079352362963284784009352945821898580322278474593586525419727691311626457155317083186941115199446153500834705661066692043763610023495381013629111156868098219693590638305557415713401807883493227779097339245379536569391753568143276401805446414612718518486558009414763740665940042221745698515005962854171729750908332070552550130708174128655645778424645235717924114459933943209766811401331334767638362474900086406326110226790523246367515066349209386699117796610496847268256250835462552995455258262325658380486317325257597381960485134319125660384267700823272610171826469980338456265572467258093048967757241496088326806506378583628080083113084434214736876703084504302649385276510086091887366022871355696428394743317016891149721932352306208812848157016961654391410394325015977180387830755314295489608715960115713898070165352384455875072461938788825034713141457303099100669935813198364907263765859920627873010176813250131813264813023682846309086150473664455721705272120688531462539750294750052847761998885134624598001953222432985057714819350186015200010756923481735230428552026935805929303932859220181642539995974261834398135346241121719629038270848503166941932956153811409642294000125831799712942655716484732998241988351573249723668600848119789827963192182188304308591712915601404630169639499009438746049284990154443369924735517342399105176869893, 1496659000615941584407734484588829850728304118828556247056779117760682838119664297518763402435360122611912490604110920137032434504477224881263654609394077873460550326937760375709490639566096990346471568639028877350727815752628378921872993925084756606195598964304228783216415605202051041961668649292363336162054283970911098886934777512781918227307774813433521729229631930699195374583571517207689660258971102194703635966438854632921845894280190855501406974823934411022994070816577750342997563576692508228327617045300461219502631288818350785009785031530524771015014067287060630828565639593891295156617093508798523471543637929591376265348154545233020750331506098236483537245382482244477343031819118498272997078867084863798354083893848717176845507689752332194419723469521857486218361730178465800815814857704598052634955893220351541369249415452593168283841997307361704422554020899578136861297683790928701567434764985323103873803349822652998109760179809394410253006236579680102963115132169965169093294031121714830618497049516857052986425648529147623113053679527762772650210102584827682964347931786621582320233927241321798158971377761624676631558340928818980701588547227795316843387149157771647989367554639687305192546004909207776936333109371022750107680373143262189972151371054955594560348987464791467294949065493321828448468262540451206164286718549938722541478103087416795018994179536158485072860510217446588107512978106487433071003022337989968234496049837274366911112459047292625973289864197363790013754503377523218170686004785469133045256760933680018429536775074872621186036457709313267593479792592326790611218297633513676958566974425892878145250984442427511876378441052141982947903630513755750318013321495602954098695056499844011896717010704404195591520712929292140498189030407423836264175661085488032651836253391916672102483220925125770601538672861264930381262222019191417987402947808906218875319539142067853389060839489446866368144299443438612485176564974092529835948343113011762247651542220726075003316844225482682834576923059449029878978457468869036042113703243565846655957382628054823675425161508455882196553310438696985546538597545042531751185963340740089372872066881593853634612743640681509505643469293616207945585248790435071107948673713695243463411744117604885067869208648940798998331059690488329802391890501577093146470951646134195859047182439190124598206488920236943475654931470908863234421932228996623334677993864526277599340858068443151948878681247882711248455691119483750103548302728040897340056167310489534281002943438005303119827368613826403689481935651360310427382355276811511925416022789623988843201353393641295608845183319633331240613602061429263141089944627576111777021746376798119003019048710197653022866442454708677289945168871239253745566764645918608849603172283129355886950845142598266418077228379064738789785270125191145056154431612058610272266478593394237944338416256244093097007850458588428123272623880978764881648330053445413976037326821353674451804066829350748909656349275128585372284865965212813050015618292009626430040914478087860495595446130303126038807029372395604911743309389260523085099226835945362961280235858119072716934635219112476573786647323522867753098018137618310815161216941151742322948113415796722498648730848037468494599600426775641817159507071857161495935161775001939361441868319469833469647653522176187548072665661545122991848124092299593090826151702785338733589113382535992848698998812275316757987008602918511413261719590163033676391188059467453017387824134937429400293468828731017810910219705966029843359529624000179110969121689378051199812189435555474609284150531556082255528913734594888689588374716663118343670254142462150804476878889363608028710903942581116897069498797642068455229291173349217064494909282711830705524408294325769025832020229973004598042632888049211588366582336031600781126486902073501022473259917349101640378178562313793790309383346068814141513096470850454064740427141319112494270471908947408818541205179623703897226032043482130445887131919228142640765831895663673616666191238254927501695870256686056392936990206455291686878214445896494235663130691789966216900660177572534971499128194336101168861701739842588235207698926135621582120058237829379586845444748762610517681387833036273528978646095683757353395489138173907324598872911537618171665147831485462605858462668312422514993426674485617853119158162139842801370329797611683430645730062820577874109831223629810577990029536823548211397858182479758058704866227848265284340200888455143437713382116049785373853271137779311234010060515354978560654956263106791482171475476391186184153036507353029699975097264426110811457778792998985204323442100424538896460221277908104268586232433481182246643244280554452271177253455224717707961273393715511940761693452693722259133590622948001551381576053856694697350468602173233527891669872543322165076082401786806564290940284084200698220904844852116982053180889758577882573411772588724545223470601172585994497060893178638089192791102354063780670017669146823726580079591022240479756931186280190172499518390305192701844268892228726604912168599110477488676593366308842493197069066869308151074007248323598682975169193670314800782293015655458951873278449586630483289401124377926321442148958611571384196076084208120973737488283358671505978357827850101573125993499927976501590081643585339023969336297919572576945799170163062544438703364700447633086135210008033995197999512885309499873926546374915347623714177158453541399362626038683925226946045626156183924586820378623848455057743329978406066180374221187930856564263622091718072777032003092813325373361389578017318550563870580841475179231401445012012603707398856750344262468977346221251491206545972769824639710357545692184230678527037947201078036526990600394864201158916962864518043770425620843478126045825832106134099857141077889154045267038761333294880955379187623713969928263848671724073574709037617134607145524173878360480677885339500654040051929886772056765036437368003222436899065093011114315458295234525113855446806886979920432326853033515974088381014983737115814935206091937571080897152484889872712677670640383045206826055524560155732305388383290671589059528693401233785756709627649305599280772169665141366250143628123760935271404321797744470863506894589241319861759455581627460676960505239331110431717188810615639226605662883632082452327049311305867407467984809958928510581758156166295535245661441798160122731538819996506924204317331146918650096798984963211653969268824403934563880467432542588885504782033978300169057382283515367896095752446291381748450872841720983462839, 1706380736242298498901165629659252564281001174510987042998667354676853088385223406134024443519009365076310548721700196350227372751810729116346527796869061603042143224018020277004376442876336700202392737325378074343979053737060747631000057929746940034845595948521708241559168268594363595812705219253950905412851506974163319813148646278609066094731018830492801527491844980261813129504156297332519959992564374620291665465025639204620760472956123223551413659975466332169488830095053314549812944320568605384860705226142080411261646782596687351123168530643755826847118058296328138483728411751952372942121239509983572407581774018645494084381347563269493784081323413194402967355939051529056150720459240929471791015915275189960401882803373716716493845190382782318847858645601915368916747485019433478813841594749855990399098178366992738351424641806777060075245747300856502718721719426572695995573713700785639723029355956835608615737076986614230507864431194330811652800387687912093894707455156830823612044571149546294714148214664462517477378849904584318825529340440849744186772222405331807370066673706667313660114060640669012608455082110918640168727339046089081091745879021391888709747727434106438432036356489041416666425500518117848789136036054798423372419288419265996718824721248843862857992912150441456900499001147628789988935329794510950893719271561711842956755843275456347575455085649151321290943117433966501586495022072427210484065646832510920231462044015907788971100984641103836982012019502585525883841972559684114969705389193921885931487485723190407078601656519185204054145252681997840192512674972399506095361505604479210051646228986423933257070481217921026952805801446380145210644295809924305717254560234902923133216155336173496318645664371721021659957981983745865455295284099788226861388391595269499542312893677395105736637162918592631538123674949025745983187814599839419356621907647190668885019028016308547405318785136777674419777178193224440929619140817050363629261659725518381265623184295329743924808182826812417347082326155897493646358859284021467221149740630769848664426712222974554621632378591789789212422100394858419727143984972877569926914162574877856077805342480575052898899521050199913035832490487675062617735380729482851837203882607871261721007995852409042017351444371188727530890490955103264211720073912870048243887774708682529757328199415942322775338987130721664823093388041616616296865689372027177377588858874353604184303279767763617473730324320815559257443334268064286754471743866537805565124521303436651859984280379325315462796210099245117217527321116639612647096253777468781413488820257213403221537651855121728599513223609514603025548738198807786079599639281009455682172246005282551048814324038407169011542686139818874433050534821284824260473371012069340345719424573966786996875025203708744803406226996511915600166376488677018435334599185439278987852506745141531329564096185760574538191405153153342827012138882763282152289855858865219292457582846380352982841033214845315021500240488010380350038016493975742969498565055249600911011700408913335580180424257666134337011039053140354419717935268399663323872946801671045969073930424912872608231087619167965073729974325882147681340532591602493384566445856282247852622956244393871330420276177500590499180265130499441345634288665780338880395195575036712596514258901725544090907975283938379750287114793443976518389986025322350340432504685777885963494171532741916899866002339296071940065842451235531441051917017952266104678817084647793668355949748639211893490295862850747752550986561954652302782535527143889015896274724662055818515337241966726239665083015382933229487531916608510496473560628588264777683386074660599076745944412723922219485528863987035238835087347432378495709415447533531676722317065200683758081500470938108811314108991817513495854593671341425075022044057968053072412340501104118518434952345462270732721375974708306375314736127136443876332794971255897608710509094876350690539730810651352810756578910665668119329965783206929231346092587530336132390194985347199623898284557580461404053819905697800566451789285517978330658074355253063017972973457704481822561550948380675259597082137455271493455905939125220057295873346334350376740818253442192497872440213597825994211828223939937890656659286916879511292956151697480971608141631635318574535147384537140566550252392715885968630278193269478566945015917242503520900684935773130325882330064501472115872627156342655806061928781564886722980022323515393072057711037870416782549004301127807370909032669977580632361805794801395479588463003191804848862407675342144774070836666022944633996459832083454546061604667789940300958071983947675444061225229628613808367521144829750362296762363297830584180205331017821228037719822606136703424324694371904412285096334941072916928946719576067735992986326770663916412351044432733188299749767809870773257013430248824769960566343123076732351739359455932566995667818900507282639907319867131574647964759495364339282416452654697102828152990476000604511766945258545617458239590753275354492059685341283097045486426048649707017489297680757097508250006519044717131698381496682427663421989624060053169933703224823854968985552101131867311980507546330228585978288288687090586514973020152951827163998726857519560078551866032712251395331180054643996910715177367522694234742543429993880673582744485100953842581128972814422349864837150686840804226220334327473893724683283181553740740447005494866823875333046526504158777631126991161758297837338132944933603283984041976817932575963027672380783163774204891071376361481475915674491150092023185249138047950017851300731497527211247492440633994228489741747684529036870390925989939853503436449040890904215860336200169021096054888256652637810811661847251703807149710325360618835357394321156851868909339099588295878749209204745297135614792947489291754050819701055418116027482068923657612444244675932323995153333228452974684703013182685416701157601029559986317104093959082439695165926847571673328091421062898358510948598691415806107131066982947104470773634369749036229608996465794132495202630882755511598058482182639204661069889656703458779131583270821924378820014586327371265719092236527609543564299522763618127359455452006696619203079918692759821583255696564142562355191009115434253617859925145051322355657063680300232822827692077215184382042856582766440661819864824144825689545778637939618176271418466426013413990709694656514729325110313314330329795812494842010274881209100351928884796190529411845570218310336483263491283887063791958632405868353503272990652076837499933591627465706843224460896739206, 1558488545870282153755574023815508983791403907576098169753843517009603088720823602490099846837572127445397376684585850732909248424185330318249809917347986692607030769021169639428562276924101827421378616156845225340517282742747972473054696670349396696024692627687238080294928058099706983113081447851222074309290043513789895254886618924576435595932884355679872148052573439494472666572891040433950522382133491497998501357118895387777291238338339696254499171298689601017380415511864747737929341020005603550170011312201089566226467574743584741851237544848791653211381746257591126966761663330980045998798551758832044133623175108405343570715053135181928548959445937848344412654458541599821889212348487564090403516407064174641729716004773184959821614747036285253697975850187481814017697665872554285755236181656316967770177509256804902497484551267738509792692398883586651266635976574136283695576252687847659857699151219870059056061393493990966865959200793891792010712323090916713130319199517769880591239054341601498362711738390866540998291885097279118554399030204581183604203593051336828884659998868668395842114590346088857956153898519765361315215556261083046126762825829540216063187189930917946046988351263569153061362811305650953669115607996024080927094523040090551313469625666354154281790058518895606953179257102626978959412658008256198068020019111445602757708608657461668477100442891246927808626011054574851187997711241405769107563157265182421948778962482831344462562212146910174967838609075468453533380026532596150905352752152650555046494891104545898175030830066364894047729824580599011530575340250865282761457951756692059110751828062655410189550294039079329132368084717285690984087125390344913342773745335702272577753428371519673900387013893629532238250964881106182223877408672520276055485470677102946327174483844033059430193328238160506459817665514085399414518035666943561148609864221202776563243877929518513973254053661051567027475415028635356036987356074252292246397818023204609135775136862267863438913023014196645353162903515493222103768639587101261865020705525214382388373067352506139269059241373630649939588410714027895042320633504219973499896454668450465047249044423984224312554225206385258864325178162918181928160886969917036492876939296493499025374024986210386552713748391846247920432515034473246839085790411619380632618455728274742430154255302868277127591316160785334452166302377518238499291543787940498705110821189326969735743968186048335718527582525492605529465593408442009867707972855167345215459850817551215635053052283946835604903284049227187550707094823647176190063465941466317662968991673361667890708616032325038488328077553951786933340596145332352496894823772987262090388410230830418269693643360645261190711284582895548487454744768029559137724773218347721645874455941013695579593464206675455621769179388776547505072869179929163833556285923330871251547432218874250558252059103171803554946626642220573812796857882829341632479562183135224864266343023309321295204551403417737987087758861708055123007734233089980227256583799089265882072201133144141104463554370892922020902045431988922278251492916412620655215408340921260343775994649416726764553112696325881056446816626249155912383379673476053005798299528194015108583558510355961180353994272817222491257816723542305139282086126412287166825753847113033703811449159107500628707289068715049696996290869279396736802639798314948832951750576681074332786739616432949716403873118251492482521736883232673039720572000218595503483328168135952478725547500205499104656780793691443968800174326157953331827879298842556804601274909373836614424439621010847399614447505303373350002599225013683575533180021594694491020681932555289756538064750449525439831613669451774468517659617257689333429358867246564150292830023532781776377046774704830881029731449061943389250469242201676392374838218079362897240060569931267131388514770154156515466143892987912550827321641860933219505102520107254663925698127806193337404663306860073706887572900794961465481460842747942418709137269394852629582077044293404923878446764270387840849448192258594340973044610904875993297940439230985445296734062398608331316361329202005567081592819071400256065868092343925057568660274606380930265025388104159053889404703731491805267354031298214619734290892525936600529114183851757003037108574790348674473206856540066916756161378813734178044069442435189017645976208986612225589644358535189518299909066636290632047221767006260528395873319917210055484265488719189124826853278436651401082967175647949563798339368978058762247767028787832580279138098119621056778601469907258001660617802722623595286207230737304870435857869913430202343154204349724737920301617515526897359304338939232474022819856705111717287609198699737688018967304213570783746156859004426799220089656497100330166310654280230222858303995991290136809205939586231392383171629137340076633176470566321208050756310490983200782986311589676803705308516972933088935306075247366773830191114423419705875761649911452558063211608488812893212229676434853756774574864374272226237788585099923554943898482419789418321779440409402388133160775099737027318270705403661855019623376834963138133150970451101591016985254175989142469662363103004520580756283851965252792327990391967494585546710133310780401524364200658791029705633265866317971688113866522225346487631411708620241358764811386125591251764635321523397284588084402852596056567447684109597436991356934881436921742199451371097197333735415483859706502216637417947910924824094200552433229533788128837220365364269730823309444802656698234028325822159632199992258381257931157824131459513924073693085252188580851753697794934143063296736126486523669447864624813628409280233055206632258041088160199319410017120772929863417569667611913783790503456154125884199333603369412089352228545779037816186650119614175419329147882255556276434408643684549435972480068238665416724578253894982581373604290173645768137061009056934614095652391754655546275522253368052579310285422978420438583231780020998240787131342142085718473996340675910569539043952095166996054489311139975687161737116087650863379927592933691697850911338184483288882297184079169169933293537516204324496123722190883232400125334689466854608001507267930501682846907196387727754089971717364946681731132546372960219943325923686702420965920897861799996518776279313235135727315269976463011139334719261146154446609617597360303492148474475265978115884654092461561330725478567930173784592325757452413178273311738733477019416263302031203967967976211688545030342456001559000777407903692874009494499445260890100054365555313919918322799713144, 1565102383947504806473957162884266883635280041985432726215574694028482173982164080364407418073184272251903024765680494226321394524652431566747563035735704630943028171571919940821535179988199859061548901749739800251413467815887965590254591324495219730489497978000849001235907486459722849034476075184103812786511554684924740079716386783444334419034239750412712156085037723439790033029867744071547792942747735349230415529621722321848375581163696374635010469262478997980114719634682162580685459111657831588459380708430860884293984535569104537218046415201211452407585998963691073557463670514608969252174253258262038234809636395306964402204335288788927356298343403526400456861361303750499653157048392496354116509419215692755248904003149507342788456955277198658545078118261629240708294899578678637284291347547526908832315229660192210848817411188107835681074653767338833366824620121393673730592607084570055579508570517584882188730195952180504695909421349897913844424066266360629430078781573370306337996930746890029004837529488705185670119037283338641393989583285956536966697012319065272748261787787061738320171458413965592566080176323569115344043318649972548569795545246163525206808954505185069676598514205903589795113760368461572042627518068180186562905364958672185603908827218837079831062983695228942323806264916618938569596803017123719181949999240222113302361528106476284125939431005484942645744214545032931438119166234851543923349174959621879166372436400480341657792852327746000327025941002163996954575358756976965579088557376426194507997262750953993372144438491959993806263252659915741685074500031297586059479210647003837558357231289479641704012549523911501622759171557330766410476945236728037571254738167544033228975542748775554034320350862312465983702617288108443481569384044520666572381169281772325150597057760828125877519832434231438866009102063341127150930389184212985053233256585872557929128791340871067823520553972084456381400926516589278893858104970398040837484704455270905849507810598625957338280328597038858792464117714728226760383107898133941080378743627433877124718104667156324035445261161261025512753180492487484683256512013265542418967855500677342439717165611545393006094455352837179121679187405547259677151101178140799430641913151929509211780309494900073226050072051087151334679820751894184082810913908436877335361761074467509526618751317472720825495812154097148026994165636391586316072198802642973971946221968316789617009517183940506190183287355711013281879576850179881601987082278721838183265036913454042700002731366447277089299872870928297412949782832526637165812864167718774963114682019175312396775566581904460936189980878025223935534849040535589168642468345721042987262224637797152896686865665011688485306749225862410272510180383019262618820635470055871805135835137378889857458475828270746877324223158582199905475986691099014218265962194453403023223547269281937440971464619912355531567700277993805436430592244961536915582239145974786253478698773567079099137933652745077154305808992984277455174080858142519994044835522787192049444395690484766663103881662855861709436562028912976997827958750921411178410896923008461916510577831651836102662895829119029371417045283315778124655957306646996944833395637020536847406731042368435246623758556439038534126763459321390274174861840437729993184838550363967747935261288427254416587858331086107774517984568100836395921494012394652332302865966831386777519770758507991562094296918106402064965872622088837784034071801594538574176323581622030892765415213006177416121573059629913118606534349991128233561145493226655713389821687089518955981397146572113433974991096887455641461349883340803754130957279029462380159922777326452687668184071765290425039089843864299888922147103208203935331209875770457698863924557335161762560525629692661883687287940859524210437622534353874401316806817738680744819065759357011084491156024413424066111823343122661216374248369619465111611358200098040529662335028057336608425791067279946682667354632752751902286005005583473575292489803160698741207732133336483433200979059662281156370448331311304935797483770491212039342843889107493299627336135496680787861020734210128907897434390435571605282350274248367418395831187037827772167638363805071033169418762400516105687811809583096684895016992063302683209644290779870706913119333832160151797539313107417246344468257676457715405409279318327880510817568903420696614645531324886188719068975504386930551204912157883653194548836546416729687069614530094277206889288018883759877561174714512850044157465672200086131677772046155874917298957553422995742830182222000117137792224266260180921526517376387596364980385771262167609947003690385555963755622263306195263603623449917063521156445205890457168927958869808548506633480816104290323481286533984609216826037498313300781449644334925870303176865899666890428969716718743992593938081294959380217283132582990400351930514999062650295546427719117874984341203932351538700977615525406448985309253977277488529497808843763903356047579790937122713970498378701301014098045571795552645652203769224573883894814617844717443702126375605480942954599405830754626529959453231089852781224527017255615599299067945250595347085315502837446252362621865223563780189803274184254666850255489931707327503582514202408022905427194856459053795518748106318315550368859916892844654755844599489834038268114029224143742048472529021042765933939125716042372942495721314649950492807822751080903416877750776299792113925642529898470373916757999725762941825358858448812716357648136131803017039282618112738317489769889450406020233763326992240376822169810520861416365884252563155797976442232849713417079765429845945974976691985881167741543725610649845975427149348695702457366162751822937532388011691932337264171418975243162816730613812184240720982049834043949831918436313292011817921871870859999465287190705541849091031378866195795327320796453108247203445368100449015363427814195873140527927484573782358101164906957607632451577434267836926503259184643813935284430542990174333182971508564645210651688260609484073296939941171873573309495881567606470635187622922504433913326941976207378692114273857487734678048655327770843881021832527332310848926823353068082144863695137800288269707624829955048028372976210422407754342155064345289509020426518135948844093435262026288194623067866263372715860969623240170619791428749371627868710888348105921576358974714794433190583867608378464528830787122041283468566529375077657256616336993153291742100958528898935263600621037704090998449931058845802764920606287474125876897800051468227284702760079270169861435935107528142109976, 680493613288352268464624561037506708029240962397454458829936279683041234062448436279809193902854022127068633297844396563990183217162019832235178126647941546131481844643037445608197324253410145293914489598905538721265864894931976633609505318960297589988939625991015764984546721074140321860124642230985472956465493656915586053958445435619137310241152492630684043608886216424449306543054823341050362942951207396272802993353022486547618318911373421953515603099303387896163113293599680717606096119394368437528309984076576025177141253893135657236430539971096253264392877354997836169864375658569262628542226546795277563858652070597410798768265249426332340362245786155720038775120991226188720005703377346051604360109319054222069072078394564363925229536527553920457233012003821984666184634264624169567769799131962087881970139241368195901139746666322584872865105606069029168365650602105685414589079653833160583719831921963432054796627612528216735958741247096691234716816947724290687067421702871365152665656446338367246418708299598623800419333250519455837909956864222312034635463285826934250349593464896182265812702939111428169353456062482718149980103149559317626932178993205507520583912384377532882437358323007649492042409064246971844942703013752474655054515612176962126279179110387276451896298236427510999874388123528075408581040886799079761897213837895866392229379032102899463581318842645615809976660899779416367756460400548046045747216444954962088073580488936465230363107337088242916950805311144926099225353754062175991951057455600402490784547914106815489570714517170234461324961547920485508872934976931679791779802603407872191848327841345508765155677777731260968031075705937951720867969294370985986808635595555833145451417091516706230152489236222888882371706943452012318109469044280926806833330271708740228395688533367879330436070320050482364524788294418332904912220129395883614692235683021428898050720583316325573121990322895766781793680510054435024334898117378994434707962315281309317582772974819261217641391402933899691059688567557932873689230181276180285533904353582898602354555969234563709908185623254055503315767789343299465659130320122590715440741635832831618800880049076294897015059349386475087418564737100966849024998989114593933358219719354285201804216866119956075661611046328541228745336706382526548494619189533424681384737235009066416115102234648501347779059261469308700910195610492758978684102963158010588804776901172980091200877180716358026687287347734648675941743953353021032162864840245881446366187802614526969866921105368109615792079272980398844022555500564617761775742117066660786275074366429986656681320507396254654101631229870479751253040946620064298341967277284625819366142993098782138918052538396159165880421846807446384915351126757312102032638900889554333652460990626807621575082776063411600906441353151542392252240174316245696735329087816886534229335309237784134535917558396029036274522636683450164386049693552372937534504177105939707316537422480076765272534362915814417031211365642731001456868582874716895373190475276190474137950525301602827543804578057196104262274730536646316930610530894121037517746827056170480781074513302866677171905215618604211052598255076968948779122728837579692087484906421348227841437987009031408231296818764159117263046786971498521564129949540069403287464182185457752182324630005313354666586695153637099155643762709662710428557322558337355497420425438182409675955272154831362633043179453105968484436768188799974791585984132161764017170283762222734761028083713478060641884506222245366240130966186184032435121444269416027117572794881744997728967355532234015795932887065174031992595690886348771102527377388018014721290334315561279649456056724218362140568233221027862810878663214646070921581491995424640753474812034045388559791290014920391125042405603121840980885625232696919610594425295590524140708085812052797561029652810123373203503808155270382048497934901896432945342846915432866122513835334152271445782706016112028870171818004960240693228386404665228875284455654281892774857788771778542821339872348679846369411371669219636464857393625125567118056125787089274818888294358017176836371887659098403172187760353393378225927329347819676430084842884601193386283577676742636981382108568532652740832004478390245388053599280305394145239533583117798097361208463327797927420843522619062870484620273549089570974237860698485209460392631136240570725552210633823887362104023782743948154949417108156439725144220425131667555613296375339034072894393809341883065643263204960759412616326880270437687053386716435262904459120484832246406922480566896256652409426080765104570041269966023450621231766862511000400427629919079366929558222177832730109996986648410352076217752517005859606202424630717740580187865034928159546468140701179320182836069359321212334436079411323289741858251028296244176451532634670470354830536581476371206802358550836052437308408837516324134891341142987626980739121582310343963667197200275862457756214467431838909185082397072074933644097324675006284311165379360912444037069365051237302827958215328633363712617007541551771061919084516797450754659280659544088315108124892338640955139081083039393097300416832969009217083134621938657093615171183302167552308901940570962302580767197923650536618154444432413799055620926577047631186147202803759550949037950550557667407267134108242877850615588899096322196625366449092152810218662412750950490782893906480466103612140701659111565642728207668504616711189694759672288548177565528769026429358967760550037389719963099943192611889505685011224689997395257810892598902931321769905918738441939552823707955730052919397019833505506414134386277716592544046395187190200529498155663675816573639025518826065897047991161411921197238889529069965003166417809408194100623933458313307318123760750729012587679218066101215058290469506436179487864565236594797980247216229906982730962766592721448264141840475988903082242694309979276565815042122144744938308639617410319105264674198886678760405931026345956596201050387682380754322205605307130335025726590032610803312944242527992034988913102334590946909344387142656772082675686450174854574941771018320567572318663961393353242617006273709080863191246050377640742132395944430544980068042527052115841899369952940158367824191136351286686025261519114049112747961628503524345330021144451476444898552333694796846364111605666642978329780076431633221435031709044213604976535626883736959702470771402640758885644502567151473648972502007155001460934554894628696915496217235375240584371400932757536027365534135420177106599525201696438220695004544655290587215514330969057144], 'aut_phi_ratio': 15.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 125, 1, 1], [2, 135, 1, 1], [2, 675, 1, 1], [3, 4, 2, 1], [3, 6, 1, 1], [3, 12, 1, 1], [3, 1800, 1, 1], [4, 2250, 1, 2], [4, 4050, 1, 2], [5, 12, 1, 1], [5, 12, 2, 1], [5, 16, 1, 1], [5, 24, 1, 1], [5, 48, 1, 1], [6, 270, 1, 1], [6, 500, 2, 1], [6, 750, 1, 1], [6, 1350, 1, 1], [6, 1500, 1, 1], [6, 9000, 1, 1], [9, 1800, 2, 1], [10, 540, 2, 2], [10, 1080, 1, 1], [10, 2700, 1, 1], [12, 2250, 2, 2], [12, 4500, 1, 2], [12, 4500, 2, 2], [15, 16, 2, 1], [15, 24, 1, 1], [15, 24, 2, 3], [15, 48, 1, 3], [15, 48, 2, 16], [15, 48, 4, 7], [15, 3600, 2, 1], [18, 9000, 2, 1], [20, 8100, 2, 2], [30, 1080, 2, 3], [30, 5400, 1, 1], [45, 3600, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_{15}\\wr S_3.C_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': 180, 'autcentquo_group': '648000.v', 'autcentquo_hash': 2811864275658790406, 'autcentquo_nilpotent': False, 'autcentquo_order': 648000, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'D_{15}\\wr S_3.C_4', 'cc_stats': [[1, 1, 1], [2, 125, 1], [2, 135, 1], [2, 675, 1], [3, 4, 2], [3, 6, 1], [3, 12, 1], [3, 1800, 1], [4, 2250, 2], [4, 4050, 2], [5, 12, 3], [5, 16, 1], [5, 24, 1], [5, 48, 1], [6, 270, 1], [6, 500, 2], [6, 750, 1], [6, 1350, 1], [6, 1500, 1], [6, 9000, 1], [9, 1800, 2], [10, 540, 4], [10, 1080, 1], [10, 2700, 1], [12, 2250, 4], [12, 4500, 6], [15, 16, 2], [15, 24, 7], [15, 48, 63], [15, 3600, 2], [18, 9000, 2], [20, 8100, 4], [30, 1080, 6], [30, 5400, 1], [45, 3600, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '162000.x', 'commutator_count': 1, 'commutator_label': '40500.j', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '5.1', '5.1', '5.1'], 'composition_length': 11, 'conjugacy_classes_known': True, 'counter': 24, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 125, 1, 1], [2, 135, 1, 1], [2, 675, 1, 1], [3, 4, 2, 1], [3, 6, 1, 1], [3, 12, 1, 1], [3, 1800, 1, 1], [4, 2250, 2, 1], [4, 4050, 2, 1], [5, 12, 1, 1], [5, 12, 2, 1], [5, 16, 1, 1], [5, 24, 1, 1], [5, 48, 1, 1], [6, 270, 1, 1], [6, 500, 2, 1], [6, 750, 1, 1], [6, 1350, 1, 1], [6, 1500, 1, 1], [6, 9000, 1, 1], [9, 1800, 2, 1], [10, 540, 2, 2], [10, 1080, 1, 1], [10, 2700, 1, 1], [12, 2250, 4, 1], [12, 4500, 2, 1], [12, 4500, 4, 1], [15, 16, 2, 1], [15, 24, 1, 1], [15, 24, 2, 3], [15, 48, 1, 3], [15, 48, 2, 16], [15, 48, 4, 7], [15, 3600, 2, 1], [18, 9000, 2, 1], [20, 8100, 4, 1], [30, 1080, 2, 3], [30, 5400, 1, 1], [45, 3600, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 14508, 'exponent': 180, 'exponents_of_order': [4, 4, 3], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[16, 0, 6], [24, -1, 2], [24, 0, 4], [24, 1, 8], [48, 0, 52], [48, 1, 11]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '162000.x', 'hash': 242777464014375236, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 180, 'inner_gen_orders': [4, 15, 2, 30, 15, 15], 'inner_gens': [[1, 86468, 151356, 12036, 1440, 624], [154737, 4, 6660, 116460, 140400, 48], [11377, 7036, 12, 696, 720, 151200], [21421, 62488, 60, 24, 10080, 151200], [10081, 22324, 12, 1464, 720, 10800], [10897, 11476, 21612, 21624, 720, 10800]], 'inner_hash': 242777464014375236, 'inner_nilpotent': False, 'inner_order': 162000, 'inner_split': True, 'inner_tex': '(C_{15}^3.A_4):C_4', 'inner_used': [1, 2], 'irrC_degree': 16, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 4], [2, 2], [3, 4], [4, 8], [6, 8], [8, 4], [12, 16], [16, 9], [24, 16], [48, 64]], 'label': '162000.x', 'linC_count': 102, 'linC_degree': 16, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 4, 'linQ_dim': 18, 'linQ_dim_count': 4, 'linR_count': 32, 'linR_degree': 18, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': '(C15^3.A4):C4', 'ngens': 11, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 74, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 135, 'number_divisions': 68, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 980, 'number_subgroup_classes': 980, 'number_subgroups': 310712, 'old_label': None, 'order': 162000, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 935], [3, 1826], [4, 12600], [5, 124], [6, 13870], [9, 3600], [10, 5940], [12, 36000], [15, 10424], [18, 18000], [20, 32400], [30, 11880], [45, 14400]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 64862], 'outer_gens': [[57601, 115684, 108492, 108264, 7920, 118800], [108241, 19972, 86556, 95352, 9360, 140400]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [3, 2], [6, 3], [8, 2], [12, 7], [16, 4], [24, 8], [32, 2], [48, 11], [64, 1], [96, 16], [192, 7]], 'representations': {'PC': {'code': '424922250324409693877805333070159301465645977174870554878233651364864539364771696130461007526720281856152322462472085856807028109323809294078252758173261994165940032089567797986736728951449083717149816743036193459803347027831', 'gens': [1, 3, 4, 5, 8, 10], 'pres': [11, 2, 2, 3, 2, 2, 3, 5, 3, 5, 3, 5, 22, 2853446, 1296979, 823308, 6659667, 1193558, 73285, 661984, 1551675, 1601351, 3227, 158, 1425605, 17440, 83187, 3734, 258, 4989606, 83188, 3735, 126727, 126738, 3088829, 37011, 348, 427688, 427699, 2405730, 35692, 68649, 6534020, 1351, 1386042, 693053, 438, 52282, 4388, 1306843, 653454]}, 'Perm': {'d': 24, 'gens': [1129110956016700211287, 28202584577261299481053]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_{15}^3.A_4):C_4', 'transitive_degree': 45, 'wreath_data': None, 'wreath_product': False}
-
gps_conj_classes • Show schema
Hide schema
-
id: 108945118
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 24, 'group_order': 162000, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
-
id: 108945165
{'aut_label': '2A', 'centralizer': '125.a1.a1', 'counter': 2, 'group_counter': 24, 'group_order': 162000, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 110366, 'size': 125}
-
id: 108945176
{'aut_label': '2B', 'centralizer': '135.a1.a1', 'counter': 3, 'group_counter': 24, 'group_order': 162000, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 112802, 'size': 135}
-
id: 108945187
{'aut_label': '2C', 'centralizer': '675.a1.a1', 'counter': 4, 'group_counter': 24, 'group_order': 162000, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 108060, 'size': 675}
-
id: 108945198
{'aut_label': '3A1', 'centralizer': '4.b1.a1', 'counter': 5, 'group_counter': 24, 'group_order': 162000, 'label': '3A1', 'order': 3, 'powers': [6, 1, 6], 'representative': 57840, 'size': 4}
-
id: 108945209
{'aut_label': '3A1', 'centralizer': '4.b1.a1', 'counter': 6, 'group_counter': 24, 'group_order': 162000, 'label': '3A-1', 'order': 3, 'powers': [5, 1, 5], 'representative': 115680, 'size': 4}
-
id: 108945220
{'aut_label': '3B', 'centralizer': '6.b1.a1', 'counter': 7, 'group_counter': 24, 'group_order': 162000, 'label': '3B', 'order': 3, 'powers': [7, 1, 7], 'representative': 54000, 'size': 6}
-
id: 108945231
{'aut_label': '3C', 'centralizer': '12.d1.a1', 'counter': 8, 'group_counter': 24, 'group_order': 162000, 'label': '3C', 'order': 3, 'powers': [8, 1, 8], 'representative': 54240, 'size': 12}
-
id: 108945242
{'aut_label': '3D', 'centralizer': '1800.j1.a1', 'counter': 9, 'group_counter': 24, 'group_order': 162000, 'label': '3D', 'order': 3, 'powers': [9, 1, 9], 'representative': 59120, 'size': 1800}
-
id: 108945119
{'aut_label': '4A1', 'centralizer': '2250.a1.a1', 'counter': 10, 'group_counter': 24, 'group_order': 162000, 'label': '4A1', 'order': 4, 'powers': [2, 11, 10], 'representative': 78345, 'size': 2250}
-
id: 108945130
{'aut_label': '4A-1', 'centralizer': '2250.a1.a1', 'counter': 11, 'group_counter': 24, 'group_order': 162000, 'label': '4A-1', 'order': 4, 'powers': [2, 10, 11], 'representative': 67043, 'size': 2250}
-
id: 108945141
{'aut_label': '4B1', 'centralizer': '4050.b1.a1', 'counter': 12, 'group_counter': 24, 'group_order': 162000, 'label': '4B1', 'order': 4, 'powers': [3, 13, 12], 'representative': 161775, 'size': 4050}
-
id: 108945152
{'aut_label': '4B-1', 'centralizer': '4050.b1.a1', 'counter': 13, 'group_counter': 24, 'group_order': 162000, 'label': '4B-1', 'order': 4, 'powers': [3, 12, 13], 'representative': 44893, 'size': 4050}
-
id: 108945159
{'aut_label': '5A', 'centralizer': '12.f1.a1', 'counter': 14, 'group_counter': 24, 'group_order': 162000, 'label': '5A', 'order': 5, 'powers': [14, 14, 1], 'representative': 432, 'size': 12}
-
id: 108945160
{'aut_label': '5B1', 'centralizer': '12.e1.a1', 'counter': 15, 'group_counter': 24, 'group_order': 162000, 'label': '5B1', 'order': 5, 'powers': [16, 16, 1], 'representative': 34560, 'size': 12}
-
id: 108945161
{'aut_label': '5B1', 'centralizer': '12.e1.a1', 'counter': 16, 'group_counter': 24, 'group_order': 162000, 'label': '5B2', 'order': 5, 'powers': [15, 15, 1], 'representative': 69120, 'size': 12}
-
id: 108945162
{'aut_label': '5C', 'centralizer': '16.a1.a1', 'counter': 17, 'group_counter': 24, 'group_order': 162000, 'label': '5C', 'order': 5, 'powers': [17, 17, 1], 'representative': 99792, 'size': 16}
-
id: 108945163
{'aut_label': '5D', 'centralizer': '24.d1.a1', 'counter': 18, 'group_counter': 24, 'group_order': 162000, 'label': '5D', 'order': 5, 'powers': [18, 18, 1], 'representative': 32544, 'size': 24}
-
id: 108945164
{'aut_label': '5E', 'centralizer': '48.a1.a1', 'counter': 19, 'group_counter': 24, 'group_order': 162000, 'label': '5E', 'order': 5, 'powers': [19, 19, 1], 'representative': 34704, 'size': 48}
-
id: 108945166
{'aut_label': '6A', 'centralizer': '270.a1.a1', 'counter': 20, 'group_counter': 24, 'group_order': 162000, 'label': '6A', 'order': 6, 'powers': [7, 3, 20], 'representative': 157802, 'size': 270}
-
id: 108945167
{'aut_label': '6B1', 'centralizer': '500.a1.a1', 'counter': 21, 'group_counter': 24, 'group_order': 162000, 'label': '6B1', 'order': 6, 'powers': [6, 2, 22], 'representative': 10046, 'size': 500}
-
id: 108945168
{'aut_label': '6B1', 'centralizer': '500.a1.a1', 'counter': 22, 'group_counter': 24, 'group_order': 162000, 'label': '6B-1', 'order': 6, 'powers': [5, 2, 21], 'representative': 60206, 'size': 500}
-
id: 108945169
{'aut_label': '6C', 'centralizer': '750.a1.a1', 'counter': 23, 'group_counter': 24, 'group_order': 162000, 'label': '6C', 'order': 6, 'powers': [7, 2, 23], 'representative': 12446, 'size': 750}
-
id: 108945170
{'aut_label': '6D', 'centralizer': '1350.e1.a1', 'counter': 24, 'group_counter': 24, 'group_order': 162000, 'label': '6D', 'order': 6, 'powers': [7, 4, 24], 'representative': 111660, 'size': 1350}
-
id: 108945171
{'aut_label': '6E', 'centralizer': '1500.c1.a1', 'counter': 25, 'group_counter': 24, 'group_order': 162000, 'label': '6E', 'order': 6, 'powers': [8, 2, 25], 'representative': 155918, 'size': 1500}
-
id: 108945172
{'aut_label': '6F', 'centralizer': '9000.b1.a1', 'counter': 26, 'group_counter': 24, 'group_order': 162000, 'label': '6F', 'order': 6, 'powers': [9, 2, 26], 'representative': 89002, 'size': 9000}
-
id: 108945173
{'aut_label': '9A1', 'centralizer': '1800.k1.a1', 'counter': 27, 'group_counter': 24, 'group_order': 162000, 'label': '9A1', 'order': 9, 'powers': [28, 6, 28], 'representative': 10112, 'size': 1800}
-
id: 108945174
{'aut_label': '9A1', 'centralizer': '1800.k1.a1', 'counter': 28, 'group_counter': 24, 'group_order': 162000, 'label': '9A-1', 'order': 9, 'powers': [27, 5, 27], 'representative': 33232, 'size': 1800}
-
id: 108945175
{'aut_label': '10A1', 'centralizer': '540.bk1.a1', 'counter': 29, 'group_counter': 24, 'group_order': 162000, 'label': '10A1', 'order': 10, 'powers': [16, 30, 3], 'representative': 15458, 'size': 540}
-
id: 108945177
{'aut_label': '10A1', 'centralizer': '540.bk1.a1', 'counter': 30, 'group_counter': 24, 'group_order': 162000, 'label': '10A3', 'order': 10, 'powers': [15, 29, 3], 'representative': 144770, 'size': 540}
-
id: 108945178
{'aut_label': '10B1', 'centralizer': '540.bo1.a1', 'counter': 31, 'group_counter': 24, 'group_order': 162000, 'label': '10B1', 'order': 10, 'powers': [14, 32, 3], 'representative': 82790, 'size': 540}
-
id: 108945179
{'aut_label': '10B1', 'centralizer': '540.bo1.a1', 'counter': 32, 'group_counter': 24, 'group_order': 162000, 'label': '10B3', 'order': 10, 'powers': [14, 31, 3], 'representative': 17990, 'size': 540}
-
id: 108945180
{'aut_label': '10C', 'centralizer': '1080.bg1.a1', 'counter': 33, 'group_counter': 24, 'group_order': 162000, 'label': '10C', 'order': 10, 'powers': [18, 33, 3], 'representative': 18458, 'size': 1080}
-
id: 108945181
{'aut_label': '10D', 'centralizer': '2700.bo1.a1', 'counter': 34, 'group_counter': 24, 'group_order': 162000, 'label': '10D', 'order': 10, 'powers': [14, 34, 4], 'representative': 112380, 'size': 2700}
-
id: 108945182
{'aut_label': '12A1', 'centralizer': '2250.a1.a1', 'counter': 35, 'group_counter': 24, 'group_order': 162000, 'label': '12A1', 'order': 12, 'powers': [23, 11, 37], 'representative': 51913, 'size': 2250}
-
id: 108945183
{'aut_label': '12A-1', 'centralizer': '2250.a1.a1', 'counter': 36, 'group_counter': 24, 'group_order': 162000, 'label': '12A-1', 'order': 12, 'powers': [23, 10, 38], 'representative': 139095, 'size': 2250}
-
id: 108945184
{'aut_label': '12A1', 'centralizer': '2250.a1.a1', 'counter': 37, 'group_counter': 24, 'group_order': 162000, 'label': '12A5', 'order': 12, 'powers': [23, 11, 35], 'representative': 48313, 'size': 2250}
-
id: 108945185
{'aut_label': '12A-1', 'centralizer': '2250.a1.a1', 'counter': 38, 'group_counter': 24, 'group_order': 162000, 'label': '12A-5', 'order': 12, 'powers': [23, 10, 36], 'representative': 131895, 'size': 2250}
-
id: 108945186
{'aut_label': '12B1', 'centralizer': '4500.f1.a1', 'counter': 39, 'group_counter': 24, 'group_order': 162000, 'label': '12B1', 'order': 12, 'powers': [25, 11, 39], 'representative': 81913, 'size': 4500}
-
id: 108945188
{'aut_label': '12B-1', 'centralizer': '4500.f1.a1', 'counter': 40, 'group_counter': 24, 'group_order': 162000, 'label': '12B-1', 'order': 12, 'powers': [25, 10, 40], 'representative': 30087, 'size': 4500}
-
id: 108945189
{'aut_label': '12C1', 'centralizer': '4500.f1.a1', 'counter': 41, 'group_counter': 24, 'group_order': 162000, 'label': '12C1', 'order': 12, 'powers': [21, 10, 43], 'representative': 125123, 'size': 4500}
-
id: 108945190
{'aut_label': '12C-1', 'centralizer': '4500.f1.a1', 'counter': 42, 'group_counter': 24, 'group_order': 162000, 'label': '12C-1', 'order': 12, 'powers': [22, 11, 44], 'representative': 31065, 'size': 4500}
-
id: 108945191
{'aut_label': '12C1', 'centralizer': '4500.f1.a1', 'counter': 43, 'group_counter': 24, 'group_order': 162000, 'label': '12C5', 'order': 12, 'powers': [22, 10, 41], 'representative': 20483, 'size': 4500}
-
id: 108945192
{'aut_label': '12C-1', 'centralizer': '4500.f1.a1', 'counter': 44, 'group_counter': 24, 'group_order': 162000, 'label': '12C-5', 'order': 12, 'powers': [21, 11, 42], 'representative': 135705, 'size': 4500}
-
id: 108945193
{'aut_label': '15A1', 'centralizer': '16.a1.a1', 'counter': 45, 'group_counter': 24, 'group_order': 162000, 'label': '15A1', 'order': 15, 'powers': [46, 17, 6], 'representative': 89616, 'size': 16}
-
id: 108945194
{'aut_label': '15A1', 'centralizer': '16.a1.a1', 'counter': 46, 'group_counter': 24, 'group_order': 162000, 'label': '15A-1', 'order': 15, 'powers': [45, 17, 5], 'representative': 83904, 'size': 16}
-
id: 108945195
{'aut_label': '15B', 'centralizer': '24.e1.a1', 'counter': 47, 'group_counter': 24, 'group_order': 162000, 'label': '15B', 'order': 15, 'powers': [47, 14, 7], 'representative': 10080, 'size': 24}
-
id: 108945196
{'aut_label': '15C1', 'centralizer': '24.d1.a1', 'counter': 48, 'group_counter': 24, 'group_order': 162000, 'label': '15C1', 'order': 15, 'powers': [49, 15, 7], 'representative': 117216, 'size': 24}
-
id: 108945197
{'aut_label': '15C1', 'centralizer': '24.d1.a1', 'counter': 49, 'group_counter': 24, 'group_order': 162000, 'label': '15C2', 'order': 15, 'powers': [48, 16, 7], 'representative': 60912, 'size': 24}
-
id: 108945199
{'aut_label': '15D1', 'centralizer': '24.d1.a1', 'counter': 50, 'group_counter': 24, 'group_order': 162000, 'label': '15D1', 'order': 15, 'powers': [51, 14, 7], 'representative': 32880, 'size': 24}
-
id: 108945200
{'aut_label': '15D1', 'centralizer': '24.d1.a1', 'counter': 51, 'group_counter': 24, 'group_order': 162000, 'label': '15D2', 'order': 15, 'powers': [50, 14, 7], 'representative': 65040, 'size': 24}
-
id: 108945201
{'aut_label': '15E1', 'centralizer': '24.d1.a1', 'counter': 52, 'group_counter': 24, 'group_order': 162000, 'label': '15E1', 'order': 15, 'powers': [53, 18, 7], 'representative': 60624, 'size': 24}
-
id: 108945202
{'aut_label': '15E1', 'centralizer': '24.d1.a1', 'counter': 53, 'group_counter': 24, 'group_order': 162000, 'label': '15E-1', 'order': 15, 'powers': [52, 18, 7], 'representative': 112896, 'size': 24}
-
id: 108945203
{'aut_label': '15F', 'centralizer': '48.a1.a1', 'counter': 54, 'group_counter': 24, 'group_order': 162000, 'label': '15F', 'order': 15, 'powers': [54, 18, 8], 'representative': 10848, 'size': 48}
-
id: 108945204
{'aut_label': '15G', 'centralizer': '48.a1.a1', 'counter': 55, 'group_counter': 24, 'group_order': 162000, 'label': '15G', 'order': 15, 'powers': [55, 18, 8], 'representative': 12240, 'size': 48}
-
id: 108945205
{'aut_label': '15H', 'centralizer': '48.a1.a1', 'counter': 56, 'group_counter': 24, 'group_order': 162000, 'label': '15H', 'order': 15, 'powers': [56, 14, 8], 'representative': 57744, 'size': 48}
-
id: 108945206
{'aut_label': '15I1', 'centralizer': '48.a1.a1', 'counter': 57, 'group_counter': 24, 'group_order': 162000, 'label': '15I1', 'order': 15, 'powers': [58, 18, 7], 'representative': 12960, 'size': 48}
-
id: 108945207
{'aut_label': '15I1', 'centralizer': '48.a1.a1', 'counter': 58, 'group_counter': 24, 'group_order': 162000, 'label': '15I2', 'order': 15, 'powers': [57, 18, 7], 'representative': 864, 'size': 48}
-
id: 108945208
{'aut_label': '15J1', 'centralizer': '48.a1.a1', 'counter': 59, 'group_counter': 24, 'group_order': 162000, 'label': '15J1', 'order': 15, 'powers': [60, 15, 8], 'representative': 11520, 'size': 48}
-
id: 108945210
{'aut_label': '15J1', 'centralizer': '48.a1.a1', 'counter': 60, 'group_counter': 24, 'group_order': 162000, 'label': '15J2', 'order': 15, 'powers': [59, 16, 8], 'representative': 768, 'size': 48}
-
id: 108945211
{'aut_label': '15K1', 'centralizer': '48.a1.a1', 'counter': 61, 'group_counter': 24, 'group_order': 162000, 'label': '15K1', 'order': 15, 'powers': [62, 16, 7], 'representative': 10944, 'size': 48}
-
id: 108945212
{'aut_label': '15K1', 'centralizer': '48.a1.a1', 'counter': 62, 'group_counter': 24, 'group_order': 162000, 'label': '15K2', 'order': 15, 'powers': [61, 15, 7], 'representative': 32448, 'size': 48}
-
id: 108945213
{'aut_label': '15L1', 'centralizer': '48.a1.a1', 'counter': 63, 'group_counter': 24, 'group_order': 162000, 'label': '15L1', 'order': 15, 'powers': [64, 17, 7], 'representative': 33264, 'size': 48}
-
id: 108945214
{'aut_label': '15L1', 'centralizer': '48.a1.a1', 'counter': 64, 'group_counter': 24, 'group_order': 162000, 'label': '15L-1', 'order': 15, 'powers': [63, 17, 7], 'representative': 13248, 'size': 48}
-
id: 108945215
{'aut_label': '15M1', 'centralizer': '48.a1.a1', 'counter': 65, 'group_counter': 24, 'group_order': 162000, 'label': '15M1', 'order': 15, 'powers': [66, 17, 8], 'representative': 13008, 'size': 48}
-
id: 108945216
{'aut_label': '15M1', 'centralizer': '48.a1.a1', 'counter': 66, 'group_counter': 24, 'group_order': 162000, 'label': '15M-1', 'order': 15, 'powers': [65, 17, 8], 'representative': 19488, 'size': 48}
-
id: 108945217
{'aut_label': '15N1', 'centralizer': '48.a1.a1', 'counter': 67, 'group_counter': 24, 'group_order': 162000, 'label': '15N1', 'order': 15, 'powers': [68, 19, 5], 'representative': 11568, 'size': 48}
-
id: 108945218
{'aut_label': '15N1', 'centralizer': '48.a1.a1', 'counter': 68, 'group_counter': 24, 'group_order': 162000, 'label': '15N-1', 'order': 15, 'powers': [67, 19, 6], 'representative': 23136, 'size': 48}
-
id: 108945219
{'aut_label': '15O1', 'centralizer': '48.a1.a1', 'counter': 69, 'group_counter': 24, 'group_order': 162000, 'label': '15O1', 'order': 15, 'powers': [70, 14, 8], 'representative': 54720, 'size': 48}
-
id: 108945221
{'aut_label': '15O1', 'centralizer': '48.a1.a1', 'counter': 70, 'group_counter': 24, 'group_order': 162000, 'label': '15O2', 'order': 15, 'powers': [69, 14, 8], 'representative': 3648, 'size': 48}
-
id: 108945222
{'aut_label': '15P1', 'centralizer': '48.a1.a1', 'counter': 71, 'group_counter': 24, 'group_order': 162000, 'label': '15P1', 'order': 15, 'powers': [72, 19, 7], 'representative': 15264, 'size': 48}
-
id: 108945223
{'aut_label': '15P1', 'centralizer': '48.a1.a1', 'counter': 72, 'group_counter': 24, 'group_order': 162000, 'label': '15P-1', 'order': 15, 'powers': [71, 19, 7], 'representative': 33984, 'size': 48}
-
id: 108945224
{'aut_label': '15Q1', 'centralizer': '48.a1.a1', 'counter': 73, 'group_counter': 24, 'group_order': 162000, 'label': '15Q1', 'order': 15, 'powers': [73, 19, 8], 'representative': 12384, 'size': 48}
-
id: 108945225
{'aut_label': '15Q1', 'centralizer': '48.a1.a1', 'counter': 74, 'group_counter': 24, 'group_order': 162000, 'label': '15Q-1', 'order': 15, 'powers': [74, 19, 8], 'representative': 33888, 'size': 48}
-
id: 108945226
{'aut_label': '15R1', 'centralizer': '48.a1.a1', 'counter': 75, 'group_counter': 24, 'group_order': 162000, 'label': '15R1', 'order': 15, 'powers': [76, 19, 8], 'representative': 15168, 'size': 48}
-
id: 108945227
{'aut_label': '15R1', 'centralizer': '48.a1.a1', 'counter': 76, 'group_counter': 24, 'group_order': 162000, 'label': '15R-1', 'order': 15, 'powers': [75, 19, 8], 'representative': 17328, 'size': 48}
-
id: 108945228
{'aut_label': '15S1', 'centralizer': '48.a1.a1', 'counter': 77, 'group_counter': 24, 'group_order': 162000, 'label': '15S1', 'order': 15, 'powers': [78, 19, 6], 'representative': 22368, 'size': 48}
-
id: 108945229
{'aut_label': '15S1', 'centralizer': '48.a1.a1', 'counter': 78, 'group_counter': 24, 'group_order': 162000, 'label': '15S-1', 'order': 15, 'powers': [77, 19, 5], 'representative': 13728, 'size': 48}
-
id: 108945230
{'aut_label': '15T1', 'centralizer': '48.a1.a1', 'counter': 79, 'group_counter': 24, 'group_order': 162000, 'label': '15T1', 'order': 15, 'powers': [80, 17, 6], 'representative': 12288, 'size': 48}
-
id: 108945232
{'aut_label': '15T1', 'centralizer': '48.a1.a1', 'counter': 80, 'group_counter': 24, 'group_order': 162000, 'label': '15T-1', 'order': 15, 'powers': [79, 17, 5], 'representative': 24576, 'size': 48}
-
id: 108945233
{'aut_label': '15U1', 'centralizer': '48.a1.a1', 'counter': 81, 'group_counter': 24, 'group_order': 162000, 'label': '15U1', 'order': 15, 'powers': [81, 17, 8], 'representative': 12528, 'size': 48}
-
id: 108945234
{'aut_label': '15U1', 'centralizer': '48.a1.a1', 'counter': 82, 'group_counter': 24, 'group_order': 162000, 'label': '15U-1', 'order': 15, 'powers': [82, 17, 8], 'representative': 66288, 'size': 48}
-
id: 108945235
{'aut_label': '15V1', 'centralizer': '48.a1.a1', 'counter': 83, 'group_counter': 24, 'group_order': 162000, 'label': '15V1', 'order': 15, 'powers': [84, 18, 6], 'representative': 14448, 'size': 48}
-
id: 108945236
{'aut_label': '15V1', 'centralizer': '48.a1.a1', 'counter': 84, 'group_counter': 24, 'group_order': 162000, 'label': '15V-1', 'order': 15, 'powers': [83, 18, 5], 'representative': 18048, 'size': 48}
-
id: 108945237
{'aut_label': '15W1', 'centralizer': '48.a1.a1', 'counter': 85, 'group_counter': 24, 'group_order': 162000, 'label': '15W1', 'order': 15, 'powers': [86, 18, 5], 'representative': 55488, 'size': 48}
-
id: 108945238
{'aut_label': '15W1', 'centralizer': '48.a1.a1', 'counter': 86, 'group_counter': 24, 'group_order': 162000, 'label': '15W-1', 'order': 15, 'powers': [85, 18, 6], 'representative': 109488, 'size': 48}
-
id: 108945239
{'aut_label': '15X1', 'centralizer': '48.a1.a1', 'counter': 87, 'group_counter': 24, 'group_order': 162000, 'label': '15X1', 'order': 15, 'powers': [88, 14, 5], 'representative': 57648, 'size': 48}
-
id: 108945240
{'aut_label': '15X1', 'centralizer': '48.a1.a1', 'counter': 88, 'group_counter': 24, 'group_order': 162000, 'label': '15X-1', 'order': 15, 'powers': [87, 14, 6], 'representative': 61248, 'size': 48}
-
id: 108945241
{'aut_label': '15Y1', 'centralizer': '48.a1.a1', 'counter': 89, 'group_counter': 24, 'group_order': 162000, 'label': '15Y1', 'order': 15, 'powers': [91, 19, 7], 'representative': 13104, 'size': 48}
-
id: 108945243
{'aut_label': '15Y1', 'centralizer': '48.a1.a1', 'counter': 90, 'group_counter': 24, 'group_order': 162000, 'label': '15Y-1', 'order': 15, 'powers': [92, 19, 7], 'representative': 33552, 'size': 48}
-
id: 108945244
{'aut_label': '15Y1', 'centralizer': '48.a1.a1', 'counter': 91, 'group_counter': 24, 'group_order': 162000, 'label': '15Y2', 'order': 15, 'powers': [89, 19, 7], 'representative': 98064, 'size': 48}
-
id: 108945245
{'aut_label': '15Y1', 'centralizer': '48.a1.a1', 'counter': 92, 'group_counter': 24, 'group_order': 162000, 'label': '15Y-2', 'order': 15, 'powers': [90, 19, 7], 'representative': 34608, 'size': 48}
-
id: 108945246
{'aut_label': '15Z1', 'centralizer': '48.a1.a1', 'counter': 93, 'group_counter': 24, 'group_order': 162000, 'label': '15Z1', 'order': 15, 'powers': [95, 19, 8], 'representative': 11664, 'size': 48}
-
id: 108945247
{'aut_label': '15Z1', 'centralizer': '48.a1.a1', 'counter': 94, 'group_counter': 24, 'group_order': 162000, 'label': '15Z-1', 'order': 15, 'powers': [96, 19, 8], 'representative': 25968, 'size': 48}
-
id: 108945248
{'aut_label': '15Z1', 'centralizer': '48.a1.a1', 'counter': 95, 'group_counter': 24, 'group_order': 162000, 'label': '15Z2', 'order': 15, 'powers': [93, 19, 8], 'representative': 15216, 'size': 48}
-
id: 108945249
{'aut_label': '15Z1', 'centralizer': '48.a1.a1', 'counter': 96, 'group_counter': 24, 'group_order': 162000, 'label': '15Z-2', 'order': 15, 'powers': [94, 19, 8], 'representative': 33168, 'size': 48}
-
id: 108945250
{'aut_label': '15AA1', 'centralizer': '48.a1.a1', 'counter': 97, 'group_counter': 24, 'group_order': 162000, 'label': '15AA1', 'order': 15, 'powers': [99, 19, 8], 'representative': 11808, 'size': 48}
-
id: 108945251
{'aut_label': '15AA1', 'centralizer': '48.a1.a1', 'counter': 98, 'group_counter': 24, 'group_order': 162000, 'label': '15AA-1', 'order': 15, 'powers': [100, 19, 8], 'representative': 11952, 'size': 48}
-
id: 108945252
{'aut_label': '15AA1', 'centralizer': '48.a1.a1', 'counter': 99, 'group_counter': 24, 'group_order': 162000, 'label': '15AA2', 'order': 15, 'powers': [97, 19, 8], 'representative': 97968, 'size': 48}
-
id: 108945120
{'aut_label': '15AA1', 'centralizer': '48.a1.a1', 'counter': 100, 'group_counter': 24, 'group_order': 162000, 'label': '15AA-2', 'order': 15, 'powers': [98, 19, 8], 'representative': 65568, 'size': 48}
-
id: 108945121
{'aut_label': '15AB1', 'centralizer': '48.a1.a1', 'counter': 101, 'group_counter': 24, 'group_order': 162000, 'label': '15AB1', 'order': 15, 'powers': [103, 19, 5], 'representative': 23088, 'size': 48}
-
id: 108945122
{'aut_label': '15AB1', 'centralizer': '48.a1.a1', 'counter': 102, 'group_counter': 24, 'group_order': 162000, 'label': '15AB-1', 'order': 15, 'powers': [104, 19, 6], 'representative': 13776, 'size': 48}
-
id: 108945123
{'aut_label': '15AB1', 'centralizer': '48.a1.a1', 'counter': 103, 'group_counter': 24, 'group_order': 162000, 'label': '15AB2', 'order': 15, 'powers': [101, 19, 6], 'representative': 24528, 'size': 48}
-
id: 108945124
{'aut_label': '15AB1', 'centralizer': '48.a1.a1', 'counter': 104, 'group_counter': 24, 'group_order': 162000, 'label': '15AB-2', 'order': 15, 'powers': [102, 19, 5], 'representative': 12336, 'size': 48}
-
id: 108945125
{'aut_label': '15AC1', 'centralizer': '48.a1.a1', 'counter': 105, 'group_counter': 24, 'group_order': 162000, 'label': '15AC1', 'order': 15, 'powers': [107, 18, 8], 'representative': 54864, 'size': 48}
-
id: 108945126
{'aut_label': '15AC1', 'centralizer': '48.a1.a1', 'counter': 106, 'group_counter': 24, 'group_order': 162000, 'label': '15AC-1', 'order': 15, 'powers': [108, 18, 8], 'representative': 56208, 'size': 48}
-
id: 108945127
{'aut_label': '15AC1', 'centralizer': '48.a1.a1', 'counter': 107, 'group_counter': 24, 'group_order': 162000, 'label': '15AC2', 'order': 15, 'powers': [105, 18, 8], 'representative': 13200, 'size': 48}
-
id: 108945128
{'aut_label': '15AC1', 'centralizer': '48.a1.a1', 'counter': 108, 'group_counter': 24, 'group_order': 162000, 'label': '15AC-2', 'order': 15, 'powers': [106, 18, 8], 'representative': 33360, 'size': 48}
-
id: 108945129
{'aut_label': '15AD1', 'centralizer': '48.a1.a1', 'counter': 109, 'group_counter': 24, 'group_order': 162000, 'label': '15AD1', 'order': 15, 'powers': [111, 16, 8], 'representative': 14544, 'size': 48}
-
id: 108945131
{'aut_label': '15AD1', 'centralizer': '48.a1.a1', 'counter': 110, 'group_counter': 24, 'group_order': 162000, 'label': '15AD-1', 'order': 15, 'powers': [112, 16, 8], 'representative': 18144, 'size': 48}
-
id: 108945132
{'aut_label': '15AD1', 'centralizer': '48.a1.a1', 'counter': 111, 'group_counter': 24, 'group_order': 162000, 'label': '15AD2', 'order': 15, 'powers': [109, 15, 8], 'representative': 39648, 'size': 48}
-
id: 108945133
{'aut_label': '15AD1', 'centralizer': '48.a1.a1', 'counter': 112, 'group_counter': 24, 'group_order': 162000, 'label': '15AD-2', 'order': 15, 'powers': [110, 15, 8], 'representative': 36048, 'size': 48}
-
id: 108945134
{'aut_label': '15AE1', 'centralizer': '48.a1.a1', 'counter': 113, 'group_counter': 24, 'group_order': 162000, 'label': '15AE1', 'order': 15, 'powers': [115, 16, 6], 'representative': 54768, 'size': 48}
-
id: 108945135
{'aut_label': '15AE1', 'centralizer': '48.a1.a1', 'counter': 114, 'group_counter': 24, 'group_order': 162000, 'label': '15AE-1', 'order': 15, 'powers': [116, 16, 5], 'representative': 108768, 'size': 48}
-
id: 108945136
{'aut_label': '15AE1', 'centralizer': '48.a1.a1', 'counter': 115, 'group_counter': 24, 'group_order': 162000, 'label': '15AE2', 'order': 15, 'powers': [113, 15, 5], 'representative': 25248, 'size': 48}
-
id: 108945137
{'aut_label': '15AE1', 'centralizer': '48.a1.a1', 'counter': 116, 'group_counter': 24, 'group_order': 162000, 'label': '15AE-2', 'order': 15, 'powers': [114, 15, 6], 'representative': 11760, 'size': 48}
-
id: 108945138
{'aut_label': '15AF1', 'centralizer': '3600.j1.a1', 'counter': 117, 'group_counter': 24, 'group_order': 162000, 'label': '15AF1', 'order': 15, 'powers': [117, 17, 9], 'representative': 151696, 'size': 3600}
-
id: 108945139
{'aut_label': '15AF1', 'centralizer': '3600.j1.a1', 'counter': 118, 'group_counter': 24, 'group_order': 162000, 'label': '15AF-1', 'order': 15, 'powers': [118, 17, 9], 'representative': 87776, 'size': 3600}
-
id: 108945140
{'aut_label': '18A1', 'centralizer': '9000.c1.a1', 'counter': 119, 'group_counter': 24, 'group_order': 162000, 'label': '18A1', 'order': 18, 'powers': [27, 21, 120], 'representative': 153198, 'size': 9000}
-
id: 108945142
{'aut_label': '18A1', 'centralizer': '9000.c1.a1', 'counter': 120, 'group_counter': 24, 'group_order': 162000, 'label': '18A-1', 'order': 18, 'powers': [28, 22, 119], 'representative': 139210, 'size': 9000}
-
id: 108945143
{'aut_label': '20A1', 'centralizer': '8100.i1.a1', 'counter': 121, 'group_counter': 24, 'group_order': 162000, 'label': '20A1', 'order': 20, 'powers': [29, 123, 12], 'representative': 31743, 'size': 8100}
-
id: 108945144
{'aut_label': '20A-1', 'centralizer': '8100.i1.a1', 'counter': 122, 'group_counter': 24, 'group_order': 162000, 'label': '20A-1', 'order': 20, 'powers': [29, 124, 13], 'representative': 12925, 'size': 8100}
-
id: 108945145
{'aut_label': '20A-1', 'centralizer': '8100.i1.a1', 'counter': 123, 'group_counter': 24, 'group_order': 162000, 'label': '20A3', 'order': 20, 'powers': [30, 121, 13], 'representative': 142237, 'size': 8100}
-
id: 108945146
{'aut_label': '20A1', 'centralizer': '8100.i1.a1', 'counter': 124, 'group_counter': 24, 'group_order': 162000, 'label': '20A-3', 'order': 20, 'powers': [30, 122, 12], 'representative': 64431, 'size': 8100}
-
id: 108945147
{'aut_label': '30A1', 'centralizer': '1080.bg1.a1', 'counter': 125, 'group_counter': 24, 'group_order': 162000, 'label': '30A1', 'order': 30, 'powers': [48, 30, 20], 'representative': 97610, 'size': 1080}
-
id: 108945148
{'aut_label': '30A1', 'centralizer': '1080.bg1.a1', 'counter': 126, 'group_counter': 24, 'group_order': 162000, 'label': '30A7', 'order': 30, 'powers': [49, 29, 20], 'representative': 102218, 'size': 1080}
-
id: 108945149
{'aut_label': '30B1', 'centralizer': '1080.bg1.a1', 'counter': 127, 'group_counter': 24, 'group_order': 162000, 'label': '30B1', 'order': 30, 'powers': [50, 31, 20], 'representative': 49910, 'size': 1080}
-
id: 108945150
{'aut_label': '30B1', 'centralizer': '1080.bg1.a1', 'counter': 128, 'group_counter': 24, 'group_order': 162000, 'label': '30B7', 'order': 30, 'powers': [51, 32, 20], 'representative': 147110, 'size': 1080}
-
id: 108945151
{'aut_label': '30C1', 'centralizer': '1080.bg1.a1', 'counter': 129, 'group_counter': 24, 'group_order': 162000, 'label': '30C1', 'order': 30, 'powers': [52, 33, 20], 'representative': 119834, 'size': 1080}
-
id: 108945153
{'aut_label': '30C1', 'centralizer': '1080.bg1.a1', 'counter': 130, 'group_counter': 24, 'group_order': 162000, 'label': '30C-1', 'order': 30, 'powers': [53, 33, 20], 'representative': 70010, 'size': 1080}
-
id: 108945154
{'aut_label': '30D', 'centralizer': '5400.bu1.a1', 'counter': 131, 'group_counter': 24, 'group_order': 162000, 'label': '30D', 'order': 30, 'powers': [47, 34, 24], 'representative': 113100, 'size': 5400}
-
id: 108945155
{'aut_label': '45A1', 'centralizer': '3600.k1.a1', 'counter': 132, 'group_counter': 24, 'group_order': 162000, 'label': '45A1', 'order': 45, 'powers': [134, 45, 27], 'representative': 49744, 'size': 3600}
-
id: 108945156
{'aut_label': '45A1', 'centralizer': '3600.k1.a1', 'counter': 133, 'group_counter': 24, 'group_order': 162000, 'label': '45A-1', 'order': 45, 'powers': [135, 46, 28], 'representative': 155600, 'size': 3600}
-
id: 108945157
{'aut_label': '45A1', 'centralizer': '3600.k1.a1', 'counter': 134, 'group_counter': 24, 'group_order': 162000, 'label': '45A2', 'order': 45, 'powers': [132, 46, 28], 'representative': 83216, 'size': 3600}
-
id: 108945158
{'aut_label': '45A1', 'centralizer': '3600.k1.a1', 'counter': 135, 'group_counter': 24, 'group_order': 162000, 'label': '45A-2', 'order': 45, 'powers': [133, 45, 27], 'representative': 122848, 'size': 3600}
-
gps_qchar • Show schema
Hide schema
-
id: 4079004
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
-
id: 4079015
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
-
id: 4079026
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.1c', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2], 'schur_index': 1}
-
id: 4079037
{'cdim': 2, 'counter': 4, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1], 'schur_index': 1}
-
id: 4079048
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.2b', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, -2, 1, -1, -1, -2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 1, 1, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, -1, -1, -1, -1], 'schur_index': 2}
-
id: 4079059
{'cdim': 3, 'counter': 6, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 3, 3, 3, 0, 1, 1, -1, -1, 3, 3, 3, 3, 3, 3, -1, 3, 3, 3, -1, 3, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079069
{'cdim': 3, 'counter': 7, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 3, 3, 3, 0, -1, -1, 1, 1, 3, 3, 3, 3, 3, 3, -1, 3, 3, 3, -1, 3, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079070
{'cdim': 3, 'counter': 8, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.3c', 'multiplicity': 2, 'nt': [12, 27], 'qdim': 6, 'qvalues': [6, -6, 2, -2, 6, 6, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 2, -6, -6, -6, -2, -6, 0, 0, 0, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079007
{'cdim': 6, 'counter': 12, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.6a', 'multiplicity': 1, 'nt': [9, 29], 'qdim': 6, 'qvalues': [6, 6, 2, 2, -3, -3, 3, 0, 0, 2, 2, 0, 0, 6, 6, 6, 6, 6, 6, -1, -3, -3, 3, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -3, -3, 3, 3, 3, 3, 3, 3, 3, 3, -3, 0, 0, 3, -3, -3, 0, 0, 3, -3, -3, 0, 3, -3, 0, 0, -3, -3, 0, 0, 3, -3, 0, 0, 3, -3, -3, -3, -3, -3, 3, 3, 0, 0, 0, 0, 3, 0, -3, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, 3, 0, 3, 3, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079008
{'cdim': 6, 'counter': 13, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.6b', 'multiplicity': 1, 'nt': [18, 220], 'qdim': 6, 'qvalues': [6, 6, 2, 2, -3, -3, 3, 0, 0, -2, -2, 0, 0, 6, 6, 6, 6, 6, 6, -1, -3, -3, 3, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, -3, -3, 3, 3, 3, 3, 3, 3, 3, 3, -3, 0, 0, 3, -3, -3, 0, 0, 3, -3, -3, 0, 3, -3, 0, 0, -3, -3, 0, 0, 3, -3, 0, 0, 3, -3, -3, -3, -3, -3, 3, 3, 0, 0, 0, 0, 3, 0, -3, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, 3, 0, 3, 3, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079071
{'cdim': 4, 'counter': 9, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.4a', 'multiplicity': 2, 'nt': [12, 175], 'qdim': 8, 'qvalues': [8, 8, 0, 0, -1, -1, -4, 2, 2, 4, 4, 0, 0, 8, 8, 8, 8, 8, 8, 0, -1, -1, -4, 0, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, -1, -1, -4, -4, -4, -4, -4, -4, -4, -4, -1, 2, 2, -4, -1, -1, 2, 2, -4, -1, -1, 2, -4, -1, 2, 2, -1, -1, 2, 2, -4, -1, 2, 2, -4, -1, -1, -1, -1, -1, -4, -4, 2, 2, 2, 2, -4, 2, -1, -1, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, -1, 2, -4, 2, -4, -4, -1, 2, 2, -1, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
-
id: 4079005
{'cdim': 4, 'counter': 10, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.4b', 'multiplicity': 2, 'nt': [24, 1527], 'qdim': 8, 'qvalues': [8, 8, 0, 0, -1, -1, -4, 2, 2, -4, -4, 0, 0, 8, 8, 8, 8, 8, 8, 0, -1, -1, -4, 0, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -4, -4, -4, -4, -4, -4, -4, -4, -1, 2, 2, -4, -1, -1, 2, 2, -4, -1, -1, 2, -4, -1, 2, 2, -1, -1, 2, 2, -4, -1, 2, 2, -4, -1, -1, -1, -1, -1, -4, -4, 2, 2, 2, 2, -4, 2, -1, -1, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, -1, 2, -4, 2, -4, -4, -1, 2, 2, -1, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
-
id: 4079009
{'cdim': 6, 'counter': 14, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.6c', 'multiplicity': 2, 'nt': [36, 1131], 'qdim': 12, 'qvalues': [12, 12, -4, -4, -6, -6, 6, 0, 0, 0, 0, 0, 0, 12, 12, 12, 12, 12, 12, 2, -6, -6, 6, 2, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 6, 6, 6, 6, 6, 6, 6, 6, -6, 0, 0, 6, -6, -6, 0, 0, 6, -6, -6, 0, 6, -6, 0, 0, -6, -6, 0, 0, 6, -6, 0, 0, 6, -6, -6, -6, -6, -6, 6, 6, 0, 0, 0, 0, 6, 0, -6, -6, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -6, 0, 6, 0, 6, 6, -6, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079010
{'cdim': 6, 'counter': 15, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.6d', 'multiplicity': 2, 'nt': [36, 2141], 'qdim': 12, 'qvalues': [12, -12, 4, -4, -6, -6, 6, 0, 0, 0, 0, 0, 0, 12, 12, 12, 12, 12, 12, -2, 6, 6, -6, 2, 0, 0, 0, 0, 4, 4, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 6, 6, 6, 6, 6, 6, 6, 6, -6, 0, 0, 6, -6, -6, 0, 0, 6, -6, -6, 0, 6, -6, 0, 0, -6, -6, 0, 0, 6, -6, 0, 0, 6, -6, -6, -6, -6, -6, 6, 6, 0, 0, 0, 0, 6, 0, -6, -6, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -6, 0, 6, 0, 6, 6, -6, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079011
{'cdim': 6, 'counter': 16, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.6e', 'multiplicity': 2, 'nt': [36, 2147], 'qdim': 12, 'qvalues': [12, -12, -4, 4, -6, -6, 6, 0, 0, 0, 0, 0, 0, 12, 12, 12, 12, 12, 12, 2, 6, 6, -6, -2, 0, 0, 0, 0, -4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 6, 6, 6, 6, 6, 6, 6, 6, -6, 0, 0, 6, -6, -6, 0, 0, 6, -6, -6, 0, 6, -6, 0, 0, -6, -6, 0, 0, 6, -6, 0, 0, 6, -6, -6, -6, -6, -6, 6, 6, 0, 0, 0, 0, 6, 0, -6, -6, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -6, 0, 6, 0, 6, 6, -6, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079014
{'cdim': 12, 'counter': 19, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.12a', 'multiplicity': 1, 'nt': [15, 58], 'qdim': 12, 'qvalues': [12, 0, 8, 4, 12, 12, 12, 12, 0, 0, 0, 0, 0, 2, 7, 2, -3, 2, -3, 8, 0, 0, 0, 4, 0, 0, 0, 0, 3, -2, -2, 3, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 7, 2, 7, 2, 7, 2, 2, -3, -3, 7, -3, 2, 2, 2, 7, 2, -3, 2, -3, -3, -3, 2, 2, 2, 2, -3, 2, 2, -3, 2, 2, 2, 2, -3, -3, 7, -3, 2, -3, 2, -3, -3, -3, 7, -3, -3, -3, 7, 2, -3, -3, -3, 2, 2, -3, -3, -3, -3, -3, -3, -3, 2, 2, -3, -3, 2, -3, -3, 2, -3, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, -2, -2, 3, -1, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079016
{'cdim': 12, 'counter': 20, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.12b', 'multiplicity': 1, 'nt': [18, 219], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 3, 3, 0, -3, 0, 2, 2, 0, 0, 12, 12, 12, 12, 12, 12, 0, 3, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, -3, 0, 3, 3, -3, -3, 0, 3, 3, -3, 0, 3, -3, -3, 3, 3, -3, -3, 0, 3, -3, -3, 0, 3, 3, 3, 3, 3, 0, 0, -3, -3, -3, -3, 0, -3, 3, 3, -3, -3, -3, -3, -3, 3, -3, -3, -3, -3, 3, -3, 0, -3, 0, 0, 3, -3, -3, 3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079017
{'cdim': 12, 'counter': 21, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.12c', 'multiplicity': 1, 'nt': [30, 616], 'qdim': 12, 'qvalues': [12, 0, -8, 4, 12, 12, 12, 12, 0, 0, 0, 0, 0, 2, 7, 2, -3, 2, -3, -8, 0, 0, 0, 4, 0, 0, 0, 0, -3, 2, 2, -3, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 7, 2, 7, 2, 7, 2, 2, -3, -3, 7, -3, 2, 2, 2, 7, 2, -3, 2, -3, -3, -3, 2, 2, 2, 2, -3, 2, 2, -3, 2, 2, 2, 2, -3, -3, 7, -3, 2, -3, 2, -3, -3, -3, 7, -3, -3, -3, 7, 2, -3, -3, -3, 2, 2, -3, -3, -3, -3, -3, -3, -3, 2, 2, -3, -3, 2, -3, -3, 2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -3, 2, 2, -3, -1, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079018
{'cdim': 12, 'counter': 22, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.12d', 'multiplicity': 1, 'nt': [36, 1126], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 3, 3, 0, -3, 0, -2, -2, 0, 0, 12, 12, 12, 12, 12, 12, 0, 3, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, -3, 0, 3, 3, -3, -3, 0, 3, 3, -3, 0, 3, -3, -3, 3, 3, -3, -3, 0, 3, -3, -3, 0, 3, 3, 3, 3, 3, 0, 0, -3, -3, -3, -3, 0, -3, 3, 3, -3, -3, -3, -3, -3, 3, -3, -3, -3, -3, 3, -3, 0, -3, 0, 0, 3, -3, -3, 3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079006
{'cdim': 4, 'counter': 11, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.4c', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, -2, -2, -8, 4, 4, 0, 0, 0, 0, 16, 16, 16, 16, 16, 16, 0, 2, 2, 8, 0, -4, -4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -8, -8, -8, -8, -8, -8, -8, -8, -2, 4, 4, -8, -2, -2, 4, 4, -8, -2, -2, 4, -8, -2, 4, 4, -2, -2, 4, 4, -8, -2, 4, 4, -8, -2, -2, -2, -2, -2, -8, -8, 4, 4, 4, 4, -8, 4, -2, -2, 4, 4, 4, 4, 4, -2, 4, 4, 4, 4, -2, 4, -8, 4, -8, -8, -2, 4, 4, -2, 4, 4, 4, 4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2], 'schur_index': 1}
-
id: 4079012
{'cdim': 8, 'counter': 17, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.8a', 'multiplicity': 2, 'nt': [24, 1540], 'qdim': 16, 'qvalues': [16, 16, 0, 0, -2, -2, -8, 4, -2, 0, 0, 0, 0, 16, 16, 16, 16, 16, 16, 0, -2, -2, -8, 0, 4, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -8, -8, -8, -8, -8, -8, -8, -8, -2, 4, 4, -8, -2, -2, 4, 4, -8, -2, -2, 4, -8, -2, 4, 4, -2, -2, 4, 4, -8, -2, 4, 4, -8, -2, -2, -2, -2, -2, -8, -8, 4, 4, 4, 4, -8, 4, -2, -2, 4, 4, 4, 4, 4, -2, 4, 4, 4, 4, -2, 4, -8, 4, -8, -8, -2, 4, 4, -2, 4, 4, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
-
id: 4079013
{'cdim': 8, 'counter': 18, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.8b', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, -2, -2, -8, 4, -2, 0, 0, 0, 0, 16, 16, 16, 16, 16, 16, 0, 2, 2, 8, 0, -4, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -8, -8, -8, -8, -8, -8, -8, -8, -2, 4, 4, -8, -2, -2, 4, 4, -8, -2, -2, 4, -8, -2, 4, 4, -2, -2, 4, 4, -8, -2, 4, 4, -8, -2, -2, -2, -2, -2, -8, -8, 4, 4, 4, 4, -8, 4, -2, -2, 4, 4, 4, 4, 4, -2, 4, 4, 4, 4, -2, 4, -8, 4, -8, -8, -2, 4, 4, -2, 4, 4, -2, -2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
-
id: 4079024
{'cdim': 16, 'counter': 28, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.16a', 'multiplicity': 1, 'nt': [20, 360], 'qdim': 16, 'qvalues': [16, 0, 0, 0, 16, 16, 16, 16, 4, 0, 0, 0, 0, -4, -4, -4, -4, 6, 1, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, 6, 6, 1, 1, -4, -4, -4, -4, -4, -4, -4, 1, 6, 1, 1, -4, 6, -4, -4, -4, 1, 6, 6, 1, 6, -4, 6, 6, 1, 1, -4, 1, 6, 1, 6, 1, 1, 1, -4, 1, 1, -4, -4, 6, 1, -4, 1, 6, -4, 1, -4, -4, 1, -4, 1, -4, 6, -4, 1, 1, -4, 1, 1, -4, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
-
id: 4079019
{'cdim': 12, 'counter': 23, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.12e', 'multiplicity': 2, 'nt': [30, 591], 'qdim': 24, 'qvalues': [24, 0, 8, 0, 24, 24, 24, 24, 0, 0, 0, 4, 4, -1, 4, -1, -6, -6, 4, 8, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, 3, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 4, -1, 4, -1, 4, -6, -6, 4, 4, 4, -6, -1, -1, -1, 4, -1, 4, -6, 4, 4, -6, -6, -1, -1, -1, 4, -6, -6, 4, -6, -1, -6, -6, 4, 4, 4, 4, -6, 4, -6, 4, 4, 4, 4, 4, 4, -6, 4, -6, 4, -6, 4, -6, -1, 4, -6, -6, 4, -6, 4, -6, -6, -1, 4, 4, -1, 4, 4, -1, 4, 0, 0, 0, 0, -1, -1, -1, -1, -2, 3, -2, -2, 3, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079020
{'cdim': 12, 'counter': 24, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.12f', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 24, 'qvalues': [24, 0, 0, -8, 24, 24, 24, 24, 0, 0, 0, 0, 0, 4, 14, 4, -6, 4, -6, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 14, 4, 14, 4, 14, 4, 4, -6, -6, 14, -6, 4, 4, 4, 14, 4, -6, 4, -6, -6, -6, 4, 4, 4, 4, -6, 4, 4, -6, 4, 4, 4, 4, -6, -6, 14, -6, 4, -6, 4, -6, -6, -6, 14, -6, -6, -6, 14, 4, -6, -6, -6, 4, 4, -6, -6, -6, -6, -6, -6, -6, 4, 4, -6, -6, 4, -6, -6, 4, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079021
{'cdim': 12, 'counter': 25, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.12g', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 24, 'qvalues': [24, 0, 8, 0, 24, 24, 24, 24, 0, 0, 0, -4, -4, -1, 4, -1, -6, -6, 4, 8, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, 3, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 4, -1, 4, -1, 4, -6, -6, 4, 4, 4, -6, -1, -1, -1, 4, -1, 4, -6, 4, 4, -6, -6, -1, -1, -1, 4, -6, -6, 4, -6, -1, -6, -6, 4, 4, 4, 4, -6, 4, -6, 4, 4, 4, 4, 4, 4, -6, 4, -6, 4, -6, 4, -6, -1, 4, -6, -6, 4, -6, 4, -6, -6, -1, 4, 4, -1, 4, 4, -1, 4, 0, 0, 0, 0, 1, 1, 1, 1, -2, 3, -2, -2, 3, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079022
{'cdim': 12, 'counter': 26, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.12h', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 6, 6, 0, -6, 0, 0, 0, 0, 0, 24, 24, 24, 24, 24, 24, 0, -6, -6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 6, -6, -6, 0, 6, 6, -6, -6, 0, 6, 6, -6, 0, 6, -6, -6, 6, 6, -6, -6, 0, 6, -6, -6, 0, 6, 6, 6, 6, 6, 0, 0, -6, -6, -6, -6, 0, -6, 6, 6, -6, -6, -6, -6, -6, 6, -6, -6, -6, -6, 6, -6, 0, -6, 0, 0, 6, -6, -6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079029
{'cdim': 24, 'counter': 32, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.24a', 'multiplicity': 1, 'nt': [30, 607], 'qdim': 24, 'qvalues': [24, 0, 8, 0, 24, 24, 24, 24, 0, 0, 0, 0, 0, -6, 4, -6, 9, -1, -1, 8, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 4, -6, 4, -6, 4, -1, -1, -1, -1, 4, 9, -6, -6, -6, 4, -6, -1, -1, -1, -1, 9, -1, -6, -6, -6, -1, -1, -1, -1, -1, -6, -1, -1, -1, -1, 4, -1, -1, -1, -1, -1, -1, -1, 4, -1, -1, 9, 4, -1, -1, 9, -1, -1, -6, -1, 9, 9, -1, 9, -1, 9, -1, -6, -1, -1, -6, -1, -1, -6, -1, 0, 0, 0, 0, 0, 0, 0, 0, 3, -2, -2, 3, -2, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079030
{'cdim': 24, 'counter': 33, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.24b', 'multiplicity': 1, 'nt': [45, 1152], 'qdim': 24, 'qvalues': [24, 0, 0, 8, -12, -12, 12, 0, 0, 0, 0, 0, 0, 4, 14, 4, -6, 4, -6, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 2, -8, 17, -8, 2, -8, -8, -3, 3, -10, 0, 7, -2, -2, 5, -5, -3, -2, 3, 0, -3, -2, 10, -5, -2, 3, -5, -5, -3, -2, -5, -5, 7, 3, 3, -7, 3, -2, -3, 7, 0, 0, 0, 5, -3, 0, 3, -7, 10, 0, 0, 0, 10, -2, 0, 0, 0, 0, 3, 0, -3, -5, 7, -3, 3, -5, 0, 3, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079031
{'cdim': 24, 'counter': 34, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.24c', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 24, 'qvalues': [24, 0, -8, 0, 24, 24, 24, 24, 0, 0, 0, 0, 0, -6, 4, -6, 9, -1, -1, -8, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 4, -6, 4, -6, 4, -1, -1, -1, -1, 4, 9, -6, -6, -6, 4, -6, -1, -1, -1, -1, 9, -1, -6, -6, -6, -1, -1, -1, -1, -1, -6, -1, -1, -1, -1, 4, -1, -1, -1, -1, -1, -1, -1, 4, -1, -1, 9, 4, -1, -1, 9, -1, -1, -6, -1, 9, 9, -1, 9, -1, 9, -1, -6, -1, -1, -6, -1, -1, -6, -1, 0, 0, 0, 0, 0, 0, 0, 0, -3, 2, 2, -3, 2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079032
{'cdim': 24, 'counter': 35, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.24d', 'multiplicity': 1, 'nt': [180, 0], 'qdim': 24, 'qvalues': [24, 0, 0, -8, -12, -12, 12, 0, 0, 0, 0, 0, 0, 4, 14, 4, -6, 4, -6, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 2, -8, 17, -8, 2, -8, -8, -3, 3, -10, 0, 7, -2, -2, 5, -5, -3, -2, 3, 0, -3, -2, 10, -5, -2, 3, -5, -5, -3, -2, -5, -5, 7, 3, 3, -7, 3, -2, -3, 7, 0, 0, 0, 5, -3, 0, 3, -7, 10, 0, 0, 0, 10, -2, 0, 0, 0, 0, 3, 0, -3, -5, 7, -3, 3, -5, 0, 3, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], 'schur_index': 2}
-
id: 4079025
{'cdim': 16, 'counter': 29, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.16b', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 32, 'qvalues': [32, 0, 0, 0, -4, -4, -16, 8, 8, 0, 0, 0, 0, -8, -8, -8, -8, 12, 2, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 4, 4, 4, 4, 4, -6, -6, -1, -4, -2, -2, 4, 1, 1, -2, -2, -1, -9, -4, -7, 4, -9, -2, -2, 1, -4, 3, 3, -1, 6, -2, 3, -6, -4, 11, 1, -4, 6, -1, -6, -7, -7, 8, -2, -1, 8, 1, 1, -12, 8, -2, -7, 18, 1, 8, -2, -2, 8, 1, -7, 4, 3, 4, -1, 11, -2, 8, -4, -2, -7, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
-
id: 4079027
{'cdim': 16, 'counter': 30, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.16c', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 32, 'qvalues': [32, 0, 0, 0, 32, 32, 32, 32, -4, 0, 0, 0, 0, -8, -8, -8, -8, 12, 2, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, -8, -8, -8, -8, 12, 12, 2, 2, -8, -8, -8, -8, -8, -8, -8, 2, 12, 2, 2, -8, 12, -8, -8, -8, 2, 12, 12, 2, 12, -8, 12, 12, 2, 2, -8, 2, 12, 2, 12, 2, 2, 2, -8, 2, 2, -8, -8, 12, 2, -8, 2, 12, -8, 2, -8, -8, 2, -8, 2, -8, 12, -8, 2, 2, -8, 2, 2, -8, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
-
id: 4079023
{'cdim': 12, 'counter': 27, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.12i', 'multiplicity': 4, 'nt': [120, 0], 'qdim': 48, 'qvalues': [48, 0, -16, 0, 48, 48, 48, 48, 0, 0, 0, 0, 0, -2, 8, -2, -12, -12, 8, -16, 0, 0, 0, 0, 0, 0, 0, 0, 4, -6, -6, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 8, -2, 8, -2, 8, -12, -12, 8, 8, 8, -12, -2, -2, -2, 8, -2, 8, -12, 8, 8, -12, -12, -2, -2, -2, 8, -12, -12, 8, -12, -2, -12, -12, 8, 8, 8, 8, -12, 8, -12, 8, 8, 8, 8, 8, 8, -12, 8, -12, 8, -12, 8, -12, -2, 8, -12, -12, 8, -12, 8, -12, -12, -2, 8, 8, -2, 8, 8, -2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 4, -6, 4, 4, -6, 4, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079033
{'cdim': 24, 'counter': 36, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.24e', 'multiplicity': 2, 'nt': [90, 0], 'qdim': 48, 'qvalues': [48, 0, 16, 0, -24, -24, 24, 0, 0, 0, 0, 0, 0, -12, 8, -12, 18, -2, -2, -8, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, -9, 14, -6, -16, -6, 14, -11, -11, -11, 1, 20, 0, -6, 6, 6, -10, 0, 4, 1, 1, -5, 9, 1, 0, 0, 6, 1, -5, -5, 4, 1, 0, -5, 4, 1, 1, -4, 1, 1, 4, 4, -5, -5, -5, -10, 4, -5, -9, -4, 10, 10, 0, -5, 10, 6, -5, 0, 0, 10, -9, 10, 9, -5, -6, -11, 1, 0, -5, 1, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, -3, 2, 2, -3, 2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079034
{'cdim': 24, 'counter': 37, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.24f', 'multiplicity': 2, 'nt': [90, 0], 'qdim': 48, 'qvalues': [48, 0, 16, 0, -24, -24, 24, 0, 0, 0, 0, 0, 0, -2, 8, -2, -12, -12, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, -4, 6, 6, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 14, -11, -16, -11, 14, -6, -6, 14, -4, 20, 0, 4, 1, 1, -10, -5, -1, 6, -4, 5, -6, 6, 10, -5, 1, -4, 0, 0, -1, 6, -5, 0, -6, -4, -4, -4, -4, 6, -1, -6, 5, 5, 5, -10, -1, 5, 6, -4, 0, -10, 0, 5, 0, 1, 5, 0, 0, -10, 6, -10, -6, 0, 4, 14, -4, -5, 5, -4, 10, -10, 0, 0, 0, 0, 0, 0, 0, 0, 2, -3, 2, 2, -3, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079035
{'cdim': 24, 'counter': 38, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.24g', 'multiplicity': 2, 'nt': [90, 0], 'qdim': 48, 'qvalues': [48, 0, 16, 0, -24, -24, 24, 0, 0, 0, 0, 0, 0, 8, 28, 8, -12, 8, -12, -8, 0, 0, 0, 0, 0, 0, 0, 0, 6, -4, -4, 6, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 19, 14, 4, 14, 19, 14, 14, -6, 6, 10, 0, -1, -4, -4, -5, 5, -6, -4, 6, 0, -6, -4, -10, 5, -4, 6, 5, 5, -6, -4, 5, 5, -1, 6, 6, -14, 6, -4, -6, -1, 0, 0, 0, -5, -6, 0, 6, -14, -10, 0, 0, 0, -10, -4, 0, 0, 0, 0, 6, 0, -6, 5, -1, -6, 6, 5, 0, 6, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -3, 2, 2, -3, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079036
{'cdim': 24, 'counter': 39, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.24h', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 48, 'qvalues': [48, 0, -16, 0, -24, -24, 24, 0, 0, 0, 0, 0, 0, -12, 8, -12, 18, -2, -2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, -9, 14, -6, -16, -6, 14, -11, -11, -11, 1, 20, 0, -6, 6, 6, -10, 0, 4, 1, 1, -5, 9, 1, 0, 0, 6, 1, -5, -5, 4, 1, 0, -5, 4, 1, 1, -4, 1, 1, 4, 4, -5, -5, -5, -10, 4, -5, -9, -4, 10, 10, 0, -5, 10, 6, -5, 0, 0, 10, -9, 10, 9, -5, -6, -11, 1, 0, -5, 1, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 3, -2, -2, 3, -2, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079038
{'cdim': 24, 'counter': 40, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.24i', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 48, 'qvalues': [48, 0, -16, 0, -24, -24, 24, 0, 0, 0, 0, 0, 0, 8, 28, 8, -12, 8, -12, 8, 0, 0, 0, 0, 0, 0, 0, 0, -6, 4, 4, -6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 19, 14, 4, 14, 19, 14, 14, -6, 6, 10, 0, -1, -4, -4, -5, 5, -6, -4, 6, 0, -6, -4, -10, 5, -4, 6, 5, 5, -6, -4, 5, 5, -1, 6, 6, -14, 6, -4, -6, -1, 0, 0, 0, -5, -6, 0, 6, -14, -10, 0, 0, 0, -10, -4, 0, 0, 0, 0, 6, 0, -6, 5, -1, -6, 6, 5, 0, 6, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, -2, -2, 3, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079039
{'cdim': 24, 'counter': 41, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.24j', 'multiplicity': 2, 'nt': [360, 0], 'qdim': 48, 'qvalues': [48, 0, -16, 0, -24, -24, 24, 0, 0, 0, 0, 0, 0, -2, 8, -2, -12, -12, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 4, -6, -6, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 14, -11, -16, -11, 14, -6, -6, 14, -4, 20, 0, 4, 1, 1, -10, -5, -1, 6, -4, 5, -6, 6, 10, -5, 1, -4, 0, 0, -1, 6, -5, 0, -6, -4, -4, -4, -4, 6, -1, -6, 5, 5, 5, -10, -1, 5, 6, -4, 0, -10, 0, 5, 0, 1, 5, 0, 0, -10, 6, -10, -6, 0, 4, 14, -4, -5, 5, -4, 10, -10, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, -2, -2, 3, -2, 0, 0, 0, 0, 0], 'schur_index': 2}
-
id: 4079040
{'cdim': 48, 'counter': 42, 'faithful': False, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48a', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, 48, 48, 48, 48, 0, 0, 0, 0, 0, 8, -12, 8, 3, -2, -2, 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, 3, 3, -12, 8, -12, 8, -12, -2, -2, -2, -2, -12, 3, 8, 8, 8, -12, 8, -2, -2, -2, -2, 3, -2, 8, 8, 8, -2, -2, -2, -2, -2, 8, -2, -2, -2, -2, -12, -2, -2, -2, -2, -2, -2, -2, -12, -2, -2, 3, -12, -2, -2, 3, -2, -2, 8, -2, 3, 3, -2, 3, -2, 3, -2, 8, -2, -2, 8, -2, -2, 8, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079041
{'cdim': 48, 'counter': 43, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48b', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, 12, 12, 0, -12, 0, 0, 0, 0, 0, -12, 8, -12, 18, -2, -2, 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, -18, -18, -10, 0, 20, 0, -10, 10, 10, 10, 7, 8, -12, 0, -3, -3, -7, 3, -5, -8, 7, -2, 0, -8, 3, 3, -3, -8, -2, -2, -5, 7, 3, -2, -5, -8, -8, 2, 7, 7, -5, -5, -2, -2, -2, -7, -5, -2, 12, 2, 13, 13, -12, -2, -2, -3, -2, 3, 3, 13, 12, -2, 0, -2, 0, 10, -8, 3, -2, 7, 3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079042
{'cdim': 48, 'counter': 44, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48c', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, 12, 12, 0, -12, 0, 0, 0, 0, 0, -12, 8, -12, 18, -2, -2, 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, 27, 27, -10, 0, 20, 0, -10, 10, 10, 10, -8, 8, 3, 0, -3, -3, -7, 3, -5, 7, -8, -2, 0, 7, 3, 3, -3, 7, -2, -2, -5, -8, 3, -2, -5, 7, 7, 2, -8, -8, -5, -5, -2, -2, -2, -7, -5, -2, -3, 2, -2, -2, 3, -2, 13, -3, -2, -12, -12, -2, -3, 13, 0, -2, 0, 10, 7, 3, -2, -8, 3, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079043
{'cdim': 48, 'counter': 45, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48d', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, 12, 12, 0, -12, 0, 0, 0, 0, 0, 8, 28, 8, -12, 8, -12, 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, -3, -3, 10, 20, -20, 20, 10, 20, 20, 0, -3, -17, 3, -10, 2, 2, -2, -7, 0, 2, -3, 3, 0, 2, 8, -7, 2, -3, -7, -7, 0, 2, -7, -7, -10, -3, -3, 7, -3, 2, 0, -10, 3, 3, 3, -2, 0, 3, -3, 7, 8, 3, 3, 3, 8, 2, 3, 3, 3, 3, -3, 3, 0, -7, -10, 0, -3, -7, 3, -3, 8, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079028
{'cdim': 16, 'counter': 31, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.16d', 'multiplicity': 4, 'nt': [120, 0], 'qdim': 64, 'qvalues': [64, 0, 0, 0, -8, -8, -32, 16, -8, 0, 0, 0, 0, -16, -16, -16, -16, 24, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 8, 8, 8, 8, 8, -12, -12, -2, -8, -4, -4, 8, 2, 2, -4, -4, -2, -18, -8, -14, 8, -18, -4, -4, 2, -8, 6, 6, -2, 12, -4, 6, -12, -8, 22, 2, -8, 12, -2, -12, -14, -14, 16, -4, -2, 16, 2, 2, -24, 16, -4, -14, 36, 2, 16, -4, -4, 16, 2, -14, 8, 6, 8, -2, 22, -4, 16, -8, -4, -14, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
-
id: 4079044
{'cdim': 48, 'counter': 46, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48e', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, -48, -48, 48, 0, 0, 0, 0, 0, 0, -24, -24, -24, -24, 36, 6, 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, 12, 12, -12, -12, -12, -12, -12, 18, 18, 3, -3, 0, 0, -12, 12, 12, 0, 0, 3, -18, -3, 0, -12, -18, 0, 0, 12, -3, 0, 0, 3, -18, 0, 0, 18, -3, -3, 12, -3, -18, 3, 18, 0, 0, 0, 0, 3, 0, 12, 12, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 12, 0, -12, 0, -12, 3, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079045
{'cdim': 48, 'counter': 47, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48f', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, -48, -48, 48, 0, 0, 0, 0, 0, 0, -24, 16, -24, 36, -4, -4, 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, -18, -18, -2, -12, 28, -12, -2, 8, 8, 8, 2, -20, 0, -12, 12, 12, 10, 0, -7, 2, 2, 5, 18, 2, 0, 0, 12, 2, 5, 5, -7, 2, 0, 5, -7, 2, 2, -8, 2, 2, -7, -7, 5, 5, 5, 10, -7, 5, -18, -8, -10, -10, 0, 5, -10, 12, 5, 0, 0, -10, -18, -10, 18, 5, -12, 8, 2, 0, 5, 2, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079046
{'cdim': 48, 'counter': 48, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48g', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, -48, -48, 48, 0, 0, 0, 0, 0, 0, -4, 16, -4, -24, -24, 16, 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, 12, 12, -2, 8, 28, 8, -2, -12, -12, -2, -8, -20, 0, -7, 2, 2, 10, 5, 13, 12, -8, -5, -12, 12, -10, 5, 2, -8, 0, 0, 13, 12, 5, 0, -12, -8, -8, -8, -8, 12, 13, -12, -5, -5, -5, 10, 13, -5, 12, -8, 0, 10, 0, -5, 0, 2, -5, 0, 0, 10, 12, 10, -12, 0, -7, -2, -8, 5, -5, -8, -10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079047
{'cdim': 48, 'counter': 49, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48h', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, -48, -48, 48, 0, 0, 0, 0, 0, 0, 16, -24, 16, 6, -4, -4, 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, -3, -3, -12, 28, -12, 28, -12, -22, -22, 8, 2, 0, 0, -2, -8, -8, 0, 10, -7, 2, 2, 5, 3, 2, -20, 10, -8, 2, -10, -10, -7, 2, 10, -10, 8, 2, 2, 12, 2, 2, -7, 8, 5, 5, 5, 0, -7, 5, -3, 12, 20, -10, 0, 5, 20, -8, 5, 0, 0, -10, -3, -10, 3, -10, -2, 8, 2, 10, 5, 2, -20, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079049
{'cdim': 48, 'counter': 50, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48i', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, -12, -12, -48, 24, 0, 0, 0, 0, 0, -24, -24, -24, -24, 36, 6, 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, 3, 3, 12, 12, 12, 12, 12, -18, -18, -3, 3, -6, -6, 12, 3, 3, -6, -6, -3, 3, 3, 9, 12, 3, -6, -6, 3, 3, 9, 9, -3, -12, -6, 9, -18, 3, -12, 3, 3, -12, -3, -18, 9, 9, -6, -6, -3, -6, 3, 3, 24, -6, -6, 9, -6, 3, -6, -6, -6, -6, 3, 9, 12, 9, 12, -3, -12, -6, -6, 3, -6, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079050
{'cdim': 48, 'counter': 51, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48j', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, -12, -12, -48, 24, 0, 0, 0, 0, 0, -24, 16, -24, 36, -4, -4, 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, -27, -27, -8, 12, -8, 12, -8, 2, 2, 2, 8, 4, 24, 12, 3, 3, 4, -6, 2, -7, 8, -1, -18, -7, -6, -6, 3, -7, -1, -1, 2, 8, -6, -1, 2, -7, -7, -2, 8, 8, 2, 2, -1, -1, -1, 4, 2, -1, 3, -2, -16, -16, 24, -1, 14, 3, -1, -6, -6, -16, 3, 14, -18, -1, 12, 2, -7, -6, -1, 8, -6, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079051
{'cdim': 48, 'counter': 52, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48k', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, -12, -12, -48, 24, 0, 0, 0, 0, 0, -24, 16, -24, 36, -4, -4, 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, 18, 18, -8, 12, -8, 12, -8, 2, 2, 2, -7, 4, -6, 12, 3, 3, 4, -6, 2, 8, -7, -1, -18, 8, -6, -6, 3, 8, -1, -1, 2, -7, -6, -1, 2, 8, 8, -2, -7, -7, 2, 2, -1, -1, -1, 4, 2, -1, -12, -2, 14, 14, -6, -1, -16, 3, -1, 24, 24, 14, -12, -16, -18, -1, 12, 2, 8, -6, -1, -7, -6, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079052
{'cdim': 48, 'counter': 53, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48l', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, -12, -12, -48, 24, 0, 0, 0, 0, 0, 16, -24, 16, 6, -4, -4, 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, -12, -12, 12, -8, 12, -8, 12, 2, 2, 2, -7, -6, 9, -8, -2, -2, -6, 4, 2, -7, -7, 14, -3, -7, 4, 4, -2, 23, -1, -1, 2, 8, 4, -1, 2, 23, -7, 3, -7, 8, 2, 2, 14, 14, -16, -6, 2, -16, 3, 3, -16, 14, 9, 14, 14, -2, -16, -6, -6, 14, 3, -16, -3, -1, -8, 2, -7, 4, -16, -7, 4, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079053
{'cdim': 48, 'counter': 54, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48m', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, -12, -12, -48, 24, 0, 0, 0, 0, 0, 16, -24, 16, 6, -4, -4, 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, 33, 33, 12, -8, 12, -8, 12, 2, 2, 2, 8, -6, -21, -8, -2, -2, -6, 4, 2, -7, 8, -1, -3, -7, 4, 4, -2, -7, -1, -1, 2, 8, 4, -1, 2, -7, -7, 3, 8, 8, 2, 2, -1, -1, -1, -6, 2, -1, -12, 3, -16, -16, -21, -1, 14, -2, -1, 24, 24, -16, -12, 14, -3, -1, -8, 2, -7, 4, -1, 8, 4, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079054
{'cdim': 48, 'counter': 55, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48n', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, -12, -12, -48, 24, 0, 0, 0, 0, 0, 16, 56, 16, -24, 16, -24, 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, 3, 3, -28, -8, -28, -8, -28, -8, -8, 12, 3, 14, -6, -8, -2, -2, 14, 4, 12, -2, 3, -6, 12, -2, 4, 4, -2, 3, 4, 4, 12, -2, 4, 4, -8, 3, 3, -7, 3, -2, 12, -8, -6, -6, -6, 14, 12, -6, 3, -7, 4, -6, -6, -6, 4, -2, -6, -6, -6, -6, 3, -6, 12, 4, -8, 12, 3, 4, -6, 3, 4, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079055
{'cdim': 48, 'counter': 56, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48o', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, 24, 24, 0, -24, 0, 0, 0, 0, 0, -24, -24, -24, -24, 36, 6, 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, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, -6, 6, 6, 0, -6, -6, 6, 6, 0, -6, -6, 6, 0, -6, 6, 6, -6, -6, -9, -9, 0, 24, 6, -9, 0, -6, 24, -6, -6, 24, 0, 0, 6, 6, -9, 6, 0, -9, -6, -6, 6, -9, 6, 6, -24, -6, -9, 6, 6, -9, -6, 6, 0, -9, 0, 0, 24, 6, -9, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079056
{'cdim': 48, 'counter': 57, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48p', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, 24, 24, 0, -24, 0, 0, 0, 0, 0, -24, -24, -24, -24, 36, 6, 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, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 9, 6, 6, 0, -6, -6, 6, 6, 0, 24, 9, -9, 0, 24, 6, 6, -6, 9, -9, -9, 0, -6, 6, -9, 0, 9, -21, -6, 9, -6, 0, 0, -9, -9, 6, 6, 0, 6, -6, -6, -24, 6, 6, -9, 6, -6, 6, 6, 6, 6, -6, -9, 0, -9, 0, 0, -21, 6, 6, 9, 6, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079057
{'cdim': 48, 'counter': 58, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48q', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, 24, 24, 0, -24, 0, 0, 0, 0, 0, -4, 16, -4, -24, -24, 16, 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, -6, -6, -20, 20, 40, 20, -20, 0, 0, -20, 4, 16, 6, -10, -1, -1, -14, -4, 10, -6, 4, 1, 0, -6, 11, -4, -1, 4, 6, 6, 10, -6, -4, 6, 0, 4, 4, 4, 4, -6, 10, 0, 1, 1, 1, -14, 10, 1, -6, 4, 6, -14, 6, 1, 6, -1, 1, 6, 6, -14, -6, -14, 0, 6, -10, -20, 4, -4, 1, 4, 11, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079058
{'cdim': 48, 'counter': 59, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48r', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, 24, 24, 0, -24, 0, 0, 0, 0, 0, 16, -24, 16, 6, -4, -4, 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, -21, -21, 0, -20, 0, -20, 0, 20, 20, -10, -1, 6, -9, 10, 4, 4, 6, 1, 5, 14, -1, 11, 0, 14, -14, 1, 4, -16, -4, -4, 5, -16, 1, -4, -10, -16, 14, -6, -1, -16, 5, -10, 11, 11, -4, 6, 5, -4, 9, -6, -4, -4, -9, 11, 26, 4, -4, 6, 6, -4, 9, -4, 0, -4, 10, -10, 14, 1, -4, -1, -14, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079060
{'cdim': 48, 'counter': 60, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48s', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, 24, 24, 0, -24, 0, 0, 0, 0, 0, 16, -24, 16, 6, -4, -4, 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, 24, 24, 0, -20, 0, -20, 0, 20, 20, -10, -1, 6, 6, 10, 4, 4, 6, 1, 5, -16, -1, -4, 0, -16, -14, 1, 4, 14, -4, -4, 5, 14, 1, -4, -10, 14, -16, -6, -1, 14, 5, -10, -4, -4, 11, 6, 5, 11, -6, -6, 26, -4, 6, -4, -4, 4, 11, -9, -9, -4, -6, -4, 0, -4, 10, -10, -16, 1, 11, -1, -14, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079061
{'cdim': 48, 'counter': 61, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48t', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 0, 24, 24, 0, -24, 0, 0, 0, 0, 0, 16, 56, 16, -24, 16, -24, 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, -6, -6, -10, -20, 20, -20, -10, -20, -20, 0, -6, -4, 6, 10, 4, 4, -19, 1, 0, 4, -6, 6, 0, 4, -14, 1, 4, -6, 1, 1, 0, 4, 1, 1, 10, -6, -6, 14, -6, 4, 0, 10, 6, 6, 6, -19, 0, 6, -6, 14, -14, 6, 6, 6, -14, 4, 6, 6, 6, 6, -6, 6, 0, 1, 10, 0, -6, 1, 6, -6, -14, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079062
{'cdim': 48, 'counter': 62, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48u', 'multiplicity': 4, 'nt': [360, 0], 'qdim': 192, 'qvalues': [192, 0, 0, 0, -96, -96, 96, 0, 0, 0, 0, 0, 0, 32, -48, 32, 12, -8, -8, 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, -6, -6, -24, -4, -24, -4, -24, 16, 16, -14, 4, 0, 0, 26, -16, -16, 0, -10, 1, 4, 4, -5, 6, 4, 20, -10, -16, 4, 10, 10, 1, 4, -10, 10, -14, 4, 4, 24, 4, 4, 1, -14, -5, -5, -5, 0, 1, -5, -6, 24, -20, 10, 0, -5, -20, -16, -5, 0, 0, 10, -6, 10, 6, 10, 26, -14, 4, -10, -5, 4, 20, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079063
{'cdim': 48, 'counter': 63, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48v', 'multiplicity': 4, 'nt': [360, 0], 'qdim': 192, 'qvalues': [192, 0, 0, 0, -24, -24, -96, 48, 0, 0, 0, 0, 0, -8, 32, -8, -48, -48, 32, 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, 6, 6, -16, 4, -16, 4, -16, 24, 24, -16, -4, 8, -12, 4, 1, 1, 8, -2, -16, 6, -4, 8, 24, 6, -2, -2, 1, -4, -12, -12, -16, 6, -2, -12, 24, -4, -4, -4, -4, 6, -16, 24, 8, 8, 8, 8, -16, 8, 6, -4, -12, 8, -12, 8, -12, 1, 8, -12, -12, 8, 6, 8, 24, -12, 4, -16, -4, -2, 8, -4, -2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079064
{'cdim': 48, 'counter': 64, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48w', 'multiplicity': 4, 'nt': [360, 0], 'qdim': 192, 'qvalues': [192, 0, 0, 0, -24, -24, -96, 48, 0, 0, 0, 0, 0, 32, -48, 32, 12, -8, -8, 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, -24, -24, 24, -16, 24, -16, 24, 4, 4, 4, 1, -12, 18, -16, -4, -4, -12, 8, 4, 16, 1, -17, -6, 16, 8, 8, -4, -14, -2, -2, 4, -14, 8, -2, 4, -14, 16, 6, 1, -14, 4, 4, -17, -17, 13, -12, 4, 13, 6, 6, 28, -2, 18, -17, -32, -4, 13, -12, -12, -2, 6, -2, -6, -2, -16, 4, 16, 8, 13, 1, 8, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079065
{'cdim': 48, 'counter': 65, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48x', 'multiplicity': 4, 'nt': [360, 0], 'qdim': 192, 'qvalues': [192, 0, 0, 0, 48, 48, 0, -48, 0, 0, 0, 0, 0, -48, 32, -48, 72, -8, -8, 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, 18, 18, 20, 0, -40, 0, 20, -20, -20, -20, -2, -28, -18, 0, -12, -12, 2, 12, 10, -2, -2, 7, 0, -2, 12, 12, -12, -2, 7, 7, 10, -2, 12, 7, 10, -2, -2, 8, -2, -2, 10, 10, 7, 7, 7, 2, 10, 7, 18, 8, -8, -8, -18, 7, -8, -12, 7, -18, -18, -8, 18, -8, 0, 7, 0, -20, -2, 12, 7, -2, 12, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079066
{'cdim': 48, 'counter': 66, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48y', 'multiplicity': 4, 'nt': [360, 0], 'qdim': 192, 'qvalues': [192, 0, 0, 0, 48, 48, 0, -48, 0, 0, 0, 0, 0, -8, 32, -8, -48, -48, 32, 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, -12, -12, 20, -20, -40, -20, 20, 0, 0, 20, 8, -28, 12, 10, -2, -2, 2, 7, -10, -12, 8, -13, 0, -12, -8, 7, -2, 8, 12, 12, -10, -12, 7, 12, 0, 8, 8, 8, 8, -12, -10, 0, -13, -13, -13, 2, -10, -13, -12, 8, 12, 2, 12, -13, 12, -2, -13, 12, 12, 2, -12, 2, 0, 12, 10, 20, 8, 7, -13, 8, -8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079067
{'cdim': 48, 'counter': 67, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48z', 'multiplicity': 4, 'nt': [360, 0], 'qdim': 192, 'qvalues': [192, 0, 0, 0, 48, 48, 0, -48, 0, 0, 0, 0, 0, 32, -48, 32, 12, -8, -8, 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, -42, -42, 0, 20, 0, 20, 0, -20, -20, 10, -17, 12, -18, -10, 8, 8, 12, -13, -5, -2, -17, -8, 0, -2, 2, -13, 8, 28, 7, 7, -5, -2, -13, 7, 10, 28, -2, -12, -17, -2, -5, 10, -8, -8, 7, 12, -5, 7, 18, -12, -8, -8, -18, -8, -8, 8, 7, 12, 12, -8, 18, 22, 0, 7, -10, 10, -2, -13, 7, -17, 2, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4079068
{'cdim': 48, 'counter': 68, 'faithful': True, 'group': '162000.x', 'group_order': 162000, 'image': None, 'label': '162000.x.48aa', 'multiplicity': 4, 'nt': [360, 0], 'qdim': 192, 'qvalues': [192, 0, 0, 0, 48, 48, 0, -48, 0, 0, 0, 0, 0, 32, -48, 32, 12, -8, -8, 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, 48, 48, 0, 20, 0, 20, 0, -20, -20, 10, 13, 12, 12, -10, 8, 8, 12, -13, -5, -2, 13, 7, 0, -2, 2, -13, 8, -32, 7, 7, -5, -2, -13, 7, 10, -32, -2, -12, 13, -2, -5, 10, 7, 7, -8, 12, -5, -8, -12, -12, -8, 22, 12, 7, -8, 8, -8, -18, -18, 22, -12, -8, 0, 7, -10, 10, -2, -13, -8, 13, 2, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
gps_char • Show schema
Hide schema
-
id: 5852815
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 162000, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 162000, 'label': '162000.x.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
-
id: 5852862
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 162000, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 81000, 'label': '162000.x.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
-
id: 5852873
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 162000, 'counter': 3, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 40500, 'label': '162000.x.1c1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
-
id: 5852884
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 162000, 'counter': 4, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 40500, 'label': '162000.x.1c2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
-
id: 5852895
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 27000, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 27000, 'label': '162000.x.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
-
id: 5852906
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 27000, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.a1.a1', 'kernel_order': 13500, 'label': '162000.x.2b', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
-
id: 5852917
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 6750, 'counter': 7, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 6750, 'label': '162000.x.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852928
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 6750, 'counter': 8, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 6750, 'label': '162000.x.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852939
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 6750, 'counter': 9, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '48.30', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 3375, 'label': '162000.x.3c1', 'nt': [12, 27], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852816
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 6750, 'counter': 10, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '48.30', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 3375, 'label': '162000.x.3c2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852827
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 11, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '648.704', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 250, 'label': '162000.x.4a1', 'nt': [12, 175], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]]]}
-
id: 5852838
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 12, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '648.704', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 250, 'label': '162000.x.4a2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]]]}
-
id: 5852849
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 13, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '648.704', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 250, 'label': '162000.x.4b1', 'nt': [24, 1527], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]]]}
-
id: 5852856
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 14, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '648.704', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 250, 'label': '162000.x.4b2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]]]}
-
id: 5852857
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 15, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '1296.3086', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 125, 'label': '162000.x.4c1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-1, 0], [3, 2]], [[2, 0], [-3, 2]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[1, 3]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[1, 0], [-3, 2]], [[1, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0], [3, 2]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]]]}
-
id: 5852858
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 16, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '1296.3086', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 125, 'label': '162000.x.4c2', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[2, 0], [-3, 2]], [[-1, 0], [3, 2]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 1]], [[-2, 1]], [[2, 5]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[-2, 0], [3, 2]], [[1, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [-3, 2]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]]]}
-
id: 5852859
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 17, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '1296.3086', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 125, 'label': '162000.x.4c3', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-1, 0], [3, 2]], [[2, 0], [-3, 2]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 5]], [[-2, 5]], [[2, 1]], [[-1, 3]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[1, 0], [-3, 2]], [[1, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0], [3, 2]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]]]}
-
id: 5852860
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 18, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '1296.3086', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 125, 'label': '162000.x.4c4', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[2, 0], [-3, 2]], [[-1, 0], [3, 2]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[-2, 0], [3, 2]], [[1, 0]], [[-2, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[-2, 0], [3, 2]], [[-2, 0], [3, 2]], [[1, 0], [-3, 2]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [-3, 2]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0], [3, 2]], [[1, 0]], [[1, 0]], [[1, 0], [-3, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]]]}
-
id: 5852861
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 19, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '648.704', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 250, 'label': '162000.x.6a', 'nt': [9, 29], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852863
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 20, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '648.704', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 250, 'label': '162000.x.6b', 'nt': [18, 220], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852864
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 21, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '648.704', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 250, 'label': '162000.x.6c1', 'nt': [36, 1131], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852865
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 22, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '648.704', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 250, 'label': '162000.x.6c2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852866
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 23, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '1296.3086', 'image_order': 1296, 'indicator': 1, 'kernel': '1296.a1.a1', 'kernel_order': 125, 'label': '162000.x.6d1', 'nt': [36, 2141], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852867
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 24, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '1296.3086', 'image_order': 1296, 'indicator': 1, 'kernel': '1296.a1.a1', 'kernel_order': 125, 'label': '162000.x.6d2', 'nt': [36, 2141], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852868
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 25, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '1296.3086', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 125, 'label': '162000.x.6e1', 'nt': [36, 2147], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-2, 1]], [[2, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852869
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 26, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '1296.3086', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 125, 'label': '162000.x.6e2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[2, 1]], [[-2, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852870
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 27, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '648.704', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 250, 'label': '162000.x.8a1', 'nt': [24, 1540], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[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]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[-4, 0], [-6, 1]], [[2, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0], [6, 1]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]]]}
-
id: 5852871
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 28, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '648.704', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 250, 'label': '162000.x.8a2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[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]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[2, 0], [6, 1]], [[2, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]]]}
-
id: 5852872
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 29, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '1296.3086', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 125, 'label': '162000.x.8b1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[4, 0], [6, 1]], [[-2, 0], [-6, 1]], [[4, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[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]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[-4, 0], [-6, 1]], [[2, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0], [6, 1]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]]]}
-
id: 5852874
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 30, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '1296.3086', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 125, 'label': '162000.x.8b2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[-2, 0], [-6, 1]], [[4, 0], [6, 1]], [[4, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[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]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[2, 0], [6, 1]], [[2, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]]]}
-
id: 5852875
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 31, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 1, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.12a', 'nt': [15, 58], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[8, 0]], [[4, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852876
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 32, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '648.704', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 250, 'label': '162000.x.12b', 'nt': [18, 219], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 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]]]}
-
id: 5852877
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 33, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 1, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.12c', 'nt': [30, 616], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[-8, 0]], [[4, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852878
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 34, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '648.704', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 250, 'label': '162000.x.12d', 'nt': [36, 1126], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 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]]]}
-
id: 5852879
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 35, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 1, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.12e1', 'nt': [30, 591], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0], [5, 2], [5, -2]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0], [5, 2], [5, -2]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[2, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[2, 1], [2, -1]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852880
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 36, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 1, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.12e2', 'nt': [30, 591], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[2, 0], [5, 2], [5, -2]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[2, 1], [2, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0], [5, 2], [5, -2]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0], [5, 2], [5, -2]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[2, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852881
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 37, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 1, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.12f1', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 2], [2, -2]], [[2, 0], [4, 2], [4, -2]], [[-2, 0], [-4, 2], [-4, -2]], [[-1, 0], [-2, 2], [-2, -2]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 2], [4, -2]], [[1, 0], [2, 2], [2, -2]], [[0, 0]], [[-2, 0], [-4, 2], [-4, -2]], [[-1, 0], [-2, 2], [-2, -2]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852882
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 38, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 1, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.12f2', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 2], [-2, -2]], [[-2, 0], [-4, 2], [-4, -2]], [[2, 0], [4, 2], [4, -2]], [[1, 0], [2, 2], [2, -2]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 2], [-4, -2]], [[-1, 0], [-2, 2], [-2, -2]], [[0, 0]], [[2, 0], [4, 2], [4, -2]], [[1, 0], [2, 2], [2, -2]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852883
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 39, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 1, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.12g1', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0], [5, 2], [5, -2]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0], [5, 2], [5, -2]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[2, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[2, 1], [2, -1]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852885
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 40, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 1, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.12g2', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[2, 0], [5, 2], [5, -2]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[2, 1], [2, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0], [5, 2], [5, -2]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0], [5, 2], [5, -2]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[2, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[2, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852886
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 41, 'cyclotomic_n': 4, 'dim': 12, 'faithful': False, 'field': [1, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '1296.3086', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 125, 'label': '162000.x.12h1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 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]]]}
-
id: 5852887
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 250, 'counter': 42, 'cyclotomic_n': 4, 'dim': 12, 'faithful': False, 'field': [1, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '1296.3086', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 125, 'label': '162000.x.12h2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 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]]]}
-
id: 5852888
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 43, 'cyclotomic_n': 20, 'dim': 12, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 0, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.12i1', 'nt': [120, 0], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 5]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[2, 0], [5, 4], [-5, 6]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[-1, 0], [1, 4], [-1, 6]], [[-2, 0], [-1, 4], [1, 6]], [[2, 2], [2, -2]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0], [5, 4], [-5, 6]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0], [5, 4], [-5, 6]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0], [-5, 4], [5, 6]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[2, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[2, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 5], [1, 7]], [[-1, 3], [-1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[1, 3], [1, 7]], [[1, 0]], [[-1, 0], [1, 4], [-1, 6]], [[-2, 4], [-2, -4]], [[1, 0]], [[-2, 0], [-1, 4], [1, 6]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852889
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 44, 'cyclotomic_n': 20, 'dim': 12, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 0, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.12i2', 'nt': [120, 4], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 5]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[2, 0], [5, 4], [-5, 6]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[-1, 0], [1, 4], [-1, 6]], [[-2, 0], [-1, 4], [1, 6]], [[2, 2], [2, -2]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0], [5, 4], [-5, 6]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0], [5, 4], [-5, 6]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0], [-5, 4], [5, 6]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[2, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[2, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 5], [-1, 7]], [[1, 3], [1, 7]], [[1, 3], [-1, 5], [1, 7]], [[-1, 3], [-1, 7]], [[1, 0]], [[-1, 0], [1, 4], [-1, 6]], [[-2, 4], [-2, -4]], [[1, 0]], [[-2, 0], [-1, 4], [1, 6]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852890
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 45, 'cyclotomic_n': 20, 'dim': 12, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 0, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.12i3', 'nt': [120, 0], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 5]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0], [-5, 4], [5, 6]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 0], [-1, 4], [1, 6]], [[-1, 0], [1, 4], [-1, 6]], [[-2, 4], [-2, -4]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0], [-5, 4], [5, 6]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0], [5, 4], [-5, 6]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0], [5, 4], [-5, 6]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[2, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[2, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 7]], [[1, 3], [-1, 5], [1, 7]], [[1, 3], [1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[1, 0]], [[-2, 0], [-1, 4], [1, 6]], [[2, 2], [2, -2]], [[1, 0]], [[-1, 0], [1, 4], [-1, 6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852891
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 46, 'cyclotomic_n': 20, 'dim': 12, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 0, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.12i4', 'nt': [120, 4], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 5]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0], [-5, 4], [5, 6]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 0], [-1, 4], [1, 6]], [[-1, 0], [1, 4], [-1, 6]], [[-2, 4], [-2, -4]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0], [-5, 4], [5, 6]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0], [5, 4], [-5, 6]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0], [5, 4], [-5, 6]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[2, 0]], [[2, 0], [5, 4], [-5, 6]], [[2, 0]], [[2, 0]], [[-3, 0], [-5, 4], [5, 6]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[-1, 3], [-1, 7]], [[1, 3], [-1, 5], [1, 7]], [[1, 0]], [[-2, 0], [-1, 4], [1, 6]], [[2, 2], [2, -2]], [[1, 0]], [[-1, 0], [1, 4], [-1, 6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852892
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 47, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 1, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.16a', 'nt': [20, 360], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 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]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[6, 0]], [[1, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[6, 0]], [[-4, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[-1, 0]], [[-1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
-
id: 5852893
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 48, 'cyclotomic_n': 3, 'dim': 16, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.16b1', 'nt': [60, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0], [-12, 1]], [[4, 0], [12, 1]], [[-8, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[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]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0], [10, 1]], [[-8, 0], [-10, 1]], [[2, 0], [5, 1]], [[-1, 0], [2, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [5, 1]], [[-8, 0], [-7, 1]], [[-3, 0], [-2, 1]], [[-6, 0], [-5, 1]], [[2, 0]], [[-1, 0], [7, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [2, 1]], [[-1, 0], [-5, 1]], [[-1, 0], [-5, 1]], [[2, 0], [5, 1]], [[2, 0], [-2, 1]], [[-1, 0]], [[4, 0], [5, 1]], [[-3, 0]], [[-3, 0], [-2, 1]], [[4, 0], [-3, 1]], [[2, 0], [3, 1]], [[-3, 0], [-2, 1]], [[4, 0], [2, 1]], [[-3, 0], [-5, 1]], [[-3, 0]], [[-6, 0], [-5, 1]], [[-1, 0], [5, 1]], [[4, 0]], [[-1, 0]], [[-3, 0], [-5, 1]], [[4, 0]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[-6, 0]], [[4, 0]], [[-1, 0]], [[-1, 0], [5, 1]], [[9, 0]], [[-1, 0], [-3, 1]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[2, 0], [3, 1]], [[-1, 0], [5, 1]], [[2, 0]], [[4, 0], [5, 1]], [[2, 0]], [[-3, 0], [-5, 1]], [[7, 0], [3, 1]], [[-1, 0]], [[4, 0]], [[-1, 0], [2, 1]], [[-1, 0]], [[-6, 0], [-5, 1]], [[-1, 0]], [[-1, 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]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]]]}
-
id: 5852894
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 49, 'cyclotomic_n': 3, 'dim': 16, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.16b2', 'nt': [60, 2], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0], [12, 1]], [[-8, 0], [-12, 1]], [[-8, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[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]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-8, 0], [-10, 1]], [[2, 0], [10, 1]], [[-3, 0], [-5, 1]], [[-3, 0], [-2, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-3, 0], [-5, 1]], [[-1, 0], [7, 1]], [[-1, 0], [2, 1]], [[-1, 0], [5, 1]], [[2, 0]], [[-8, 0], [-7, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[-3, 0], [-2, 1]], [[4, 0], [5, 1]], [[4, 0], [5, 1]], [[-3, 0], [-5, 1]], [[4, 0], [2, 1]], [[-1, 0]], [[-1, 0], [-5, 1]], [[-3, 0]], [[-1, 0], [2, 1]], [[7, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [2, 1]], [[2, 0], [-2, 1]], [[2, 0], [5, 1]], [[-3, 0]], [[-1, 0], [5, 1]], [[-6, 0], [-5, 1]], [[4, 0]], [[-1, 0]], [[2, 0], [5, 1]], [[4, 0]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-6, 0]], [[4, 0]], [[-1, 0]], [[-6, 0], [-5, 1]], [[9, 0]], [[2, 0], [3, 1]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0], [-3, 1]], [[-6, 0], [-5, 1]], [[2, 0]], [[-1, 0], [-5, 1]], [[2, 0]], [[2, 0], [5, 1]], [[4, 0], [-3, 1]], [[-1, 0]], [[4, 0]], [[-3, 0], [-2, 1]], [[-1, 0]], [[-1, 0], [5, 1]], [[-1, 0]], [[-1, 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]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]]]}
-
id: 5852896
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 50, 'cyclotomic_n': 15, 'dim': 16, 'faithful': False, 'field': [4, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 0, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.16c1', 'nt': [60, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 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]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[6, 0]], [[1, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[6, 0]], [[-4, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[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]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]]]}
-
id: 5852897
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 51, 'cyclotomic_n': 15, 'dim': 16, 'faithful': False, 'field': [4, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 0, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.16c2', 'nt': [60, 2], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 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]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[6, 0]], [[1, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[6, 0]], [[-4, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[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]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]]]}
-
id: 5852898
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 52, 'cyclotomic_n': 15, 'dim': 16, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.16d1', 'nt': [120, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0], [-12, 5]], [[4, 0], [12, 5]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -5]], [[-2, 5]], [[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]], [[2, 0], [3, 5]], [[-1, 0], [-3, 5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0], [10, 5]], [[-8, 0], [-10, 5]], [[2, 0], [5, 5]], [[-1, 0], [2, 5]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0], [3, 5]], [[-1, 0], [-3, 5]], [[-1, 0]], [[-1, 0]], [[2, 0], [5, 5]], [[-8, 0], [-7, 5]], [[-3, 0], [-2, 5]], [[-6, 0], [-5, 5]], [[2, 0]], [[-1, 0], [7, 5]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 5]], [[-1, 0], [2, 5]], [[-1, 0], [-5, 5]], [[-1, 0], [-5, 5]], [[2, 0], [5, 5]], [[2, 0], [-2, 5]], [[-1, 0]], [[4, 0], [5, 5]], [[-3, 0]], [[-3, 0], [-2, 5]], [[4, 0], [-3, 5]], [[2, 0], [3, 5]], [[-3, 0], [-2, 5]], [[4, 0], [2, 5]], [[-3, 0], [-5, 5]], [[-3, 0]], [[-6, 0], [-5, 5]], [[-1, 0], [5, 5]], [[4, 0]], [[-1, 0]], [[-3, 0], [-5, 5]], [[4, 0]], [[-1, 0], [-3, 5]], [[-1, 0], [-3, 5]], [[-6, 0]], [[4, 0]], [[-1, 0]], [[-1, 0], [5, 5]], [[9, 0]], [[-1, 0], [-3, 5]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[2, 0], [3, 5]], [[-1, 0], [5, 5]], [[2, 0]], [[4, 0], [5, 5]], [[2, 0]], [[-3, 0], [-5, 5]], [[7, 0], [3, 5]], [[-1, 0]], [[4, 0]], [[-1, 0], [2, 5]], [[-1, 0]], [[-6, 0], [-5, 5]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[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]], [[1, 1], [-1, 2], [1, 3], [1, 4], [-1, 7]], [[-1, 1], [1, 2], [-1, 3], [-1, 4], [1, 5], [1, 7]], [[1, 0], [-1, 1], [-2, 2], [2, 3], [-1, 4], [-2, 7]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [1, 4], [-1, 5], [2, 7]]]}
-
id: 5852899
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 53, 'cyclotomic_n': 15, 'dim': 16, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.16d2', 'nt': [120, 4], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0], [12, 5]], [[-8, 0], [-12, 5]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[-2, -5]], [[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]], [[-1, 0], [-3, 5]], [[2, 0], [3, 5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-8, 0], [-10, 5]], [[2, 0], [10, 5]], [[-3, 0], [-5, 5]], [[-3, 0], [-2, 5]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0], [-3, 5]], [[2, 0], [3, 5]], [[-1, 0]], [[-1, 0]], [[-3, 0], [-5, 5]], [[-1, 0], [7, 5]], [[-1, 0], [2, 5]], [[-1, 0], [5, 5]], [[2, 0]], [[-8, 0], [-7, 5]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 5]], [[-3, 0], [-2, 5]], [[4, 0], [5, 5]], [[4, 0], [5, 5]], [[-3, 0], [-5, 5]], [[4, 0], [2, 5]], [[-1, 0]], [[-1, 0], [-5, 5]], [[-3, 0]], [[-1, 0], [2, 5]], [[7, 0], [3, 5]], [[-1, 0], [-3, 5]], [[-1, 0], [2, 5]], [[2, 0], [-2, 5]], [[2, 0], [5, 5]], [[-3, 0]], [[-1, 0], [5, 5]], [[-6, 0], [-5, 5]], [[4, 0]], [[-1, 0]], [[2, 0], [5, 5]], [[4, 0]], [[2, 0], [3, 5]], [[2, 0], [3, 5]], [[-6, 0]], [[4, 0]], [[-1, 0]], [[-6, 0], [-5, 5]], [[9, 0]], [[2, 0], [3, 5]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0], [-3, 5]], [[-6, 0], [-5, 5]], [[2, 0]], [[-1, 0], [-5, 5]], [[2, 0]], [[2, 0], [5, 5]], [[4, 0], [-3, 5]], [[-1, 0]], [[4, 0]], [[-3, 0], [-2, 5]], [[-1, 0]], [[-1, 0], [5, 5]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[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]], [[1, 0], [-1, 1], [-2, 2], [2, 3], [-1, 4], [-2, 7]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [1, 4], [-1, 5], [2, 7]], [[1, 1], [-1, 2], [1, 3], [1, 4], [-1, 7]], [[-1, 1], [1, 2], [-1, 3], [-1, 4], [1, 5], [1, 7]]]}
-
id: 5852900
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 54, 'cyclotomic_n': 15, 'dim': 16, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.16d3', 'nt': [120, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0], [-12, 5]], [[4, 0], [12, 5]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -5]], [[-2, 5]], [[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]], [[2, 0], [3, 5]], [[-1, 0], [-3, 5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0], [10, 5]], [[-8, 0], [-10, 5]], [[2, 0], [5, 5]], [[-1, 0], [2, 5]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0], [3, 5]], [[-1, 0], [-3, 5]], [[-1, 0]], [[-1, 0]], [[2, 0], [5, 5]], [[-8, 0], [-7, 5]], [[-3, 0], [-2, 5]], [[-6, 0], [-5, 5]], [[2, 0]], [[-1, 0], [7, 5]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 5]], [[-1, 0], [2, 5]], [[-1, 0], [-5, 5]], [[-1, 0], [-5, 5]], [[2, 0], [5, 5]], [[2, 0], [-2, 5]], [[-1, 0]], [[4, 0], [5, 5]], [[-3, 0]], [[-3, 0], [-2, 5]], [[4, 0], [-3, 5]], [[2, 0], [3, 5]], [[-3, 0], [-2, 5]], [[4, 0], [2, 5]], [[-3, 0], [-5, 5]], [[-3, 0]], [[-6, 0], [-5, 5]], [[-1, 0], [5, 5]], [[4, 0]], [[-1, 0]], [[-3, 0], [-5, 5]], [[4, 0]], [[-1, 0], [-3, 5]], [[-1, 0], [-3, 5]], [[-6, 0]], [[4, 0]], [[-1, 0]], [[-1, 0], [5, 5]], [[9, 0]], [[-1, 0], [-3, 5]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[2, 0], [3, 5]], [[-1, 0], [5, 5]], [[2, 0]], [[4, 0], [5, 5]], [[2, 0]], [[-3, 0], [-5, 5]], [[7, 0], [3, 5]], [[-1, 0]], [[4, 0]], [[-1, 0], [2, 5]], [[-1, 0]], [[-6, 0], [-5, 5]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[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]], [[-1, 1], [1, 2], [-1, 3], [-1, 4], [1, 5], [1, 7]], [[1, 1], [-1, 2], [1, 3], [1, 4], [-1, 7]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [1, 4], [-1, 5], [2, 7]], [[1, 0], [-1, 1], [-2, 2], [2, 3], [-1, 4], [-2, 7]]]}
-
id: 5852901
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 55, 'cyclotomic_n': 15, 'dim': 16, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.16d4', 'nt': [120, 4], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0], [12, 5]], [[-8, 0], [-12, 5]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[-2, -5]], [[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]], [[-1, 0], [-3, 5]], [[2, 0], [3, 5]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-8, 0], [-10, 5]], [[2, 0], [10, 5]], [[-3, 0], [-5, 5]], [[-3, 0], [-2, 5]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0], [-3, 5]], [[2, 0], [3, 5]], [[-1, 0]], [[-1, 0]], [[-3, 0], [-5, 5]], [[-1, 0], [7, 5]], [[-1, 0], [2, 5]], [[-1, 0], [5, 5]], [[2, 0]], [[-8, 0], [-7, 5]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 5]], [[-3, 0], [-2, 5]], [[4, 0], [5, 5]], [[4, 0], [5, 5]], [[-3, 0], [-5, 5]], [[4, 0], [2, 5]], [[-1, 0]], [[-1, 0], [-5, 5]], [[-3, 0]], [[-1, 0], [2, 5]], [[7, 0], [3, 5]], [[-1, 0], [-3, 5]], [[-1, 0], [2, 5]], [[2, 0], [-2, 5]], [[2, 0], [5, 5]], [[-3, 0]], [[-1, 0], [5, 5]], [[-6, 0], [-5, 5]], [[4, 0]], [[-1, 0]], [[2, 0], [5, 5]], [[4, 0]], [[2, 0], [3, 5]], [[2, 0], [3, 5]], [[-6, 0]], [[4, 0]], [[-1, 0]], [[-6, 0], [-5, 5]], [[9, 0]], [[2, 0], [3, 5]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0], [-3, 5]], [[-6, 0], [-5, 5]], [[2, 0]], [[-1, 0], [-5, 5]], [[2, 0]], [[2, 0], [5, 5]], [[4, 0], [-3, 5]], [[-1, 0]], [[4, 0]], [[-3, 0], [-2, 5]], [[-1, 0]], [[-1, 0], [5, 5]], [[2, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-1, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[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]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [1, 4], [-1, 5], [2, 7]], [[1, 0], [-1, 1], [-2, 2], [2, 3], [-1, 4], [-2, 7]], [[-1, 1], [1, 2], [-1, 3], [-1, 4], [1, 5], [1, 7]], [[1, 1], [-1, 2], [1, 3], [1, 4], [-1, 7]]]}
-
id: 5852902
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 56, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 1, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.24a', 'nt': [30, 607], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[24, 0]], [[24, 0]], [[24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[9, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[9, 0]], [[9, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[9, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[-1, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-6, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[-1, 0]], [[-1, 0]], [[-6, 0]], [[-1, 0]], [[9, 0]], [[9, 0]], [[-1, 0]], [[9, 0]], [[-1, 0]], [[9, 0]], [[-1, 0]], [[-6, 0]], [[-1, 0]], [[-1, 0]], [[-6, 0]], [[-1, 0]], [[-1, 0]], [[-6, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852903
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 57, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24b', 'nt': [45, 1152], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[14, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[2, 0]], [[-8, 0]], [[17, 0]], [[-8, 0]], [[2, 0]], [[-8, 0]], [[-8, 0]], [[-3, 0]], [[3, 0]], [[-10, 0]], [[0, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[5, 0]], [[-5, 0]], [[-3, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-2, 0]], [[10, 0]], [[-5, 0]], [[-2, 0]], [[3, 0]], [[-5, 0]], [[-5, 0]], [[-3, 0]], [[-2, 0]], [[-5, 0]], [[-5, 0]], [[7, 0]], [[3, 0]], [[3, 0]], [[-7, 0]], [[3, 0]], [[-2, 0]], [[-3, 0]], [[7, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-7, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-5, 0]], [[7, 0]], [[-3, 0]], [[3, 0]], [[-5, 0]], [[0, 0]], [[3, 0]], [[10, 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]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852904
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 58, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 1, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.24c', 'nt': [60, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[24, 0]], [[24, 0]], [[24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[9, 0]], [[-1, 0]], [[-1, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[9, 0]], [[9, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[9, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[-1, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-6, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[9, 0]], [[-1, 0]], [[-1, 0]], [[-6, 0]], [[-1, 0]], [[9, 0]], [[9, 0]], [[-1, 0]], [[9, 0]], [[-1, 0]], [[9, 0]], [[-1, 0]], [[-6, 0]], [[-1, 0]], [[-1, 0]], [[-6, 0]], [[-1, 0]], [[-1, 0]], [[-6, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852905
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 59, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24d', 'nt': [180, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[14, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[2, 0]], [[-8, 0]], [[17, 0]], [[-8, 0]], [[2, 0]], [[-8, 0]], [[-8, 0]], [[-3, 0]], [[3, 0]], [[-10, 0]], [[0, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[5, 0]], [[-5, 0]], [[-3, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-2, 0]], [[10, 0]], [[-5, 0]], [[-2, 0]], [[3, 0]], [[-5, 0]], [[-5, 0]], [[-3, 0]], [[-2, 0]], [[-5, 0]], [[-5, 0]], [[7, 0]], [[3, 0]], [[3, 0]], [[-7, 0]], [[3, 0]], [[-2, 0]], [[-3, 0]], [[7, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-7, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-5, 0]], [[7, 0]], [[-3, 0]], [[3, 0]], [[-5, 0]], [[0, 0]], [[3, 0]], [[10, 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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852907
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 60, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24e1', 'nt': [90, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[9, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0], [-15, 1]], [[3, 0], [15, 1]], [[7, 0]], [[-3, 0]], [[-8, 0]], [[-3, 0]], [[7, 0]], [[-3, 0], [5, 1]], [[-8, 0], [-5, 1]], [[-8, 0], [-5, 1]], [[-2, 0], [-5, 1]], [[10, 0]], [[5, 0], [10, 1]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-5, 0]], [[0, 0]], [[2, 0]], [[-2, 0], [-5, 1]], [[3, 0], [5, 1]], [[5, -1]], [[7, 0], [5, 1]], [[3, 0], [5, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0], [5, 1]], [[5, 1]], [[5, 1]], [[2, 0]], [[3, 0], [5, 1]], [[0, 0]], [[5, -1]], [[2, 0]], [[-2, 0], [-5, 1]], [[3, 0], [5, 1]], [[-2, 0]], [[3, 0], [5, 1]], [[-2, 0], [-5, 1]], [[2, 0]], [[2, 0]], [[5, -1]], [[5, 1]], [[5, -1]], [[-5, 0]], [[2, 0]], [[5, -1]], [[-7, 0], [-5, 1]], [[-2, 0]], [[5, 0]], [[5, 0]], [[-5, 0], [-10, 1]], [[5, 1]], [[5, 0]], [[3, 0]], [[5, 1]], [[0, 0]], [[0, 0]], [[5, 0]], [[-2, 0], [5, 1]], [[5, 0]], [[2, 0], [-5, 1]], [[5, -1]], [[-3, 0]], [[-3, 0], [5, 1]], [[-2, 0], [-5, 1]], [[0, 0]], [[5, 1]], [[-2, 0], [-5, 1]], [[0, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0], [-5, 1]], [[1, 0]], [[1, 0]], [[1, 0], [5, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852908
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 61, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24e2', 'nt': [90, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[9, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0], [15, 1]], [[-12, 0], [-15, 1]], [[7, 0]], [[-3, 0]], [[-8, 0]], [[-3, 0]], [[7, 0]], [[-8, 0], [-5, 1]], [[-3, 0], [5, 1]], [[-3, 0], [5, 1]], [[3, 0], [5, 1]], [[10, 0]], [[-5, 0], [-10, 1]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-5, 0]], [[0, 0]], [[2, 0]], [[3, 0], [5, 1]], [[-2, 0], [-5, 1]], [[5, 1]], [[2, 0], [-5, 1]], [[-2, 0], [-5, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-2, 0], [-5, 1]], [[5, -1]], [[5, -1]], [[2, 0]], [[-2, 0], [-5, 1]], [[0, 0]], [[5, 1]], [[2, 0]], [[3, 0], [5, 1]], [[-2, 0], [-5, 1]], [[-2, 0]], [[-2, 0], [-5, 1]], [[3, 0], [5, 1]], [[2, 0]], [[2, 0]], [[5, 1]], [[5, -1]], [[5, 1]], [[-5, 0]], [[2, 0]], [[5, 1]], [[-2, 0], [5, 1]], [[-2, 0]], [[5, 0]], [[5, 0]], [[5, 0], [10, 1]], [[5, -1]], [[5, 0]], [[3, 0]], [[5, -1]], [[0, 0]], [[0, 0]], [[5, 0]], [[-7, 0], [-5, 1]], [[5, 0]], [[7, 0], [5, 1]], [[5, 1]], [[-3, 0]], [[-8, 0], [-5, 1]], [[3, 0], [5, 1]], [[0, 0]], [[5, -1]], [[3, 0], [5, 1]], [[0, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [5, 1]], [[1, 0]], [[1, 0]], [[-4, 0], [-5, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852909
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 62, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24f1', 'nt': [90, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0], [10, 2], [10, -2]], [[4, 0]], [[-6, 0], [-10, 2], [-10, -2]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[4, 0], [2, 2], [2, -2]], [[2, 0], [-2, 2], [-2, -2]], [[4, 2], [4, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[4, 0], [-6, 2], [-6, -2]], [[-2, 0], [7, 2], [7, -2]], [[-8, 0]], [[-9, 0], [-7, 2], [-7, -2]], [[10, 0], [6, 2], [6, -2]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-2, 0]], [[10, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[3, 0], [5, 2], [5, -2]], [[-2, 0], [-5, 2], [-5, -2]], [[-2, 0], [6, 2], [6, -2]], [[-3, 0], [-1, 2], [-1, -2]], [[1, 0], [3, 2], [3, -2]], [[3, 0]], [[-2, 0]], [[1, 0], [-3, 2], [-3, -2]], [[-3, 0]], [[3, 0]], [[4, 0], [-2, 2], [-2, -2]], [[-3, 0], [-1, 2], [-1, -2]], [[-2, 0], [-5, 2], [-5, -2]], [[-2, 0]], [[3, 0], [6, 2], [6, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[-2, 0], [-3, 2], [-3, -2]], [[3, 0]], [[-2, 0], [1, 2], [1, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[6, 1], [6, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[1, 0], [3, 2], [3, -2]], [[6, 2], [6, -2]], [[4, 0], [3, 2], [3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[4, 0], [3, 2], [3, -2]], [[-8, 0], [-6, 2], [-6, -2]], [[-2, 0], [-3, 2], [-3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[3, 0]], [[-2, 0]], [[0, 0]], [[-5, 0]], [[0, 0]], [[4, 0], [3, 2], [3, -2]], [[0, 0]], [[3, 0], [5, 2], [5, -2]], [[1, 0], [-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[-5, 0]], [[3, 0]], [[-5, 0]], [[-3, 0]], [[3, 0], [6, 2], [6, -2]], [[-4, 1], [-4, -1]], [[7, 0]], [[-2, 0]], [[-2, 0], [1, 2], [1, -2]], [[4, 0], [3, 2], [3, -2]], [[-2, 0]], [[6, 0], [2, 2], [2, -2]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-2, 1], [-2, -1]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852910
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 63, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24f2', 'nt': [90, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0], [-10, 2], [-10, -2]], [[4, 0]], [[4, 0], [10, 2], [10, -2]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[2, 0], [-2, 2], [-2, -2]], [[4, 0], [2, 2], [2, -2]], [[4, 1], [4, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[10, 0], [6, 2], [6, -2]], [[-9, 0], [-7, 2], [-7, -2]], [[-8, 0]], [[-2, 0], [7, 2], [7, -2]], [[4, 0], [-6, 2], [-6, -2]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-2, 0]], [[10, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[-2, 0], [-5, 2], [-5, -2]], [[3, 0], [5, 2], [5, -2]], [[-8, 0], [-6, 2], [-6, -2]], [[-2, 0], [1, 2], [1, -2]], [[-2, 0], [-3, 2], [-3, -2]], [[3, 0]], [[-2, 0]], [[4, 0], [3, 2], [3, -2]], [[-3, 0]], [[3, 0]], [[6, 0], [2, 2], [2, -2]], [[-2, 0], [1, 2], [1, -2]], [[3, 0], [5, 2], [5, -2]], [[-2, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[3, 0], [6, 2], [6, -2]], [[1, 0], [3, 2], [3, -2]], [[3, 0]], [[-3, 0], [-1, 2], [-1, -2]], [[3, 0], [6, 2], [6, -2]], [[6, 2], [6, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0], [-3, 2], [-3, -2]], [[6, 1], [6, -1]], [[1, 0], [-3, 2], [-3, -2]], [[4, 0], [3, 2], [3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[-2, 0], [6, 2], [6, -2]], [[1, 0], [3, 2], [3, -2]], [[4, 0], [3, 2], [3, -2]], [[3, 0]], [[-2, 0]], [[0, 0]], [[-5, 0]], [[0, 0]], [[1, 0], [-3, 2], [-3, -2]], [[0, 0]], [[-2, 0], [-5, 2], [-5, -2]], [[4, 0], [3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[-5, 0]], [[3, 0]], [[-5, 0]], [[-3, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[-4, 2], [-4, -2]], [[7, 0]], [[-2, 0]], [[-3, 0], [-1, 2], [-1, -2]], [[1, 0], [-3, 2], [-3, -2]], [[-2, 0]], [[4, 0], [-2, 2], [-2, -2]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-2, 2], [-2, -2]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852911
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 64, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24g1', 'nt': [90, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[14, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0], [2, 2], [2, -2]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[2, 0], [-2, 2], [-2, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[11, 0], [3, 2], [3, -2]], [[4, 0], [-6, 2], [-6, -2]], [[2, 0]], [[10, 0], [6, 2], [6, -2]], [[8, 0], [-3, 2], [-3, -2]], [[7, 0]], [[7, 0]], [[-3, 0]], [[3, 0]], [[5, 0]], [[0, 0]], [[-2, 0], [-3, 2], [-3, -2]], [[-2, 0]], [[-2, 0]], [[-4, 0], [-3, 2], [-3, -2]], [[4, 0], [3, 2], [3, -2]], [[6, 2], [6, -2]], [[-2, 0]], [[3, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[-3, 0]], [[-2, 0]], [[-2, 0], [6, 2], [6, -2]], [[4, 0], [3, 2], [3, -2]], [[-2, 0]], [[3, 0]], [[1, 0], [-3, 2], [-3, -2]], [[4, 0], [3, 2], [3, -2]], [[6, 1], [6, -1]], [[-2, 0]], [[1, 0], [-3, 2], [-3, -2]], [[4, 0], [3, 2], [3, -2]], [[1, 0], [3, 2], [3, -2]], [[3, 0]], [[3, 0]], [[-7, 0]], [[3, 0]], [[-2, 0]], [[6, 2], [6, -2]], [[-2, 0], [-3, 2], [-3, -2]], [[3, 0], [6, 2], [6, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[3, 0], [6, 2], [6, -2]], [[-1, 0], [3, 2], [3, -2]], [[6, 1], [6, -1]], [[-3, 0], [-6, 2], [-6, -2]], [[3, 0]], [[-7, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[3, 0], [6, 2], [6, -2]], [[-5, 0]], [[-2, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[1, 0], [-3, 2], [-3, -2]], [[1, 0], [3, 2], [3, -2]], [[-3, 0]], [[3, 0]], [[1, 0], [-3, 2], [-3, -2]], [[3, 0], [6, 2], [6, -2]], [[3, 0]], [[-8, 0], [-6, 2], [-6, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 2], [-2, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[-2, 1], [-2, -1]], [[-1, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852912
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 65, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24g2', 'nt': [90, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[14, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-2, 2], [-2, -2]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[4, 0], [2, 2], [2, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[8, 0], [-3, 2], [-3, -2]], [[10, 0], [6, 2], [6, -2]], [[2, 0]], [[4, 0], [-6, 2], [-6, -2]], [[11, 0], [3, 2], [3, -2]], [[7, 0]], [[7, 0]], [[-3, 0]], [[3, 0]], [[5, 0]], [[0, 0]], [[1, 0], [3, 2], [3, -2]], [[-2, 0]], [[-2, 0]], [[-1, 0], [3, 2], [3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[6, 1], [6, -1]], [[-2, 0]], [[3, 0]], [[3, 0], [6, 2], [6, -2]], [[-3, 0]], [[-2, 0]], [[-8, 0], [-6, 2], [-6, -2]], [[1, 0], [-3, 2], [-3, -2]], [[-2, 0]], [[3, 0]], [[4, 0], [3, 2], [3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[6, 2], [6, -2]], [[-2, 0]], [[4, 0], [3, 2], [3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[-2, 0], [-3, 2], [-3, -2]], [[3, 0]], [[3, 0]], [[-7, 0]], [[3, 0]], [[-2, 0]], [[6, 1], [6, -1]], [[1, 0], [3, 2], [3, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[3, 0], [6, 2], [6, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[-4, 0], [-3, 2], [-3, -2]], [[6, 2], [6, -2]], [[3, 0], [6, 2], [6, -2]], [[3, 0]], [[-7, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[-5, 0]], [[-2, 0]], [[3, 0], [6, 2], [6, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[4, 0], [3, 2], [3, -2]], [[-2, 0], [-3, 2], [-3, -2]], [[-3, 0]], [[3, 0]], [[4, 0], [3, 2], [3, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[3, 0]], [[-2, 0], [6, 2], [6, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 1], [-2, -1]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[-2, 2], [-2, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852913
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 66, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24h1', 'nt': [180, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[9, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0], [-15, 1]], [[3, 0], [15, 1]], [[7, 0]], [[-3, 0]], [[-8, 0]], [[-3, 0]], [[7, 0]], [[-3, 0], [5, 1]], [[-8, 0], [-5, 1]], [[-8, 0], [-5, 1]], [[-2, 0], [-5, 1]], [[10, 0]], [[5, 0], [10, 1]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-5, 0]], [[0, 0]], [[2, 0]], [[-2, 0], [-5, 1]], [[3, 0], [5, 1]], [[5, -1]], [[7, 0], [5, 1]], [[3, 0], [5, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0], [5, 1]], [[5, 1]], [[5, 1]], [[2, 0]], [[3, 0], [5, 1]], [[0, 0]], [[5, -1]], [[2, 0]], [[-2, 0], [-5, 1]], [[3, 0], [5, 1]], [[-2, 0]], [[3, 0], [5, 1]], [[-2, 0], [-5, 1]], [[2, 0]], [[2, 0]], [[5, -1]], [[5, 1]], [[5, -1]], [[-5, 0]], [[2, 0]], [[5, -1]], [[-7, 0], [-5, 1]], [[-2, 0]], [[5, 0]], [[5, 0]], [[-5, 0], [-10, 1]], [[5, 1]], [[5, 0]], [[3, 0]], [[5, 1]], [[0, 0]], [[0, 0]], [[5, 0]], [[-2, 0], [5, 1]], [[5, 0]], [[2, 0], [-5, 1]], [[5, -1]], [[-3, 0]], [[-3, 0], [5, 1]], [[-2, 0], [-5, 1]], [[0, 0]], [[5, 1]], [[-2, 0], [-5, 1]], [[0, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0], [5, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-5, 1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852914
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 67, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24h2', 'nt': [180, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[9, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0], [15, 1]], [[-12, 0], [-15, 1]], [[7, 0]], [[-3, 0]], [[-8, 0]], [[-3, 0]], [[7, 0]], [[-8, 0], [-5, 1]], [[-3, 0], [5, 1]], [[-3, 0], [5, 1]], [[3, 0], [5, 1]], [[10, 0]], [[-5, 0], [-10, 1]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-5, 0]], [[0, 0]], [[2, 0]], [[3, 0], [5, 1]], [[-2, 0], [-5, 1]], [[5, 1]], [[2, 0], [-5, 1]], [[-2, 0], [-5, 1]], [[0, 0]], [[0, 0]], [[3, 0]], [[-2, 0], [-5, 1]], [[5, -1]], [[5, -1]], [[2, 0]], [[-2, 0], [-5, 1]], [[0, 0]], [[5, 1]], [[2, 0]], [[3, 0], [5, 1]], [[-2, 0], [-5, 1]], [[-2, 0]], [[-2, 0], [-5, 1]], [[3, 0], [5, 1]], [[2, 0]], [[2, 0]], [[5, 1]], [[5, -1]], [[5, 1]], [[-5, 0]], [[2, 0]], [[5, 1]], [[-2, 0], [5, 1]], [[-2, 0]], [[5, 0]], [[5, 0]], [[5, 0], [10, 1]], [[5, -1]], [[5, 0]], [[3, 0]], [[5, -1]], [[0, 0]], [[0, 0]], [[5, 0]], [[-7, 0], [-5, 1]], [[5, 0]], [[7, 0], [5, 1]], [[5, 1]], [[-3, 0]], [[-8, 0], [-5, 1]], [[3, 0], [5, 1]], [[0, 0]], [[5, -1]], [[3, 0], [5, 1]], [[0, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-5, 1]], [[-1, 0]], [[-1, 0]], [[4, 0], [5, 1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852915
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 68, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24i1', 'nt': [180, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[14, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [2, 2], [2, -2]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[-4, 0], [-2, 2], [-2, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[8, 0], [-3, 2], [-3, -2]], [[10, 0], [6, 2], [6, -2]], [[2, 0]], [[4, 0], [-6, 2], [-6, -2]], [[11, 0], [3, 2], [3, -2]], [[7, 0]], [[7, 0]], [[-3, 0]], [[3, 0]], [[5, 0]], [[0, 0]], [[1, 0], [3, 2], [3, -2]], [[-2, 0]], [[-2, 0]], [[-1, 0], [3, 2], [3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[6, 1], [6, -1]], [[-2, 0]], [[3, 0]], [[3, 0], [6, 2], [6, -2]], [[-3, 0]], [[-2, 0]], [[-8, 0], [-6, 2], [-6, -2]], [[1, 0], [-3, 2], [-3, -2]], [[-2, 0]], [[3, 0]], [[4, 0], [3, 2], [3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[6, 2], [6, -2]], [[-2, 0]], [[4, 0], [3, 2], [3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[-2, 0], [-3, 2], [-3, -2]], [[3, 0]], [[3, 0]], [[-7, 0]], [[3, 0]], [[-2, 0]], [[6, 1], [6, -1]], [[1, 0], [3, 2], [3, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[3, 0], [6, 2], [6, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[-4, 0], [-3, 2], [-3, -2]], [[6, 2], [6, -2]], [[3, 0], [6, 2], [6, -2]], [[3, 0]], [[-7, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[-5, 0]], [[-2, 0]], [[3, 0], [6, 2], [6, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[4, 0], [3, 2], [3, -2]], [[-2, 0], [-3, 2], [-3, -2]], [[-3, 0]], [[3, 0]], [[4, 0], [3, 2], [3, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[3, 0]], [[-2, 0], [6, 2], [6, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 1], [2, -1]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 2], [2, -2]], [[2, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852916
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 69, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24i2', 'nt': [180, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[14, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0], [-2, 2], [-2, -2]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-2, 0], [2, 2], [2, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[11, 0], [3, 2], [3, -2]], [[4, 0], [-6, 2], [-6, -2]], [[2, 0]], [[10, 0], [6, 2], [6, -2]], [[8, 0], [-3, 2], [-3, -2]], [[7, 0]], [[7, 0]], [[-3, 0]], [[3, 0]], [[5, 0]], [[0, 0]], [[-2, 0], [-3, 2], [-3, -2]], [[-2, 0]], [[-2, 0]], [[-4, 0], [-3, 2], [-3, -2]], [[4, 0], [3, 2], [3, -2]], [[6, 2], [6, -2]], [[-2, 0]], [[3, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[-3, 0]], [[-2, 0]], [[-2, 0], [6, 2], [6, -2]], [[4, 0], [3, 2], [3, -2]], [[-2, 0]], [[3, 0]], [[1, 0], [-3, 2], [-3, -2]], [[4, 0], [3, 2], [3, -2]], [[6, 1], [6, -1]], [[-2, 0]], [[1, 0], [-3, 2], [-3, -2]], [[4, 0], [3, 2], [3, -2]], [[1, 0], [3, 2], [3, -2]], [[3, 0]], [[3, 0]], [[-7, 0]], [[3, 0]], [[-2, 0]], [[6, 2], [6, -2]], [[-2, 0], [-3, 2], [-3, -2]], [[3, 0], [6, 2], [6, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[3, 0], [6, 2], [6, -2]], [[-1, 0], [3, 2], [3, -2]], [[6, 1], [6, -1]], [[-3, 0], [-6, 2], [-6, -2]], [[3, 0]], [[-7, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[3, 0], [6, 2], [6, -2]], [[-5, 0]], [[-2, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[1, 0], [-3, 2], [-3, -2]], [[1, 0], [3, 2], [3, -2]], [[-3, 0]], [[3, 0]], [[1, 0], [-3, 2], [-3, -2]], [[3, 0], [6, 2], [6, -2]], [[3, 0]], [[-8, 0], [-6, 2], [-6, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 2], [2, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[2, 1], [2, -1]], [[1, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852918
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 70, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': -1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24j1', 'nt': [360, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0], [10, 2], [10, -2]], [[4, 0]], [[-6, 0], [-10, 2], [-10, -2]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[-4, 0], [-2, 2], [-2, -2]], [[-2, 0], [2, 2], [2, -2]], [[-4, 2], [-4, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[4, 0], [-6, 2], [-6, -2]], [[-2, 0], [7, 2], [7, -2]], [[-8, 0]], [[-9, 0], [-7, 2], [-7, -2]], [[10, 0], [6, 2], [6, -2]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-2, 0]], [[10, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[3, 0], [5, 2], [5, -2]], [[-2, 0], [-5, 2], [-5, -2]], [[-2, 0], [6, 2], [6, -2]], [[-3, 0], [-1, 2], [-1, -2]], [[1, 0], [3, 2], [3, -2]], [[3, 0]], [[-2, 0]], [[1, 0], [-3, 2], [-3, -2]], [[-3, 0]], [[3, 0]], [[4, 0], [-2, 2], [-2, -2]], [[-3, 0], [-1, 2], [-1, -2]], [[-2, 0], [-5, 2], [-5, -2]], [[-2, 0]], [[3, 0], [6, 2], [6, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[-2, 0], [-3, 2], [-3, -2]], [[3, 0]], [[-2, 0], [1, 2], [1, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[6, 1], [6, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[1, 0], [3, 2], [3, -2]], [[6, 2], [6, -2]], [[4, 0], [3, 2], [3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[4, 0], [3, 2], [3, -2]], [[-8, 0], [-6, 2], [-6, -2]], [[-2, 0], [-3, 2], [-3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[3, 0]], [[-2, 0]], [[0, 0]], [[-5, 0]], [[0, 0]], [[4, 0], [3, 2], [3, -2]], [[0, 0]], [[3, 0], [5, 2], [5, -2]], [[1, 0], [-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[-5, 0]], [[3, 0]], [[-5, 0]], [[-3, 0]], [[3, 0], [6, 2], [6, -2]], [[-4, 1], [-4, -1]], [[7, 0]], [[-2, 0]], [[-2, 0], [1, 2], [1, -2]], [[4, 0], [3, 2], [3, -2]], [[-2, 0]], [[6, 0], [2, 2], [2, -2]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[2, 1], [2, -1]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852919
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 71, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': -1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.24j2', 'nt': [360, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0], [-10, 2], [-10, -2]], [[4, 0]], [[4, 0], [10, 2], [10, -2]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[-2, 0], [2, 2], [2, -2]], [[-4, 0], [-2, 2], [-2, -2]], [[-4, 1], [-4, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[10, 0], [6, 2], [6, -2]], [[-9, 0], [-7, 2], [-7, -2]], [[-8, 0]], [[-2, 0], [7, 2], [7, -2]], [[4, 0], [-6, 2], [-6, -2]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-2, 0]], [[10, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[-2, 0], [-5, 2], [-5, -2]], [[3, 0], [5, 2], [5, -2]], [[-8, 0], [-6, 2], [-6, -2]], [[-2, 0], [1, 2], [1, -2]], [[-2, 0], [-3, 2], [-3, -2]], [[3, 0]], [[-2, 0]], [[4, 0], [3, 2], [3, -2]], [[-3, 0]], [[3, 0]], [[6, 0], [2, 2], [2, -2]], [[-2, 0], [1, 2], [1, -2]], [[3, 0], [5, 2], [5, -2]], [[-2, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[3, 0], [6, 2], [6, -2]], [[1, 0], [3, 2], [3, -2]], [[3, 0]], [[-3, 0], [-1, 2], [-1, -2]], [[3, 0], [6, 2], [6, -2]], [[6, 2], [6, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0], [-3, 2], [-3, -2]], [[6, 1], [6, -1]], [[1, 0], [-3, 2], [-3, -2]], [[4, 0], [3, 2], [3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[-2, 0], [6, 2], [6, -2]], [[1, 0], [3, 2], [3, -2]], [[4, 0], [3, 2], [3, -2]], [[3, 0]], [[-2, 0]], [[0, 0]], [[-5, 0]], [[0, 0]], [[1, 0], [-3, 2], [-3, -2]], [[0, 0]], [[-2, 0], [-5, 2], [-5, -2]], [[4, 0], [3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[-5, 0]], [[3, 0]], [[-5, 0]], [[-3, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[-4, 2], [-4, -2]], [[7, 0]], [[-2, 0]], [[-3, 0], [-1, 2], [-1, -2]], [[1, 0], [-3, 2], [-3, -2]], [[-2, 0]], [[4, 0], [-2, 2], [-2, -2]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 5852920
{'center': '6000.a1.a1', 'center_index': 6000, 'center_order': 27, 'counter': 72, 'cyclotomic_n': 1, 'dim': 48, 'faithful': False, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '6000.bm', 'image_order': 6000, 'indicator': 1, 'kernel': '6000.a1.a1', 'kernel_order': 27, 'label': '162000.x.48a', 'nt': [60, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[48, 0]], [[48, 0]], [[48, 0]], [[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[3, 0]], [[3, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-12, 0]], [[3, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-12, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-12, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-12, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[8, 0]], [[-2, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[8, 0]], [[-2, 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]]]}
-
id: 5852852
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 132, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48aa1', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[12, 0]], [[12, 0]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[0, 0]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[10, -5]], [[10, 5]], [[-5, 5]], [[-3, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [10, 7]], [[3, 0]], [[3, 0]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[2, 0]], [[2, 0]], [[-6, 3], [-6, -3]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [3, 5], [6, 7]], [[-2, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [5, 5], [4, 7]], [[-3, 0], [-5, 5]], [[2, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 7]], [[1, 1], [5, 2], [-5, 3], [1, 4], [2, 5], [5, 7]], [[0, 0]], [[2, 0], [5, 5]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[-1, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [-3, 5], [-3, 7]], [[2, 0]], [[-13, 0], [-10, 5]], [[-1, 0], [3, 1], [3, 4], [-4, 5]], [[2, 0], [-3, 1], [-3, 4], [-1, 5]], [[7, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [10, 5], [-4, 7]], [[2, 0], [5, 5]], [[-13, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-12, 5], [3, 7]], [[3, 1], [3, 2], [-3, 3], [3, 4], [1, 5], [3, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[-3, 0], [10, 5]], [[2, 0], [5, 5]], [[-3, 0]], [[2, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 5], [-5, 7]], [[-3, 0], [-5, 5]], [[-2, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [-5, 5], [-1, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[6, 0], [-1, 1], [-5, 2], [5, 3], [-1, 4], [3, 5], [-5, 7]], [[-1, 0], [-1, 1], [4, 2], [-4, 3], [-1, 4], [-2, 5], [4, 7]], [[-8, 1], [-1, 2], [1, 3], [-8, 4], [-1, 5], [-1, 7]], [[-6, 6], [-6, -6]], [[-8, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [-10, 5], [1, 7]], [[-9, 0], [8, 1], [1, 2], [-1, 3], [8, 4], [-9, 5], [1, 7]], [[-3, 0]], [[-3, 0]], [[-2, 0]], [[4, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[3, 0]], [[2, 0], [1, 1], [-4, 2], [4, 3], [1, 4], [-3, 5], [-4, 7]], [[-2, 0]], [[2, 0]], [[8, 0], [-8, 1], [-7, 2], [7, 3], [-8, 4], [9, 5], [-7, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[7, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[6, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [4, 5], [-3, 7]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-5, -5]], [[-3, 0], [-5, 5]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [12, 5], [-6, 7]], [[-7, 0], [8, 1], [7, 2], [-7, 3], [8, 4], [1, 5], [7, 7]], [[12, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [5, 5], [-10, 7]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[-2, 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]]]}
-
id: 5852853
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 133, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48aa2', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[12, 0]], [[12, 0]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[0, 0]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[10, 5]], [[10, -5]], [[-5, -5]], [[2, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 7]], [[3, 0]], [[3, 0]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[2, 0]], [[2, 0]], [[-6, 3], [-6, -3]], [[-1, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [-3, 5], [-3, 7]], [[-2, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [-5, 5], [-1, 7]], [[2, 0], [5, 5]], [[-3, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [10, 7]], [[-1, 0], [-1, 1], [4, 2], [-4, 3], [-1, 4], [-2, 5], [4, 7]], [[0, 0]], [[-3, 0], [-5, 5]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [3, 5], [6, 7]], [[2, 0]], [[-3, 0], [10, 5]], [[6, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [4, 5], [-3, 7]], [[3, 1], [3, 2], [-3, 3], [3, 4], [1, 5], [3, 7]], [[-8, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [-10, 5], [1, 7]], [[-3, 0], [-5, 5]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [12, 5], [-6, 7]], [[2, 0], [-3, 1], [-3, 4], [-1, 5]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[-13, 0], [-10, 5]], [[-3, 0], [-5, 5]], [[-3, 0]], [[12, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [5, 5], [-10, 7]], [[2, 0], [5, 5]], [[-2, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [5, 5], [4, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[2, 0], [1, 1], [-4, 2], [4, 3], [1, 4], [-3, 5], [-4, 7]], [[1, 1], [5, 2], [-5, 3], [1, 4], [2, 5], [5, 7]], [[-7, 0], [8, 1], [7, 2], [-7, 3], [8, 4], [1, 5], [7, 7]], [[-6, 6], [-6, -6]], [[7, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [10, 5], [-4, 7]], [[8, 0], [-8, 1], [-7, 2], [7, 3], [-8, 4], [9, 5], [-7, 7]], [[-3, 0]], [[-3, 0]], [[-2, 0]], [[7, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[3, 0]], [[6, 0], [-1, 1], [-5, 2], [5, 3], [-1, 4], [3, 5], [-5, 7]], [[-2, 0]], [[2, 0]], [[-9, 0], [8, 1], [1, 2], [-1, 3], [8, 4], [-9, 5], [1, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[4, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[-1, 0], [3, 1], [3, 4], [-4, 5]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-5, 5]], [[2, 0], [5, 5]], [[-13, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-12, 5], [3, 7]], [[-8, 1], [-1, 2], [1, 3], [-8, 4], [-1, 5], [-1, 7]], [[2, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 5], [-5, 7]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[-2, 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]]]}
-
id: 5852854
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 134, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48aa3', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[12, 0]], [[12, 0]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[0, 0]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[10, -5]], [[10, 5]], [[-5, 5]], [[12, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [5, 5], [-10, 7]], [[3, 0]], [[3, 0]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[2, 0]], [[2, 0]], [[-6, 6], [-6, -6]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [12, 5], [-6, 7]], [[7, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [10, 5], [-4, 7]], [[-3, 0], [-5, 5]], [[2, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 5], [-5, 7]], [[6, 0], [-1, 1], [-5, 2], [5, 3], [-1, 4], [3, 5], [-5, 7]], [[0, 0]], [[2, 0], [5, 5]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[-13, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-12, 5], [3, 7]], [[2, 0]], [[-13, 0], [-10, 5]], [[2, 0], [-3, 1], [-3, 4], [-1, 5]], [[-1, 0], [3, 1], [3, 4], [-4, 5]], [[-2, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [5, 5], [4, 7]], [[2, 0], [5, 5]], [[-1, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [-3, 5], [-3, 7]], [[6, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [4, 5], [-3, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[-3, 0], [10, 5]], [[2, 0], [5, 5]], [[-3, 0]], [[2, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 7]], [[-3, 0], [-5, 5]], [[-8, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [-10, 5], [1, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[1, 1], [5, 2], [-5, 3], [1, 4], [2, 5], [5, 7]], [[2, 0], [1, 1], [-4, 2], [4, 3], [1, 4], [-3, 5], [-4, 7]], [[-9, 0], [8, 1], [1, 2], [-1, 3], [8, 4], [-9, 5], [1, 7]], [[-6, 3], [-6, -3]], [[-2, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [-5, 5], [-1, 7]], [[-8, 1], [-1, 2], [1, 3], [-8, 4], [-1, 5], [-1, 7]], [[-3, 0]], [[-3, 0]], [[-2, 0]], [[7, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[3, 0]], [[-1, 0], [-1, 1], [4, 2], [-4, 3], [-1, 4], [-2, 5], [4, 7]], [[-2, 0]], [[2, 0]], [[-7, 0], [8, 1], [7, 2], [-7, 3], [8, 4], [1, 5], [7, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[4, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[3, 1], [3, 2], [-3, 3], [3, 4], [1, 5], [3, 7]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-5, -5]], [[-3, 0], [-5, 5]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [3, 5], [6, 7]], [[8, 0], [-8, 1], [-7, 2], [7, 3], [-8, 4], [9, 5], [-7, 7]], [[-3, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [10, 7]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[-2, 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]]]}
-
id: 5852855
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 135, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48aa4', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[12, 0]], [[12, 0]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[0, 0]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[10, 5]], [[10, -5]], [[-5, -5]], [[2, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 5], [-5, 7]], [[3, 0]], [[3, 0]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[2, 0]], [[2, 0]], [[-6, 6], [-6, -6]], [[-13, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-12, 5], [3, 7]], [[-8, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [-10, 5], [1, 7]], [[2, 0], [5, 5]], [[12, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [5, 5], [-10, 7]], [[2, 0], [1, 1], [-4, 2], [4, 3], [1, 4], [-3, 5], [-4, 7]], [[0, 0]], [[-3, 0], [-5, 5]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [12, 5], [-6, 7]], [[2, 0]], [[-3, 0], [10, 5]], [[3, 1], [3, 2], [-3, 3], [3, 4], [1, 5], [3, 7]], [[6, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [4, 5], [-3, 7]], [[-2, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [-5, 5], [-1, 7]], [[-3, 0], [-5, 5]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [3, 5], [6, 7]], [[-1, 0], [3, 1], [3, 4], [-4, 5]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[-13, 0], [-10, 5]], [[-3, 0], [-5, 5]], [[-3, 0]], [[-3, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [10, 7]], [[2, 0], [5, 5]], [[7, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [10, 5], [-4, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[-1, 0], [-1, 1], [4, 2], [-4, 3], [-1, 4], [-2, 5], [4, 7]], [[6, 0], [-1, 1], [-5, 2], [5, 3], [-1, 4], [3, 5], [-5, 7]], [[8, 0], [-8, 1], [-7, 2], [7, 3], [-8, 4], [9, 5], [-7, 7]], [[-6, 3], [-6, -3]], [[-2, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [5, 5], [4, 7]], [[-7, 0], [8, 1], [7, 2], [-7, 3], [8, 4], [1, 5], [7, 7]], [[-3, 0]], [[-3, 0]], [[-2, 0]], [[4, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[3, 0]], [[1, 1], [5, 2], [-5, 3], [1, 4], [2, 5], [5, 7]], [[-2, 0]], [[2, 0]], [[-8, 1], [-1, 2], [1, 3], [-8, 4], [-1, 5], [-1, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[7, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[2, 0], [-3, 1], [-3, 4], [-1, 5]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-5, 5]], [[2, 0], [5, 5]], [[-1, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [-3, 5], [-3, 7]], [[-9, 0], [8, 1], [1, 2], [-1, 3], [8, 4], [-9, 5], [1, 7]], [[2, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 7]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[-2, 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]]]}
-
id: 5852921
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 73, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48b', 'nt': [90, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[18, 0]], [[-2, 0]], [[-2, 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]], [[-18, 0]], [[-18, 0]], [[-10, 0]], [[0, 0]], [[20, 0]], [[0, 0]], [[-10, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[7, 0]], [[8, 0]], [[-12, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-7, 0]], [[3, 0]], [[-5, 0]], [[-8, 0]], [[7, 0]], [[-2, 0]], [[0, 0]], [[-8, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[-5, 0]], [[7, 0]], [[3, 0]], [[-2, 0]], [[-5, 0]], [[-8, 0]], [[-8, 0]], [[2, 0]], [[7, 0]], [[7, 0]], [[-5, 0]], [[-5, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-7, 0]], [[-5, 0]], [[-2, 0]], [[12, 0]], [[2, 0]], [[13, 0]], [[13, 0]], [[-12, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[-2, 0]], [[3, 0]], [[3, 0]], [[13, 0]], [[12, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[10, 0]], [[-8, 0]], [[3, 0]], [[-2, 0]], [[7, 0]], [[3, 0]], [[-2, 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]]]}
-
id: 5852922
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 74, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48c', 'nt': [90, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[18, 0]], [[-2, 0]], [[-2, 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]], [[27, 0]], [[27, 0]], [[-10, 0]], [[0, 0]], [[20, 0]], [[0, 0]], [[-10, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[-8, 0]], [[8, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-7, 0]], [[3, 0]], [[-5, 0]], [[7, 0]], [[-8, 0]], [[-2, 0]], [[0, 0]], [[7, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[7, 0]], [[-2, 0]], [[-2, 0]], [[-5, 0]], [[-8, 0]], [[3, 0]], [[-2, 0]], [[-5, 0]], [[7, 0]], [[7, 0]], [[2, 0]], [[-8, 0]], [[-8, 0]], [[-5, 0]], [[-5, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-7, 0]], [[-5, 0]], [[-2, 0]], [[-3, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[13, 0]], [[-3, 0]], [[-2, 0]], [[-12, 0]], [[-12, 0]], [[-2, 0]], [[-3, 0]], [[13, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[10, 0]], [[7, 0]], [[3, 0]], [[-2, 0]], [[-8, 0]], [[3, 0]], [[13, 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]]]}
-
id: 5852923
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 75, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48d', 'nt': [90, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[28, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[-12, 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]], [[-3, 0]], [[-3, 0]], [[10, 0]], [[20, 0]], [[-20, 0]], [[20, 0]], [[10, 0]], [[20, 0]], [[20, 0]], [[0, 0]], [[-3, 0]], [[-17, 0]], [[3, 0]], [[-10, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-7, 0]], [[0, 0]], [[2, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[8, 0]], [[-7, 0]], [[2, 0]], [[-3, 0]], [[-7, 0]], [[-7, 0]], [[0, 0]], [[2, 0]], [[-7, 0]], [[-7, 0]], [[-10, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[-10, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[7, 0]], [[8, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[8, 0]], [[2, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[-7, 0]], [[-10, 0]], [[0, 0]], [[-3, 0]], [[-7, 0]], [[3, 0]], [[-3, 0]], [[8, 0]], [[3, 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]]]}
-
id: 5852924
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 76, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48e1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[18, 0]], [[3, 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]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[4, 0], [-10, 1]], [[14, 0], [10, 1]], [[-1, 0], [-5, 1]], [[-4, 0], [-5, 1]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-5, 1]], [[-4, 0], [10, 1]], [[1, 0], [5, 1]], [[-5, 0], [-10, 1]], [[-6, 0]], [[-14, 0], [-10, 1]], [[0, 0]], [[0, 0]], [[6, 0]], [[-4, 0], [-5, 1]], [[-5, 0], [-10, 1]], [[-5, 0], [-10, 1]], [[-1, 0], [-5, 1]], [[-14, 0], [-10, 1]], [[0, 0]], [[5, 0], [10, 1]], [[9, 0]], [[1, 0], [5, 1]], [[6, 0], [15, 1]], [[6, 0]], [[1, 0], [5, 1]], [[-4, 0], [10, 1]], [[4, 0], [5, 1]], [[9, 0]], [[-5, 0], [-10, 1]], [[5, 0], [10, 1]], [[0, 0]], [[0, 0]], [[4, 0], [5, 1]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0], [10, 1]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[5, 0], [10, 1]], [[-6, 0]], [[5, 0], [10, 1]], [[-6, 0]], [[4, 0], [5, 1]], [[-9, 0], [-15, 1]], [[0, 0]], [[0, 0]], [[-4, 0], [-5, 1]], [[0, 0]], [[-5, 0], [-10, 1]], [[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]]]}
-
id: 5852925
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 77, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48e2', 'nt': [180, 2], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[18, 0]], [[3, 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]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[14, 0], [10, 1]], [[4, 0], [-10, 1]], [[4, 0], [5, 1]], [[1, 0], [5, 1]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[4, 0], [5, 1]], [[-14, 0], [-10, 1]], [[-4, 0], [-5, 1]], [[5, 0], [10, 1]], [[-6, 0]], [[-4, 0], [10, 1]], [[0, 0]], [[0, 0]], [[6, 0]], [[1, 0], [5, 1]], [[5, 0], [10, 1]], [[5, 0], [10, 1]], [[4, 0], [5, 1]], [[-4, 0], [10, 1]], [[0, 0]], [[-5, 0], [-10, 1]], [[9, 0]], [[-4, 0], [-5, 1]], [[-9, 0], [-15, 1]], [[6, 0]], [[-4, 0], [-5, 1]], [[-14, 0], [-10, 1]], [[-1, 0], [-5, 1]], [[9, 0]], [[5, 0], [10, 1]], [[-5, 0], [-10, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-5, 1]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0], [-10, 1]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-5, 0], [-10, 1]], [[-6, 0]], [[-5, 0], [-10, 1]], [[-6, 0]], [[-1, 0], [-5, 1]], [[6, 0], [15, 1]], [[0, 0]], [[0, 0]], [[1, 0], [5, 1]], [[0, 0]], [[5, 0], [10, 1]], [[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]]]}
-
id: 5852926
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 78, 'cyclotomic_n': 5, 'dim': 48, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48f1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[18, 0]], [[-2, 0]], [[-2, 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]], [[-9, 0]], [[-9, 0]], [[2, 0], [6, 2], [6, -2]], [[12, 1], [12, -1]], [[14, 0]], [[12, 2], [12, -2]], [[-4, 0], [-6, 2], [-6, -2]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-10, 0]], [[0, 0]], [[-9, 0], [-6, 2], [-6, -2]], [[6, 0]], [[6, 0]], [[2, 0], [-6, 2], [-6, -2]], [[3, 0], [6, 2], [6, -2]], [[-5, 0], [-3, 2], [-3, -2]], [[1, 0]], [[1, 0]], [[4, 0], [3, 2], [3, -2]], [[9, 0]], [[1, 0]], [[6, 0], [12, 2], [12, -2]], [[3, 0], [6, 2], [6, -2]], [[6, 0]], [[1, 0]], [[7, 0], [9, 2], [9, -2]], [[-2, 0], [-9, 2], [-9, -2]], [[-2, 0], [3, 2], [3, -2]], [[1, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[-2, 0], [-9, 2], [-9, -2]], [[-8, 0], [-9, 2], [-9, -2]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-5, 0], [-3, 2], [-3, -2]], [[1, 0], [9, 2], [9, -2]], [[1, 0], [-3, 2], [-3, -2]], [[4, 0], [3, 2], [3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[8, 0], [6, 2], [6, -2]], [[-2, 0], [3, 2], [3, -2]], [[4, 0], [3, 2], [3, -2]], [[-9, 0]], [[-4, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[1, 0], [-3, 2], [-3, -2]], [[-5, 0]], [[6, 0]], [[4, 0], [3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-9, 0]], [[-5, 0]], [[9, 0]], [[7, 0], [9, 2], [9, -2]], [[-3, 0], [6, 2], [6, -2]], [[4, 0]], [[1, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[1, 0], [-3, 2], [-3, -2]], [[1, 0]], [[-6, 0], [-12, 2], [-12, -2]], [[-5, 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]]]}
-
id: 5852927
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 79, 'cyclotomic_n': 5, 'dim': 48, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48f2', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[18, 0]], [[-2, 0]], [[-2, 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]], [[-9, 0]], [[-9, 0]], [[-4, 0], [-6, 2], [-6, -2]], [[12, 2], [12, -2]], [[14, 0]], [[12, 1], [12, -1]], [[2, 0], [6, 2], [6, -2]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-10, 0]], [[0, 0]], [[-3, 0], [6, 2], [6, -2]], [[6, 0]], [[6, 0]], [[8, 0], [6, 2], [6, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[-2, 0], [3, 2], [3, -2]], [[1, 0]], [[1, 0]], [[1, 0], [-3, 2], [-3, -2]], [[9, 0]], [[1, 0]], [[-6, 0], [-12, 2], [-12, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[6, 0]], [[1, 0]], [[-2, 0], [-9, 2], [-9, -2]], [[7, 0], [9, 2], [9, -2]], [[-5, 0], [-3, 2], [-3, -2]], [[1, 0]], [[3, 0], [6, 2], [6, -2]], [[7, 0], [9, 2], [9, -2]], [[1, 0], [9, 2], [9, -2]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [3, 2], [3, -2]], [[-8, 0], [-9, 2], [-9, -2]], [[4, 0], [3, 2], [3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[4, 0], [3, 2], [3, -2]], [[2, 0], [-6, 2], [-6, -2]], [[-5, 0], [-3, 2], [-3, -2]], [[1, 0], [-3, 2], [-3, -2]], [[-9, 0]], [[-4, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[4, 0], [3, 2], [3, -2]], [[-5, 0]], [[6, 0]], [[1, 0], [-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-9, 0]], [[-5, 0]], [[9, 0]], [[-2, 0], [-9, 2], [-9, -2]], [[-9, 0], [-6, 2], [-6, -2]], [[4, 0]], [[1, 0]], [[3, 0], [6, 2], [6, -2]], [[4, 0], [3, 2], [3, -2]], [[1, 0]], [[6, 0], [12, 2], [12, -2]], [[-5, 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]]]}
-
id: 5852929
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 80, 'cyclotomic_n': 5, 'dim': 48, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48g1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0], [20, 2], [20, -2]], [[8, 0]], [[-12, 0], [-20, 2], [-20, -2]], [[-12, 0]], [[-12, 0]], [[8, 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]], [[6, 0]], [[6, 0]], [[2, 0], [6, 2], [6, -2]], [[-8, 1], [-8, -1]], [[14, 0]], [[-8, 2], [-8, -2]], [[-4, 0], [-6, 2], [-6, -2]], [[-6, 0]], [[-6, 0]], [[-1, 0]], [[-4, 0]], [[-10, 0]], [[0, 0]], [[-9, 0], [-11, 2], [-11, -2]], [[6, 0], [10, 2], [10, -2]], [[-4, 0], [-10, 2], [-10, -2]], [[2, 0], [-6, 2], [-6, -2]], [[3, 0], [1, 2], [1, -2]], [[5, 0], [-3, 2], [-3, -2]], [[6, 0]], [[-4, 0]], [[-1, 0], [3, 2], [3, -2]], [[-6, 0]], [[6, 0]], [[-4, 0], [2, 2], [2, -2]], [[3, 0], [1, 2], [1, -2]], [[-4, 0], [-10, 2], [-10, -2]], [[-4, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[3, 0], [6, 2], [6, -2]], [[8, 0], [3, 2], [3, -2]], [[6, 0]], [[2, 0], [-1, 2], [-1, -2]], [[3, 0], [6, 2], [6, -2]], [[-3, 0], [6, 2], [6, -2]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[5, 0], [-3, 2], [-3, -2]], [[-9, 0], [-6, 2], [-6, -2]], [[-4, 0], [-3, 2], [-3, -2]], [[-1, 0], [3, 2], [3, -2]], [[-4, 0], [-3, 2], [-3, -2]], [[8, 0], [6, 2], [6, -2]], [[8, 0], [3, 2], [3, -2]], [[-1, 0], [3, 2], [3, -2]], [[6, 0]], [[-4, 0]], [[0, 0]], [[5, 0]], [[0, 0]], [[-4, 0], [-3, 2], [-3, -2]], [[0, 0]], [[6, 0], [10, 2], [10, -2]], [[-1, 0], [3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[5, 0]], [[6, 0]], [[5, 0]], [[-6, 0]], [[-3, 0], [-6, 2], [-6, -2]], [[2, 0], [11, 2], [11, -2]], [[-1, 0]], [[-4, 0]], [[2, 0], [-1, 2], [-1, -2]], [[-4, 0], [-3, 2], [-3, -2]], [[-4, 0]], [[-6, 0], [-2, 2], [-2, -2]], [[5, 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]]]}
-
id: 5852930
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 81, 'cyclotomic_n': 5, 'dim': 48, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48g2', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0], [-20, 2], [-20, -2]], [[8, 0]], [[8, 0], [20, 2], [20, -2]], [[-12, 0]], [[-12, 0]], [[8, 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]], [[6, 0]], [[6, 0]], [[-4, 0], [-6, 2], [-6, -2]], [[-8, 2], [-8, -2]], [[14, 0]], [[-8, 1], [-8, -1]], [[2, 0], [6, 2], [6, -2]], [[-6, 0]], [[-6, 0]], [[-1, 0]], [[-4, 0]], [[-10, 0]], [[0, 0]], [[2, 0], [11, 2], [11, -2]], [[-4, 0], [-10, 2], [-10, -2]], [[6, 0], [10, 2], [10, -2]], [[8, 0], [6, 2], [6, -2]], [[2, 0], [-1, 2], [-1, -2]], [[8, 0], [3, 2], [3, -2]], [[6, 0]], [[-4, 0]], [[-4, 0], [-3, 2], [-3, -2]], [[-6, 0]], [[6, 0]], [[-6, 0], [-2, 2], [-2, -2]], [[2, 0], [-1, 2], [-1, -2]], [[6, 0], [10, 2], [10, -2]], [[-4, 0]], [[3, 0], [6, 2], [6, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[5, 0], [-3, 2], [-3, -2]], [[6, 0]], [[3, 0], [1, 2], [1, -2]], [[-3, 0], [-6, 2], [-6, -2]], [[-9, 0], [-6, 2], [-6, -2]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[8, 0], [3, 2], [3, -2]], [[-3, 0], [6, 2], [6, -2]], [[-1, 0], [3, 2], [3, -2]], [[-4, 0], [-3, 2], [-3, -2]], [[-1, 0], [3, 2], [3, -2]], [[2, 0], [-6, 2], [-6, -2]], [[5, 0], [-3, 2], [-3, -2]], [[-4, 0], [-3, 2], [-3, -2]], [[6, 0]], [[-4, 0]], [[0, 0]], [[5, 0]], [[0, 0]], [[-1, 0], [3, 2], [3, -2]], [[0, 0]], [[-4, 0], [-10, 2], [-10, -2]], [[-4, 0], [-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[5, 0]], [[6, 0]], [[5, 0]], [[-6, 0]], [[3, 0], [6, 2], [6, -2]], [[-9, 0], [-11, 2], [-11, -2]], [[-1, 0]], [[-4, 0]], [[3, 0], [1, 2], [1, -2]], [[-1, 0], [3, 2], [3, -2]], [[-4, 0]], [[-4, 0], [2, 2], [2, -2]], [[5, 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]]]}
-
id: 5852931
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 82, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48h1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-9, 0], [-15, 1]], [[6, 0], [15, 1]], [[-6, 0]], [[14, 0]], [[-6, 0]], [[14, 0]], [[-6, 0]], [[-16, 0], [-10, 1]], [[-6, 0], [10, 1]], [[4, 0]], [[1, 0]], [[0, 0]], [[5, 0], [10, 1]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[5, 0]], [[-1, 0], [5, 1]], [[6, 0], [10, 1]], [[1, 0]], [[-5, -1]], [[4, 0], [5, 1]], [[-4, 0], [-10, 1]], [[-10, 0]], [[5, 0]], [[-4, 0]], [[6, 0], [10, 1]], [[10, -1]], [[10, -1]], [[-1, 0], [5, 1]], [[-4, 0], [-10, 1]], [[5, 0]], [[10, 1]], [[4, 0]], [[-4, 0], [-10, 1]], [[-4, 0], [-10, 1]], [[6, 0]], [[1, 0]], [[6, 0], [10, 1]], [[-6, 0], [-5, 1]], [[4, 0]], [[-5, -1]], [[-5, 1]], [[-5, 1]], [[0, 0]], [[-6, 0], [-5, 1]], [[-5, 1]], [[-4, 0], [-5, 1]], [[6, 0]], [[10, 0]], [[-5, 0]], [[-5, 0], [-10, 1]], [[-5, 1]], [[10, 0]], [[-4, 0]], [[-5, -1]], [[0, 0]], [[0, 0]], [[-5, 0]], [[1, 0], [5, 1]], [[10, -1]], [[-1, 0], [-5, 1]], [[10, 1]], [[-1, 0]], [[4, 0]], [[6, 0], [10, 1]], [[5, 0]], [[-5, -1]], [[1, 0]], [[-10, 0]], [[10, 1]], [[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]]]}
-
id: 5852932
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 83, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48h2', 'nt': [180, 2], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[6, 0], [15, 1]], [[-9, 0], [-15, 1]], [[-6, 0]], [[14, 0]], [[-6, 0]], [[14, 0]], [[-6, 0]], [[-6, 0], [10, 1]], [[-16, 0], [-10, 1]], [[4, 0]], [[1, 0]], [[0, 0]], [[-5, 0], [-10, 1]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[5, 0]], [[-6, 0], [-5, 1]], [[-4, 0], [-10, 1]], [[1, 0]], [[-5, 1]], [[-1, 0], [-5, 1]], [[6, 0], [10, 1]], [[-10, 0]], [[5, 0]], [[-4, 0]], [[-4, 0], [-10, 1]], [[10, 1]], [[10, 1]], [[-6, 0], [-5, 1]], [[6, 0], [10, 1]], [[5, 0]], [[10, -1]], [[4, 0]], [[6, 0], [10, 1]], [[6, 0], [10, 1]], [[6, 0]], [[1, 0]], [[-4, 0], [-10, 1]], [[-1, 0], [5, 1]], [[4, 0]], [[-5, 1]], [[-5, -1]], [[-5, -1]], [[0, 0]], [[-1, 0], [5, 1]], [[-5, -1]], [[1, 0], [5, 1]], [[6, 0]], [[10, 0]], [[-5, 0]], [[5, 0], [10, 1]], [[-5, -1]], [[10, 0]], [[-4, 0]], [[-5, 1]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-4, 0], [-5, 1]], [[10, 1]], [[4, 0], [5, 1]], [[10, -1]], [[-1, 0]], [[4, 0]], [[-4, 0], [-10, 1]], [[5, 0]], [[-5, 1]], [[1, 0]], [[-10, 0]], [[10, -1]], [[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]]]}
-
id: 5852933
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 84, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48i1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0], [-36, 1]], [[12, 0], [36, 1]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[18, 0]], [[3, 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]], [[6, 0], [9, 1]], [[-3, 0], [-9, 1]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-14, 0], [-10, 1]], [[-4, 0], [10, 1]], [[-4, 0], [-5, 1]], [[2, 0], [1, 1]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0], [9, 1]], [[-3, 0], [-9, 1]], [[-3, 0]], [[-3, 0]], [[-4, 0], [-5, 1]], [[-4, 0], [-11, 1]], [[1, 0], [-1, 1]], [[7, 0], [5, 1]], [[6, 0]], [[7, 0], [11, 1]], [[-3, 0]], [[-3, 0]], [[6, 0], [9, 1]], [[2, 0], [1, 1]], [[7, 0], [5, 1]], [[7, 0], [5, 1]], [[-4, 0], [-5, 1]], [[-14, 0], [-16, 1]], [[-3, 0]], [[2, 0], [-5, 1]], [[-9, 0]], [[1, 0], [-1, 1]], [[-3, 0], [6, 1]], [[6, 0], [9, 1]], [[1, 0], [-1, 1]], [[2, 0], [16, 1]], [[1, 0], [5, 1]], [[-9, 0]], [[7, 0], [5, 1]], [[2, 0], [-5, 1]], [[-3, 0]], [[-3, 0]], [[1, 0], [5, 1]], [[-3, 0]], [[-3, 0], [-9, 1]], [[-3, 0], [-9, 1]], [[12, 0]], [[-3, 0]], [[-3, 0]], [[2, 0], [-5, 1]], [[-3, 0]], [[-3, 0], [-9, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0], [9, 1]], [[2, 0], [-5, 1]], [[6, 0]], [[2, 0], [-5, 1]], [[6, 0]], [[1, 0], [5, 1]], [[-9, 0], [-6, 1]], [[-3, 0]], [[-3, 0]], [[2, 0], [1, 1]], [[-3, 0]], [[7, 0], [5, 1]], [[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]]]}
-
id: 5852934
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 85, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48i2', 'nt': [180, 2], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0], [36, 1]], [[-24, 0], [-36, 1]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[18, 0]], [[3, 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]], [[-3, 0], [-9, 1]], [[6, 0], [9, 1]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-4, 0], [10, 1]], [[-14, 0], [-10, 1]], [[1, 0], [5, 1]], [[1, 0], [-1, 1]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0], [-9, 1]], [[6, 0], [9, 1]], [[-3, 0]], [[-3, 0]], [[1, 0], [5, 1]], [[7, 0], [11, 1]], [[2, 0], [1, 1]], [[2, 0], [-5, 1]], [[6, 0]], [[-4, 0], [-11, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0], [-9, 1]], [[1, 0], [-1, 1]], [[2, 0], [-5, 1]], [[2, 0], [-5, 1]], [[1, 0], [5, 1]], [[2, 0], [16, 1]], [[-3, 0]], [[7, 0], [5, 1]], [[-9, 0]], [[2, 0], [1, 1]], [[-9, 0], [-6, 1]], [[-3, 0], [-9, 1]], [[2, 0], [1, 1]], [[-14, 0], [-16, 1]], [[-4, 0], [-5, 1]], [[-9, 0]], [[2, 0], [-5, 1]], [[7, 0], [5, 1]], [[-3, 0]], [[-3, 0]], [[-4, 0], [-5, 1]], [[-3, 0]], [[6, 0], [9, 1]], [[6, 0], [9, 1]], [[12, 0]], [[-3, 0]], [[-3, 0]], [[7, 0], [5, 1]], [[-3, 0]], [[6, 0], [9, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0], [-9, 1]], [[7, 0], [5, 1]], [[6, 0]], [[7, 0], [5, 1]], [[6, 0]], [[-4, 0], [-5, 1]], [[-3, 0], [6, 1]], [[-3, 0]], [[-3, 0]], [[1, 0], [-1, 1]], [[-3, 0]], [[2, 0], [-5, 1]], [[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]]]}
-
id: 5852935
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 86, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48j1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0], [-36, 1]], [[12, 0], [36, 1]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[18, 0]], [[-2, 0]], [[-2, 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]], [[-24, 0], [-21, 1]], [[-3, 0], [21, 1]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0], [10, 1]], [[-4, 0], [-10, 1]], [[-4, 0], [-10, 1]], [[2, 0], [-4, 1]], [[2, 0]], [[7, 0], [-10, 1]], [[6, 0]], [[6, 0], [9, 1]], [[-3, 0], [-9, 1]], [[2, 0]], [[-3, 0]], [[1, 0]], [[-4, 0], [-1, 1]], [[6, 0], [4, 1]], [[2, 0], [5, 1]], [[-4, 0], [10, 1]], [[-3, 0], [1, 1]], [[-3, 0]], [[-3, 0]], [[6, 0], [9, 1]], [[-3, 0], [1, 1]], [[-3, 0], [-5, 1]], [[-3, 0], [-5, 1]], [[1, 0]], [[6, 0], [4, 1]], [[-3, 0]], [[2, 0], [5, 1]], [[1, 0]], [[-4, 0], [-1, 1]], [[-3, 0], [1, 1]], [[-4, 0], [-6, 1]], [[6, 0], [4, 1]], [[2, 0], [-4, 1]], [[1, 0]], [[1, 0]], [[2, 0], [5, 1]], [[-3, 0], [-5, 1]], [[2, 0], [5, 1]], [[2, 0]], [[1, 0]], [[2, 0], [5, 1]], [[7, 0], [11, 1]], [[2, 0], [6, 1]], [[-8, 0]], [[-8, 0]], [[17, 0], [10, 1]], [[-3, 0], [-5, 1]], [[7, 0]], [[-3, 0], [-9, 1]], [[-3, 0], [-5, 1]], [[-3, 0]], [[-3, 0]], [[-8, 0]], [[-4, 0], [-11, 1]], [[7, 0]], [[-14, 0], [-10, 1]], [[2, 0], [5, 1]], [[6, 0]], [[6, 0], [10, 1]], [[-4, 0], [-1, 1]], [[-3, 0]], [[-3, 0], [-5, 1]], [[2, 0], [-4, 1]], [[-3, 0]], [[7, 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]]]}
-
id: 5852936
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 87, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48j2', 'nt': [180, 2], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0], [36, 1]], [[-24, 0], [-36, 1]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[18, 0]], [[-2, 0]], [[-2, 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]], [[-3, 0], [21, 1]], [[-24, 0], [-21, 1]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[-4, 0], [-10, 1]], [[6, 0], [10, 1]], [[6, 0], [10, 1]], [[6, 0], [4, 1]], [[2, 0]], [[17, 0], [10, 1]], [[6, 0]], [[-3, 0], [-9, 1]], [[6, 0], [9, 1]], [[2, 0]], [[-3, 0]], [[1, 0]], [[-3, 0], [1, 1]], [[2, 0], [-4, 1]], [[-3, 0], [-5, 1]], [[-14, 0], [-10, 1]], [[-4, 0], [-1, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0], [-9, 1]], [[-4, 0], [-1, 1]], [[2, 0], [5, 1]], [[2, 0], [5, 1]], [[1, 0]], [[2, 0], [-4, 1]], [[-3, 0]], [[-3, 0], [-5, 1]], [[1, 0]], [[-3, 0], [1, 1]], [[-4, 0], [-1, 1]], [[2, 0], [6, 1]], [[2, 0], [-4, 1]], [[6, 0], [4, 1]], [[1, 0]], [[1, 0]], [[-3, 0], [-5, 1]], [[2, 0], [5, 1]], [[-3, 0], [-5, 1]], [[2, 0]], [[1, 0]], [[-3, 0], [-5, 1]], [[-4, 0], [-11, 1]], [[-4, 0], [-6, 1]], [[-8, 0]], [[-8, 0]], [[7, 0], [-10, 1]], [[2, 0], [5, 1]], [[7, 0]], [[6, 0], [9, 1]], [[2, 0], [5, 1]], [[-3, 0]], [[-3, 0]], [[-8, 0]], [[7, 0], [11, 1]], [[7, 0]], [[-4, 0], [10, 1]], [[-3, 0], [-5, 1]], [[6, 0]], [[-4, 0], [-10, 1]], [[-3, 0], [1, 1]], [[-3, 0]], [[2, 0], [5, 1]], [[6, 0], [4, 1]], [[-3, 0]], [[7, 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]]]}
-
id: 5852937
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 88, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48k1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0], [-36, 1]], [[12, 0], [36, 1]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[18, 0]], [[-2, 0]], [[-2, 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]], [[6, 0], [-6, 1]], [[12, 0], [6, 1]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[-4, 0], [-10, 1]], [[6, 0], [10, 1]], [[6, 0], [10, 1]], [[-3, 0], [1, 1]], [[2, 0]], [[2, 0], [10, 1]], [[6, 0]], [[6, 0], [9, 1]], [[-3, 0], [-9, 1]], [[2, 0]], [[-3, 0]], [[1, 0]], [[6, 0], [4, 1]], [[-4, 0], [-1, 1]], [[-3, 0], [-5, 1]], [[-14, 0], [-10, 1]], [[2, 0], [-4, 1]], [[-3, 0]], [[-3, 0]], [[6, 0], [9, 1]], [[2, 0], [-4, 1]], [[2, 0], [5, 1]], [[2, 0], [5, 1]], [[1, 0]], [[-4, 0], [-1, 1]], [[-3, 0]], [[-3, 0], [-5, 1]], [[1, 0]], [[6, 0], [4, 1]], [[2, 0], [-4, 1]], [[-4, 0], [-6, 1]], [[-4, 0], [-1, 1]], [[-3, 0], [1, 1]], [[1, 0]], [[1, 0]], [[-3, 0], [-5, 1]], [[2, 0], [5, 1]], [[-3, 0], [-5, 1]], [[2, 0]], [[1, 0]], [[-3, 0], [-5, 1]], [[2, 0], [16, 1]], [[2, 0], [6, 1]], [[7, 0]], [[7, 0]], [[-8, 0], [-10, 1]], [[2, 0], [5, 1]], [[-8, 0]], [[-3, 0], [-9, 1]], [[2, 0], [5, 1]], [[12, 0]], [[12, 0]], [[7, 0]], [[-14, 0], [-16, 1]], [[-8, 0]], [[-4, 0], [10, 1]], [[-3, 0], [-5, 1]], [[6, 0]], [[-4, 0], [-10, 1]], [[6, 0], [4, 1]], [[-3, 0]], [[2, 0], [5, 1]], [[-3, 0], [1, 1]], [[-3, 0]], [[-8, 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]]]}
-
id: 5852938
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 89, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48k2', 'nt': [180, 2], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0], [36, 1]], [[-24, 0], [-36, 1]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[18, 0]], [[-2, 0]], [[-2, 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]], [[12, 0], [6, 1]], [[6, 0], [-6, 1]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0], [10, 1]], [[-4, 0], [-10, 1]], [[-4, 0], [-10, 1]], [[-4, 0], [-1, 1]], [[2, 0]], [[-8, 0], [-10, 1]], [[6, 0]], [[-3, 0], [-9, 1]], [[6, 0], [9, 1]], [[2, 0]], [[-3, 0]], [[1, 0]], [[2, 0], [-4, 1]], [[-3, 0], [1, 1]], [[2, 0], [5, 1]], [[-4, 0], [10, 1]], [[6, 0], [4, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0], [-9, 1]], [[6, 0], [4, 1]], [[-3, 0], [-5, 1]], [[-3, 0], [-5, 1]], [[1, 0]], [[-3, 0], [1, 1]], [[-3, 0]], [[2, 0], [5, 1]], [[1, 0]], [[2, 0], [-4, 1]], [[6, 0], [4, 1]], [[2, 0], [6, 1]], [[-3, 0], [1, 1]], [[-4, 0], [-1, 1]], [[1, 0]], [[1, 0]], [[2, 0], [5, 1]], [[-3, 0], [-5, 1]], [[2, 0], [5, 1]], [[2, 0]], [[1, 0]], [[2, 0], [5, 1]], [[-14, 0], [-16, 1]], [[-4, 0], [-6, 1]], [[7, 0]], [[7, 0]], [[2, 0], [10, 1]], [[-3, 0], [-5, 1]], [[-8, 0]], [[6, 0], [9, 1]], [[-3, 0], [-5, 1]], [[12, 0]], [[12, 0]], [[7, 0]], [[2, 0], [16, 1]], [[-8, 0]], [[-14, 0], [-10, 1]], [[2, 0], [5, 1]], [[6, 0]], [[6, 0], [10, 1]], [[2, 0], [-4, 1]], [[-3, 0]], [[-3, 0], [-5, 1]], [[-4, 0], [-1, 1]], [[-3, 0]], [[-8, 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]]]}
-
id: 5852940
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 90, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48l1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0], [-36, 1]], [[12, 0], [36, 1]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-9, 0], [-6, 1]], [[-3, 0], [6, 1]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[6, 0], [10, 1]], [[-4, 0], [-10, 1]], [[6, 0], [10, 1]], [[-3, 0], [1, 1]], [[-3, 0]], [[2, 0], [-5, 1]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-3, 0]], [[2, 0]], [[-4, 0], [-10, 1]], [[-4, 0], [-1, 1]], [[-4, 0], [-1, 1]], [[7, 0]], [[1, 0], [5, 1]], [[-3, 0], [1, 1]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[7, 0], [-9, 1]], [[-3, 0], [-5, 1]], [[-3, 0], [-5, 1]], [[-4, 0], [-10, 1]], [[6, 0], [4, 1]], [[2, 0]], [[2, 0], [5, 1]], [[1, 0]], [[16, 0], [9, 1]], [[-3, 0], [1, 1]], [[6, 0], [9, 1]], [[-4, 0], [-1, 1]], [[2, 0], [-4, 1]], [[6, 0], [10, 1]], [[1, 0]], [[7, 0]], [[7, 0]], [[-13, 0], [-10, 1]], [[-3, 0]], [[6, 0], [10, 1]], [[-13, 0], [-10, 1]], [[2, 0], [1, 1]], [[-3, 0], [-9, 1]], [[-8, 0]], [[7, 0]], [[7, 0], [5, 1]], [[7, 0]], [[7, 0]], [[2, 0], [6, 1]], [[-3, 0], [10, 1]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[1, 0], [-1, 1]], [[-13, 0], [-10, 1]], [[-4, 0], [-5, 1]], [[2, 0], [5, 1]], [[-4, 0]], [[-4, 0], [-10, 1]], [[-4, 0], [-1, 1]], [[2, 0]], [[-3, 0], [10, 1]], [[-3, 0], [1, 1]], [[2, 0]], [[-3, 0], [10, 1]], [[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]]]}
-
id: 5852941
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 91, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48l2', 'nt': [180, 2], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0], [36, 1]], [[-24, 0], [-36, 1]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-3, 0], [6, 1]], [[-9, 0], [-6, 1]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0], [-10, 1]], [[6, 0], [10, 1]], [[-4, 0], [-10, 1]], [[-4, 0], [-1, 1]], [[-3, 0]], [[7, 0], [5, 1]], [[-4, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-3, 0]], [[2, 0]], [[6, 0], [10, 1]], [[-3, 0], [1, 1]], [[-3, 0], [1, 1]], [[7, 0]], [[-4, 0], [-5, 1]], [[-4, 0], [-1, 1]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[16, 0], [9, 1]], [[2, 0], [5, 1]], [[2, 0], [5, 1]], [[6, 0], [10, 1]], [[2, 0], [-4, 1]], [[2, 0]], [[-3, 0], [-5, 1]], [[1, 0]], [[7, 0], [-9, 1]], [[-4, 0], [-1, 1]], [[-3, 0], [-9, 1]], [[-3, 0], [1, 1]], [[6, 0], [4, 1]], [[-4, 0], [-10, 1]], [[1, 0]], [[7, 0]], [[7, 0]], [[-3, 0], [10, 1]], [[-3, 0]], [[-4, 0], [-10, 1]], [[-3, 0], [10, 1]], [[1, 0], [-1, 1]], [[6, 0], [9, 1]], [[-8, 0]], [[7, 0]], [[2, 0], [-5, 1]], [[7, 0]], [[7, 0]], [[-4, 0], [-6, 1]], [[-13, 0], [-10, 1]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0], [1, 1]], [[-3, 0], [10, 1]], [[1, 0], [5, 1]], [[-3, 0], [-5, 1]], [[-4, 0]], [[6, 0], [10, 1]], [[-3, 0], [1, 1]], [[2, 0]], [[-13, 0], [-10, 1]], [[-4, 0], [-1, 1]], [[2, 0]], [[-13, 0], [-10, 1]], [[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]]]}
-
id: 5852942
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 92, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48m1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0], [-36, 1]], [[12, 0], [36, 1]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[21, 0], [9, 1]], [[12, 0], [-9, 1]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[6, 0], [10, 1]], [[-4, 0], [-10, 1]], [[-4, 0], [-10, 1]], [[2, 0], [-4, 1]], [[-3, 0]], [[-3, 0], [15, 1]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[-3, 0]], [[2, 0]], [[1, 0]], [[-4, 0], [-1, 1]], [[6, 0], [4, 1]], [[2, 0], [5, 1]], [[-9, 0], [-15, 1]], [[-3, 0], [1, 1]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[-3, 0], [1, 1]], [[-3, 0], [-5, 1]], [[-3, 0], [-5, 1]], [[1, 0]], [[6, 0], [4, 1]], [[2, 0]], [[2, 0], [5, 1]], [[1, 0]], [[-4, 0], [-1, 1]], [[-3, 0], [1, 1]], [[6, 0], [9, 1]], [[6, 0], [4, 1]], [[2, 0], [-4, 1]], [[1, 0]], [[1, 0]], [[2, 0], [5, 1]], [[-3, 0], [-5, 1]], [[2, 0], [5, 1]], [[-3, 0]], [[1, 0]], [[2, 0], [5, 1]], [[-3, 0], [6, 1]], [[-3, 0], [-9, 1]], [[-8, 0]], [[-8, 0]], [[-18, 0], [-15, 1]], [[-3, 0], [-5, 1]], [[7, 0]], [[2, 0], [6, 1]], [[-3, 0], [-5, 1]], [[12, 0]], [[12, 0]], [[-8, 0]], [[-9, 0], [-6, 1]], [[7, 0]], [[6, 0], [15, 1]], [[2, 0], [5, 1]], [[-4, 0]], [[6, 0], [10, 1]], [[-4, 0], [-1, 1]], [[2, 0]], [[-3, 0], [-5, 1]], [[2, 0], [-4, 1]], [[2, 0]], [[7, 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]]]}
-
id: 5852943
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 93, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48m2', 'nt': [180, 2], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0], [36, 1]], [[-24, 0], [-36, 1]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[12, 0], [-9, 1]], [[21, 0], [9, 1]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0], [-10, 1]], [[6, 0], [10, 1]], [[6, 0], [10, 1]], [[6, 0], [4, 1]], [[-3, 0]], [[-18, 0], [-15, 1]], [[-4, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[-3, 0]], [[2, 0]], [[1, 0]], [[-3, 0], [1, 1]], [[2, 0], [-4, 1]], [[-3, 0], [-5, 1]], [[6, 0], [15, 1]], [[-4, 0], [-1, 1]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[-4, 0], [-1, 1]], [[2, 0], [5, 1]], [[2, 0], [5, 1]], [[1, 0]], [[2, 0], [-4, 1]], [[2, 0]], [[-3, 0], [-5, 1]], [[1, 0]], [[-3, 0], [1, 1]], [[-4, 0], [-1, 1]], [[-3, 0], [-9, 1]], [[2, 0], [-4, 1]], [[6, 0], [4, 1]], [[1, 0]], [[1, 0]], [[-3, 0], [-5, 1]], [[2, 0], [5, 1]], [[-3, 0], [-5, 1]], [[-3, 0]], [[1, 0]], [[-3, 0], [-5, 1]], [[-9, 0], [-6, 1]], [[6, 0], [9, 1]], [[-8, 0]], [[-8, 0]], [[-3, 0], [15, 1]], [[2, 0], [5, 1]], [[7, 0]], [[-4, 0], [-6, 1]], [[2, 0], [5, 1]], [[12, 0]], [[12, 0]], [[-8, 0]], [[-3, 0], [6, 1]], [[7, 0]], [[-9, 0], [-15, 1]], [[-3, 0], [-5, 1]], [[-4, 0]], [[-4, 0], [-10, 1]], [[-3, 0], [1, 1]], [[2, 0]], [[2, 0], [5, 1]], [[6, 0], [4, 1]], [[2, 0]], [[7, 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]]]}
-
id: 5852944
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 94, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48n1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0], [-36, 1]], [[12, 0], [36, 1]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[28, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[-12, 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]], [[6, 0], [9, 1]], [[-3, 0], [-9, 1]], [[-14, 0]], [[-4, 0]], [[-14, 0]], [[-4, 0]], [[-14, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[-3, 0], [-9, 1]], [[7, 0]], [[-3, 0]], [[-4, 0]], [[-4, 0], [-6, 1]], [[2, 0], [6, 1]], [[7, 0]], [[2, 0]], [[6, 0]], [[-4, 0], [-6, 1]], [[6, 0], [9, 1]], [[-3, 0]], [[6, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[-3, 0], [-9, 1]], [[2, 0]], [[2, 0]], [[6, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[6, 0], [9, 1]], [[-3, 0], [-9, 1]], [[-14, 0], [-21, 1]], [[6, 0], [9, 1]], [[2, 0], [6, 1]], [[6, 0]], [[-4, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[6, 0]], [[-3, 0]], [[-3, 0], [-9, 1]], [[7, 0], [21, 1]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0], [6, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0], [9, 1]], [[-3, 0]], [[6, 0]], [[2, 0]], [[-4, 0]], [[6, 0]], [[6, 0], [9, 1]], [[2, 0]], [[-3, 0]], [[-3, 0], [-9, 1]], [[2, 0]], [[-3, 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]]]}
-
id: 5852945
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 95, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48n2', 'nt': [180, 2], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0], [36, 1]], [[-24, 0], [-36, 1]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[28, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[-12, 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]], [[-3, 0], [-9, 1]], [[6, 0], [9, 1]], [[-14, 0]], [[-4, 0]], [[-14, 0]], [[-4, 0]], [[-14, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[6, 0], [9, 1]], [[7, 0]], [[-3, 0]], [[-4, 0]], [[2, 0], [6, 1]], [[-4, 0], [-6, 1]], [[7, 0]], [[2, 0]], [[6, 0]], [[2, 0], [6, 1]], [[-3, 0], [-9, 1]], [[-3, 0]], [[6, 0]], [[-4, 0], [-6, 1]], [[2, 0]], [[2, 0]], [[2, 0], [6, 1]], [[6, 0], [9, 1]], [[2, 0]], [[2, 0]], [[6, 0]], [[2, 0], [6, 1]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-3, 0], [-9, 1]], [[6, 0], [9, 1]], [[7, 0], [21, 1]], [[-3, 0], [-9, 1]], [[-4, 0], [-6, 1]], [[6, 0]], [[-4, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[6, 0]], [[-3, 0]], [[6, 0], [9, 1]], [[-14, 0], [-21, 1]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-4, 0], [-6, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0], [-9, 1]], [[-3, 0]], [[6, 0]], [[2, 0]], [[-4, 0]], [[6, 0]], [[-3, 0], [-9, 1]], [[2, 0]], [[-3, 0]], [[6, 0], [9, 1]], [[2, 0]], [[-3, 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]]]}
-
id: 5852946
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 96, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [4, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48o1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[18, 0]], [[3, 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]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[0, 0]], [[-3, 0]], [[3, 0]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[-3, 0]], [[-3, 0]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[0, 0]], [[12, 0]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[0, 0]], [[-3, 0]], [[12, 0]], [[-3, 0]], [[-3, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[3, 0]], [[0, 0]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[3, 0]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[-12, 0]], [[-3, 0]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-3, 0]], [[3, 0]], [[0, 0]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-3, 0]], [[3, 0]], [[3, 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]]]}
-
id: 5852947
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 97, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [4, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48o2', 'nt': [180, 2], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[18, 0]], [[3, 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]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[0, 0]], [[-3, 0]], [[3, 0]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-3, 0]], [[-3, 0]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[0, 0]], [[12, 0]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[0, 0]], [[-3, 0]], [[12, 0]], [[-3, 0]], [[-3, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[3, 0]], [[0, 0]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[3, 0]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-12, 0]], [[-3, 0]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-3, 0]], [[3, 0]], [[0, 0]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-3, 0]], [[3, 0]], [[3, 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]]]}
-
id: 5852948
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 98, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48p1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[18, 0]], [[3, 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]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 0], [-20, 1]], [[10, 0], [20, 1]], [[-5, 0], [-10, 1]], [[7, 0], [5, 1]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-5, 0], [-10, 1]], [[7, 0], [-10, 1]], [[2, 0], [-5, 1]], [[-7, 0], [-5, 1]], [[0, 0]], [[17, 0], [10, 1]], [[3, 0]], [[3, 0]], [[-3, 0]], [[7, 0], [5, 1]], [[-7, 0], [-5, 1]], [[-7, 0], [-5, 1]], [[-5, 0], [-10, 1]], [[2, 0], [10, 1]], [[3, 0]], [[-2, 0], [5, 1]], [[0, 0]], [[2, 0], [-5, 1]], [[-18, 0], [-15, 1]], [[-3, 0]], [[2, 0], [-5, 1]], [[-8, 0], [-10, 1]], [[5, 0], [10, 1]], [[0, 0]], [[-7, 0], [-5, 1]], [[-2, 0], [5, 1]], [[3, 0]], [[3, 0]], [[5, 0], [10, 1]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-12, 0]], [[3, 0]], [[3, 0]], [[-2, 0], [5, 1]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-2, 0], [5, 1]], [[0, 0]], [[-2, 0], [5, 1]], [[0, 0]], [[5, 0], [10, 1]], [[-3, 0], [15, 1]], [[3, 0]], [[3, 0]], [[7, 0], [5, 1]], [[3, 0]], [[-7, 0], [-5, 1]], [[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]]]}
-
id: 5852949
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 99, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48p2', 'nt': [180, 2], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[18, 0]], [[3, 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]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[10, 0], [20, 1]], [[-10, 0], [-20, 1]], [[5, 0], [10, 1]], [[2, 0], [-5, 1]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[5, 0], [10, 1]], [[17, 0], [10, 1]], [[7, 0], [5, 1]], [[-2, 0], [5, 1]], [[0, 0]], [[7, 0], [-10, 1]], [[3, 0]], [[3, 0]], [[-3, 0]], [[2, 0], [-5, 1]], [[-2, 0], [5, 1]], [[-2, 0], [5, 1]], [[5, 0], [10, 1]], [[-8, 0], [-10, 1]], [[3, 0]], [[-7, 0], [-5, 1]], [[0, 0]], [[7, 0], [5, 1]], [[-3, 0], [15, 1]], [[-3, 0]], [[7, 0], [5, 1]], [[2, 0], [10, 1]], [[-5, 0], [-10, 1]], [[0, 0]], [[-2, 0], [5, 1]], [[-7, 0], [-5, 1]], [[3, 0]], [[3, 0]], [[-5, 0], [-10, 1]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-12, 0]], [[3, 0]], [[3, 0]], [[-7, 0], [-5, 1]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-7, 0], [-5, 1]], [[0, 0]], [[-7, 0], [-5, 1]], [[0, 0]], [[-5, 0], [-10, 1]], [[-18, 0], [-15, 1]], [[3, 0]], [[3, 0]], [[2, 0], [-5, 1]], [[3, 0]], [[-2, 0], [5, 1]], [[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]]]}
-
id: 5852817
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 100, 'cyclotomic_n': 5, 'dim': 48, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48q1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0], [20, 2], [20, -2]], [[8, 0]], [[-12, 0], [-20, 2], [-20, -2]], [[-12, 0]], [[-12, 0]], [[8, 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]], [[-3, 0]], [[-3, 0]], [[-4, 0], [12, 2], [12, -2]], [[8, 0], [-4, 2], [-4, -2]], [[20, 0]], [[12, 0], [4, 2], [4, -2]], [[-16, 0], [-12, 2], [-12, -2]], [[0, 0]], [[0, 0]], [[-10, 0]], [[2, 0]], [[8, 0]], [[3, 0]], [[-6, 0], [-2, 2], [-2, -2]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0], [5, 2], [5, -2]], [[-4, 0], [6, 2], [6, -2]], [[4, 2], [4, -2]], [[2, 0], [-6, 2], [-6, -2]], [[-3, 0]], [[2, 0]], [[-1, 0], [-3, 2], [-3, -2]], [[0, 0]], [[-3, 0]], [[2, 0], [-7, 2], [-7, -2]], [[4, 2], [4, -2]], [[2, 0], [5, 2], [5, -2]], [[2, 0]], [[-6, 1], [-6, -1]], [[-6, 2], [-6, -2]], [[8, 0], [6, 2], [6, -2]], [[-3, 0]], [[4, 1], [4, -1]], [[-6, 2], [-6, -2]], [[6, 0], [12, 2], [12, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0], [-6, 2], [-6, -2]], [[-6, 0], [-12, 2], [-12, -2]], [[2, 0], [3, 2], [3, -2]], [[-1, 0], [-3, 2], [-3, -2]], [[2, 0], [3, 2], [3, -2]], [[-10, 0], [-6, 2], [-6, -2]], [[8, 0], [6, 2], [6, -2]], [[-1, 0], [-3, 2], [-3, -2]], [[-3, 0]], [[2, 0]], [[3, 0]], [[-7, 0]], [[3, 0]], [[2, 0], [3, 2], [3, -2]], [[3, 0]], [[-3, 0], [-5, 2], [-5, -2]], [[-1, 0], [-3, 2], [-3, -2]], [[3, 0]], [[3, 0]], [[-7, 0]], [[-3, 0]], [[-7, 0]], [[0, 0]], [[-6, 1], [-6, -1]], [[-4, 0], [2, 2], [2, -2]], [[-10, 0]], [[2, 0]], [[4, 1], [4, -1]], [[2, 0], [3, 2], [3, -2]], [[2, 0]], [[9, 0], [7, 2], [7, -2]], [[-7, 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]]]}
-
id: 5852818
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 101, 'cyclotomic_n': 5, 'dim': 48, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48q2', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0], [-20, 2], [-20, -2]], [[8, 0]], [[8, 0], [20, 2], [20, -2]], [[-12, 0]], [[-12, 0]], [[8, 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]], [[-3, 0]], [[-3, 0]], [[-16, 0], [-12, 2], [-12, -2]], [[12, 0], [4, 2], [4, -2]], [[20, 0]], [[8, 0], [-4, 2], [-4, -2]], [[-4, 0], [12, 2], [12, -2]], [[0, 0]], [[0, 0]], [[-10, 0]], [[2, 0]], [[8, 0]], [[3, 0]], [[-4, 0], [2, 2], [2, -2]], [[2, 0], [5, 2], [5, -2]], [[-3, 0], [-5, 2], [-5, -2]], [[-10, 0], [-6, 2], [-6, -2]], [[4, 1], [4, -1]], [[8, 0], [6, 2], [6, -2]], [[-3, 0]], [[2, 0]], [[2, 0], [3, 2], [3, -2]], [[0, 0]], [[-3, 0]], [[9, 0], [7, 2], [7, -2]], [[4, 1], [4, -1]], [[-3, 0], [-5, 2], [-5, -2]], [[2, 0]], [[-6, 2], [-6, -2]], [[-6, 1], [-6, -1]], [[2, 0], [-6, 2], [-6, -2]], [[-3, 0]], [[4, 2], [4, -2]], [[-6, 1], [-6, -1]], [[-6, 0], [-12, 2], [-12, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[8, 0], [6, 2], [6, -2]], [[6, 0], [12, 2], [12, -2]], [[-1, 0], [-3, 2], [-3, -2]], [[2, 0], [3, 2], [3, -2]], [[-1, 0], [-3, 2], [-3, -2]], [[-4, 0], [6, 2], [6, -2]], [[2, 0], [-6, 2], [-6, -2]], [[2, 0], [3, 2], [3, -2]], [[-3, 0]], [[2, 0]], [[3, 0]], [[-7, 0]], [[3, 0]], [[-1, 0], [-3, 2], [-3, -2]], [[3, 0]], [[2, 0], [5, 2], [5, -2]], [[2, 0], [3, 2], [3, -2]], [[3, 0]], [[3, 0]], [[-7, 0]], [[-3, 0]], [[-7, 0]], [[0, 0]], [[-6, 2], [-6, -2]], [[-6, 0], [-2, 2], [-2, -2]], [[-10, 0]], [[2, 0]], [[4, 2], [4, -2]], [[-1, 0], [-3, 2], [-3, -2]], [[2, 0]], [[2, 0], [-7, 2], [-7, -2]], [[-7, 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]]]}
-
id: 5852819
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 102, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48r1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-18, 0], [-15, 1]], [[-3, 0], [15, 1]], [[0, 0]], [[-10, 0]], [[0, 0]], [[-10, 0]], [[0, 0]], [[10, 0]], [[10, 0]], [[10, -1]], [[2, 0], [5, 1]], [[3, 0]], [[-7, 0], [-5, 1]], [[5, 0]], [[2, 0]], [[2, 0]], [[3, 0]], [[-7, 0], [-15, 1]], [[-5, -1]], [[7, 0]], [[-3, 0], [-5, 1]], [[3, 0], [-5, 1]], [[-5, 0], [-10, 1]], [[7, 0]], [[-7, 0]], [[8, 0], [15, 1]], [[2, 0]], [[-13, 0], [-10, 1]], [[-2, 0]], [[-2, 0]], [[-5, -1]], [[-8, 0]], [[8, 0], [15, 1]], [[-2, 0]], [[-5, 0]], [[-3, 0], [10, 1]], [[7, 0]], [[-3, 0]], [[-3, 0], [-5, 1]], [[-8, 0]], [[-5, 1]], [[-5, 0]], [[3, 0], [-5, 1]], [[8, 0], [5, 1]], [[-2, 0]], [[3, 0]], [[-5, 1]], [[-2, 0]], [[2, 0], [-5, 1]], [[-3, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0], [5, 1]], [[8, 0], [5, 1]], [[13, 0]], [[2, 0]], [[-2, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[7, 0], [5, 1]], [[-7, 0], [-10, 1]], [[5, 0], [10, 1]], [[-2, 0]], [[5, 0]], [[10, 1]], [[7, 0]], [[-7, 0], [-15, 1]], [[-2, 0]], [[2, 0], [5, 1]], [[-7, 0]], [[3, 0], [10, 1]], [[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]]]}
-
id: 5852820
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 103, 'cyclotomic_n': 3, 'dim': 48, 'faithful': True, 'field': [1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48r2', 'nt': [180, 2], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-3, 0], [15, 1]], [[-18, 0], [-15, 1]], [[0, 0]], [[-10, 0]], [[0, 0]], [[-10, 0]], [[0, 0]], [[10, 0]], [[10, 0]], [[10, 1]], [[-3, 0], [-5, 1]], [[3, 0]], [[-2, 0], [5, 1]], [[5, 0]], [[2, 0]], [[2, 0]], [[3, 0]], [[8, 0], [15, 1]], [[-5, 1]], [[7, 0]], [[2, 0], [5, 1]], [[8, 0], [5, 1]], [[5, 0], [10, 1]], [[7, 0]], [[-7, 0]], [[-7, 0], [-15, 1]], [[2, 0]], [[-3, 0], [10, 1]], [[-2, 0]], [[-2, 0]], [[-5, 1]], [[-8, 0]], [[-7, 0], [-15, 1]], [[-2, 0]], [[-5, 0]], [[-13, 0], [-10, 1]], [[7, 0]], [[-3, 0]], [[2, 0], [5, 1]], [[-8, 0]], [[-5, -1]], [[-5, 0]], [[8, 0], [5, 1]], [[3, 0], [-5, 1]], [[-2, 0]], [[3, 0]], [[-5, -1]], [[-2, 0]], [[7, 0], [5, 1]], [[-3, 0]], [[-2, 0]], [[-2, 0]], [[-7, 0], [-5, 1]], [[3, 0], [-5, 1]], [[13, 0]], [[2, 0]], [[-2, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[2, 0], [-5, 1]], [[3, 0], [10, 1]], [[-5, 0], [-10, 1]], [[-2, 0]], [[5, 0]], [[10, -1]], [[7, 0]], [[8, 0], [15, 1]], [[-2, 0]], [[-3, 0], [-5, 1]], [[-7, 0]], [[-7, 0], [-10, 1]], [[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]]]}
-
id: 5852821
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 104, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [4, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48s1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[12, 0]], [[12, 0]], [[0, 0]], [[-10, 0]], [[0, 0]], [[-10, 0]], [[0, 0]], [[10, 0]], [[10, 0]], [[-5, 0]], [[7, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[3, 0]], [[3, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[3, 0]], [[-4, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[10, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[-8, 0]], [[-8, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[-5, 0], [4, 1], [2, 2], [-2, 3], [4, 4], [-2, 5], [2, 7]], [[0, 0]], [[-8, 0]], [[-7, 0]], [[5, 0], [-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[2, 0]], [[7, 0]], [[-11, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[7, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-5, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[7, 0]], [[-4, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-11, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[-5, 0]], [[7, 0]], [[-8, 0]], [[-3, 0]], [[7, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[7, 0]], [[-5, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[-5, 0]], [[1, 0], [-4, 1], [-2, 2], [2, 3], [-4, 4], [2, 5], [-2, 7]], [[1, 0], [-4, 1], [-2, 2], [2, 3], [-4, 4], [2, 5], [-2, 7]], [[7, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[3, 0]], [[10, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[4, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-3, 0]], [[-3, 0]], [[13, 0]], [[-8, 0], [8, 1], [4, 2], [-4, 3], [8, 4], [-4, 5], [4, 7]], [[3, 0]], [[-5, 0], [4, 1], [2, 2], [-2, 3], [4, 4], [-2, 5], [2, 7]], [[-2, 0]], [[2, 0]], [[7, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[4, 0], [-8, 1], [-4, 2], [4, 3], [-8, 4], [4, 5], [-4, 7]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[7, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[5, 0]], [[-5, 0]], [[-8, 0]], [[5, 0], [-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[4, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-8, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[-7, 0]], [[-2, 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]]]}
-
id: 5852822
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 105, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [4, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48s2', 'nt': [180, 2], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[12, 0]], [[12, 0]], [[0, 0]], [[-10, 0]], [[0, 0]], [[-10, 0]], [[0, 0]], [[10, 0]], [[10, 0]], [[-5, 0]], [[-8, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[3, 0]], [[3, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[3, 0]], [[5, 0], [-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-5, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[-8, 0]], [[7, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[1, 0], [-4, 1], [-2, 2], [2, 3], [-4, 4], [2, 5], [-2, 7]], [[0, 0]], [[-8, 0]], [[-7, 0]], [[-4, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[2, 0]], [[7, 0]], [[7, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-11, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[10, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[7, 0]], [[5, 0], [-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[7, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-5, 0]], [[7, 0]], [[-8, 0]], [[-3, 0]], [[-8, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[7, 0]], [[10, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[-5, 0]], [[-5, 0], [4, 1], [2, 2], [-2, 3], [4, 4], [-2, 5], [2, 7]], [[-5, 0], [4, 1], [2, 2], [-2, 3], [4, 4], [-2, 5], [2, 7]], [[4, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[3, 0]], [[-5, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[7, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[-3, 0]], [[-3, 0]], [[13, 0]], [[4, 0], [-8, 1], [-4, 2], [4, 3], [-8, 4], [4, 5], [-4, 7]], [[3, 0]], [[1, 0], [-4, 1], [-2, 2], [2, 3], [-4, 4], [2, 5], [-2, 7]], [[-2, 0]], [[2, 0]], [[4, 0], [2, 1], [1, 2], [-1, 3], [2, 4], [-1, 5], [1, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-8, 0], [8, 1], [4, 2], [-4, 3], [8, 4], [-4, 5], [4, 7]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[-11, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[5, 0]], [[-5, 0]], [[-8, 0]], [[-4, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[7, 0], [-2, 1], [-1, 2], [1, 3], [-2, 4], [1, 5], [-1, 7]], [[7, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[-7, 0]], [[-2, 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]]]}
-
id: 5852823
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 106, 'cyclotomic_n': 5, 'dim': 48, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48t1', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[28, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[-12, 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]], [[-3, 0]], [[-3, 0]], [[-2, 0], [6, 2], [6, -2]], [[-16, 0], [-12, 2], [-12, -2]], [[10, 0]], [[-4, 0], [12, 2], [12, -2]], [[-8, 0], [-6, 2], [-6, -2]], [[-10, 0]], [[-10, 0]], [[0, 0]], [[-3, 0]], [[-2, 0]], [[3, 0]], [[2, 0], [-6, 2], [-6, -2]], [[2, 0]], [[2, 0]], [[-8, 0], [3, 2], [3, -2]], [[-1, 0], [-3, 2], [-3, -2]], [[6, 0], [12, 2], [12, -2]], [[2, 0]], [[-3, 0]], [[-6, 1], [-6, -1]], [[0, 0]], [[2, 0]], [[-10, 0], [-6, 2], [-6, -2]], [[-1, 0], [-3, 2], [-3, -2]], [[2, 0]], [[-3, 0]], [[2, 0], [3, 2], [3, -2]], [[-1, 0], [-3, 2], [-3, -2]], [[-6, 0], [-12, 2], [-12, -2]], [[2, 0]], [[2, 0], [3, 2], [3, -2]], [[-1, 0], [-3, 2], [-3, -2]], [[8, 0], [6, 2], [6, -2]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[6, 0], [12, 2], [12, -2]], [[2, 0], [-6, 2], [-6, -2]], [[-6, 2], [-6, -2]], [[-6, 1], [-6, -1]], [[-6, 2], [-6, -2]], [[-11, 0], [-3, 2], [-3, -2]], [[-6, 0], [-12, 2], [-12, -2]], [[-6, 1], [-6, -1]], [[-3, 0]], [[7, 0]], [[-7, 0]], [[3, 0]], [[3, 0]], [[-6, 2], [-6, -2]], [[-7, 0]], [[2, 0]], [[-6, 1], [-6, -1]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[2, 0], [3, 2], [3, -2]], [[8, 0], [6, 2], [6, -2]], [[0, 0]], [[-3, 0]], [[2, 0], [3, 2], [3, -2]], [[-6, 2], [-6, -2]], [[-3, 0]], [[-4, 0], [6, 2], [6, -2]], [[3, 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]]]}
-
id: 5852824
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 107, 'cyclotomic_n': 5, 'dim': 48, 'faithful': True, 'field': [-1, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 1, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48t2', 'nt': [180, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[28, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[-12, 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]], [[-3, 0]], [[-3, 0]], [[-8, 0], [-6, 2], [-6, -2]], [[-4, 0], [12, 2], [12, -2]], [[10, 0]], [[-16, 0], [-12, 2], [-12, -2]], [[-2, 0], [6, 2], [6, -2]], [[-10, 0]], [[-10, 0]], [[0, 0]], [[-3, 0]], [[-2, 0]], [[3, 0]], [[8, 0], [6, 2], [6, -2]], [[2, 0]], [[2, 0]], [[-11, 0], [-3, 2], [-3, -2]], [[2, 0], [3, 2], [3, -2]], [[-6, 0], [-12, 2], [-12, -2]], [[2, 0]], [[-3, 0]], [[-6, 2], [-6, -2]], [[0, 0]], [[2, 0]], [[-4, 0], [6, 2], [6, -2]], [[2, 0], [3, 2], [3, -2]], [[2, 0]], [[-3, 0]], [[-1, 0], [-3, 2], [-3, -2]], [[2, 0], [3, 2], [3, -2]], [[6, 0], [12, 2], [12, -2]], [[2, 0]], [[-1, 0], [-3, 2], [-3, -2]], [[2, 0], [3, 2], [3, -2]], [[2, 0], [-6, 2], [-6, -2]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[-6, 0], [-12, 2], [-12, -2]], [[8, 0], [6, 2], [6, -2]], [[-6, 1], [-6, -1]], [[-6, 2], [-6, -2]], [[-6, 1], [-6, -1]], [[-8, 0], [3, 2], [3, -2]], [[6, 0], [12, 2], [12, -2]], [[-6, 2], [-6, -2]], [[-3, 0]], [[7, 0]], [[-7, 0]], [[3, 0]], [[3, 0]], [[-6, 1], [-6, -1]], [[-7, 0]], [[2, 0]], [[-6, 2], [-6, -2]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[-1, 0], [-3, 2], [-3, -2]], [[2, 0], [-6, 2], [-6, -2]], [[0, 0]], [[-3, 0]], [[-1, 0], [-3, 2], [-3, -2]], [[-6, 1], [-6, -1]], [[-3, 0]], [[-10, 0], [-6, 2], [-6, -2]], [[3, 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]]]}
-
id: 5852825
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 108, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48u1', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-9, 0], [-15, 5]], [[6, 0], [15, 5]], [[12, 6], [12, -6]], [[-4, 0], [6, 2], [-6, 3], [6, 7]], [[-6, 0]], [[2, 0], [-6, 2], [6, 3], [-6, 7]], [[12, 3], [12, -3]], [[4, 0]], [[4, 0]], [[-1, 0], [5, 5]], [[-4, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [5, 7]], [[0, 0]], [[5, 0], [10, 5]], [[5, 0], [3, 2], [-3, 3], [3, 7]], [[-4, 0]], [[-4, 0]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[2, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [-1, 7]], [[1, 0]], [[6, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [-5, 7]], [[-3, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [1, 7]], [[4, 0], [5, 5]], [[1, 0]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-4, 0]], [[-4, 0], [-10, 5]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[-4, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [-5, 5], [1, 7]], [[1, 0]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[-2, 0], [-3, 2], [3, 3], [-3, 7]], [[6, 0], [10, 5]], [[1, 0]], [[6, 0]], [[-9, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-10, 5], [5, 7]], [[1, 0]], [[-3, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [4, 7]], [[-5, 0], [3, 2], [-3, 3], [3, 7]], [[3, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [5, 5], [-1, 7]], [[2, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [-4, 7]], [[-2, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [5, 5], [4, 7]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[6, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [5, 5], [-4, 7]], [[7, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [10, 5], [-4, 7]], [[-4, 0], [-5, 5]], [[6, 0]], [[-5, 0]], [[-5, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[-5, 0], [-10, 5]], [[-7, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [-5, 5], [4, 7]], [[-5, 0]], [[-4, 0]], [[-8, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [-10, 5], [1, 7]], [[0, 0]], [[0, 0]], [[10, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[1, 0], [5, 5]], [[-5, -5]], [[-1, 0], [-5, 5]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[8, 0], [-3, 2], [3, 3], [-3, 7]], [[-6, 0], [-5, 5]], [[1, 0]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-2, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [-5, 5], [-1, 7]], [[11, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [10, 5], [-5, 7]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[-5, 5]], [[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]]]}
-
id: 5852826
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 109, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48u2', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[6, 0], [15, 5]], [[-9, 0], [-15, 5]], [[12, 6], [12, -6]], [[-4, 0], [6, 2], [-6, 3], [6, 7]], [[-6, 0]], [[2, 0], [-6, 2], [6, 3], [-6, 7]], [[12, 3], [12, -3]], [[4, 0]], [[4, 0]], [[-6, 0], [-5, 5]], [[6, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [-5, 7]], [[0, 0]], [[-5, 0], [-10, 5]], [[5, 0], [3, 2], [-3, 3], [3, 7]], [[-4, 0]], [[-4, 0]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-3, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [4, 7]], [[1, 0]], [[-4, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [5, 7]], [[2, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [-4, 7]], [[-1, 0], [-5, 5]], [[1, 0]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-4, 0]], [[6, 0], [10, 5]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[6, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [5, 5], [-4, 7]], [[1, 0]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[-2, 0], [-3, 2], [3, 3], [-3, 7]], [[-4, 0], [-10, 5]], [[1, 0]], [[6, 0]], [[11, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [10, 5], [-5, 7]], [[1, 0]], [[2, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [-1, 7]], [[-5, 0], [3, 2], [-3, 3], [3, 7]], [[-7, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [-5, 5], [4, 7]], [[-3, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [1, 7]], [[-2, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [-5, 5], [-1, 7]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[-4, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [-5, 5], [1, 7]], [[-8, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [-10, 5], [1, 7]], [[1, 0], [5, 5]], [[6, 0]], [[-5, 0]], [[10, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[5, 0], [10, 5]], [[3, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [5, 5], [-1, 7]], [[-5, 0]], [[-4, 0]], [[7, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [10, 5], [-4, 7]], [[0, 0]], [[0, 0]], [[-5, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[-4, 0], [-5, 5]], [[-5, 5]], [[4, 0], [5, 5]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[8, 0], [-3, 2], [3, 3], [-3, 7]], [[-1, 0], [5, 5]], [[1, 0]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-2, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [5, 5], [4, 7]], [[-9, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-10, 5], [5, 7]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[-5, -5]], [[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]]]}
-
id: 5852828
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 110, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48u3', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-9, 0], [-15, 5]], [[6, 0], [15, 5]], [[12, 3], [12, -3]], [[2, 0], [-6, 2], [6, 3], [-6, 7]], [[-6, 0]], [[-4, 0], [6, 2], [-6, 3], [6, 7]], [[12, 6], [12, -6]], [[4, 0]], [[4, 0]], [[-1, 0], [5, 5]], [[11, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [10, 5], [-5, 7]], [[0, 0]], [[5, 0], [10, 5]], [[8, 0], [-3, 2], [3, 3], [-3, 7]], [[-4, 0]], [[-4, 0]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-4, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [-5, 5], [1, 7]], [[1, 0]], [[-9, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-10, 5], [5, 7]], [[3, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [5, 5], [-1, 7]], [[4, 0], [5, 5]], [[1, 0]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-4, 0]], [[-4, 0], [-10, 5]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[2, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [-1, 7]], [[1, 0]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[-5, 0], [3, 2], [-3, 3], [3, 7]], [[6, 0], [10, 5]], [[1, 0]], [[6, 0]], [[6, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [-5, 7]], [[1, 0]], [[6, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [5, 5], [-4, 7]], [[-2, 0], [-3, 2], [3, 3], [-3, 7]], [[-3, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [1, 7]], [[-7, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [-5, 5], [4, 7]], [[7, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [10, 5], [-4, 7]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[-3, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [4, 7]], [[-2, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [5, 5], [4, 7]], [[-4, 0], [-5, 5]], [[6, 0]], [[-5, 0]], [[10, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[-5, 0], [-10, 5]], [[2, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [-4, 7]], [[-5, 0]], [[-4, 0]], [[-2, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [-5, 5], [-1, 7]], [[0, 0]], [[0, 0]], [[-5, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[1, 0], [5, 5]], [[-5, -5]], [[-1, 0], [-5, 5]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[5, 0], [3, 2], [-3, 3], [3, 7]], [[-6, 0], [-5, 5]], [[1, 0]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-8, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [-10, 5], [1, 7]], [[-4, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [5, 7]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[-5, 5]], [[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]]]}
-
id: 5852829
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 111, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48u4', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[-24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[6, 0], [15, 5]], [[-9, 0], [-15, 5]], [[12, 3], [12, -3]], [[2, 0], [-6, 2], [6, 3], [-6, 7]], [[-6, 0]], [[-4, 0], [6, 2], [-6, 3], [6, 7]], [[12, 6], [12, -6]], [[4, 0]], [[4, 0]], [[-6, 0], [-5, 5]], [[-9, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-10, 5], [5, 7]], [[0, 0]], [[-5, 0], [-10, 5]], [[8, 0], [-3, 2], [3, 3], [-3, 7]], [[-4, 0]], [[-4, 0]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[6, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [5, 5], [-4, 7]], [[1, 0]], [[11, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [10, 5], [-5, 7]], [[-7, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [-5, 5], [4, 7]], [[-1, 0], [-5, 5]], [[1, 0]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-4, 0]], [[6, 0], [10, 5]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[-3, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [4, 7]], [[1, 0]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[-5, 0], [3, 2], [-3, 3], [3, 7]], [[-4, 0], [-10, 5]], [[1, 0]], [[6, 0]], [[-4, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [5, 7]], [[1, 0]], [[-4, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [-5, 5], [1, 7]], [[-2, 0], [-3, 2], [3, 3], [-3, 7]], [[2, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [-4, 7]], [[3, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [5, 5], [-1, 7]], [[-8, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [-10, 5], [1, 7]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[2, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [-1, 7]], [[-2, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [-5, 5], [-1, 7]], [[1, 0], [5, 5]], [[6, 0]], [[-5, 0]], [[-5, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[5, 0], [10, 5]], [[-3, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [1, 7]], [[-5, 0]], [[-4, 0]], [[-2, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [5, 5], [4, 7]], [[0, 0]], [[0, 0]], [[10, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[-4, 0], [-5, 5]], [[-5, 5]], [[4, 0], [5, 5]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[5, 0], [3, 2], [-3, 3], [3, 7]], [[-1, 0], [5, 5]], [[1, 0]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[7, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [10, 5], [-4, 7]], [[6, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [-5, 7]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[-5, -5]], [[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]]]}
-
id: 5852830
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 112, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48v1', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0], [-36, 5]], [[12, 0], [36, 5]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0], [20, 2], [-20, 3], [20, 7]], [[8, 0]], [[8, 0], [-20, 2], [20, 3], [-20, 7]], [[-12, 0]], [[-12, 0]], [[8, 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]], [[6, 0], [9, 5]], [[-3, 0], [-9, 5]], [[-4, 0]], [[6, 0], [-10, 2], [10, 3], [-10, 7]], [[-4, 0]], [[-4, 0], [10, 2], [-10, 3], [10, 7]], [[-4, 0]], [[6, 0]], [[6, 0]], [[-4, 0]], [[2, 0], [6, 5]], [[2, 0]], [[-3, 0]], [[-4, 0], [10, 2], [-10, 3], [10, 7]], [[11, 0], [-15, 1], [-5, 2], [5, 3], [-15, 4], [9, 5], [-5, 7]], [[12, 0], [-15, 1], [-10, 2], [10, 3], [-15, 4], [6, 5], [-10, 7]], [[2, 0]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[-4, 0]], [[6, 0], [9, 5]], [[-4, 0], [-6, 5]], [[2, 0]], [[6, 0]], [[-3, 0], [-9, 5]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[-9, 0], [15, 1], [5, 2], [-5, 3], [15, 4], [-6, 5], [5, 7]], [[2, 0], [6, 5]], [[-3, 0]], [[-3, 0]], [[-4, 0]], [[6, 0], [9, 5]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[-3, 0]], [[6, 0]], [[-4, 0], [-6, 5]], [[2, 0], [6, 5]], [[-4, 0], [-6, 5]], [[-4, 0], [-6, 5]], [[-3, 0], [-9, 5]], [[-4, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-3, 0], [-9, 5]], [[2, 0], [6, 5]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-13, 0], [15, 1], [10, 2], [-10, 3], [15, 4], [-9, 5], [10, 7]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[6, 0], [9, 5]], [[2, 0]], [[6, 0]], [[-3, 0]], [[6, 0], [-10, 2], [10, 3], [-10, 7]], [[-4, 0]], [[-4, 0], [-6, 5]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[2, 0]], [[2, 0], [6, 5]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[2, 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]]]}
-
id: 5852831
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 113, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48v2', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0], [36, 5]], [[-24, 0], [-36, 5]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0], [20, 2], [-20, 3], [20, 7]], [[8, 0]], [[8, 0], [-20, 2], [20, 3], [-20, 7]], [[-12, 0]], [[-12, 0]], [[8, 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]], [[-3, 0], [-9, 5]], [[6, 0], [9, 5]], [[-4, 0]], [[6, 0], [-10, 2], [10, 3], [-10, 7]], [[-4, 0]], [[-4, 0], [10, 2], [-10, 3], [10, 7]], [[-4, 0]], [[6, 0]], [[6, 0]], [[-4, 0]], [[-4, 0], [-6, 5]], [[2, 0]], [[-3, 0]], [[-4, 0], [10, 2], [-10, 3], [10, 7]], [[-13, 0], [15, 1], [10, 2], [-10, 3], [15, 4], [-9, 5], [10, 7]], [[-9, 0], [15, 1], [5, 2], [-5, 3], [15, 4], [-6, 5], [5, 7]], [[2, 0]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[-4, 0]], [[-3, 0], [-9, 5]], [[2, 0], [6, 5]], [[2, 0]], [[6, 0]], [[6, 0], [9, 5]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[12, 0], [-15, 1], [-10, 2], [10, 3], [-15, 4], [6, 5], [-10, 7]], [[-4, 0], [-6, 5]], [[-3, 0]], [[-3, 0]], [[-4, 0]], [[-3, 0], [-9, 5]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[-3, 0]], [[6, 0]], [[2, 0], [6, 5]], [[-4, 0], [-6, 5]], [[2, 0], [6, 5]], [[2, 0], [6, 5]], [[6, 0], [9, 5]], [[-4, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[6, 0], [9, 5]], [[-4, 0], [-6, 5]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[11, 0], [-15, 1], [-5, 2], [5, 3], [-15, 4], [9, 5], [-5, 7]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0], [-9, 5]], [[2, 0]], [[6, 0]], [[-3, 0]], [[6, 0], [-10, 2], [10, 3], [-10, 7]], [[-4, 0]], [[2, 0], [6, 5]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[2, 0]], [[-4, 0], [-6, 5]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[2, 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]]]}
-
id: 5852832
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 114, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48v3', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0], [-36, 5]], [[12, 0], [36, 5]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0], [-20, 2], [20, 3], [-20, 7]], [[8, 0]], [[-12, 0], [20, 2], [-20, 3], [20, 7]], [[-12, 0]], [[-12, 0]], [[8, 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]], [[6, 0], [9, 5]], [[-3, 0], [-9, 5]], [[-4, 0]], [[-4, 0], [10, 2], [-10, 3], [10, 7]], [[-4, 0]], [[6, 0], [-10, 2], [10, 3], [-10, 7]], [[-4, 0]], [[6, 0]], [[6, 0]], [[-4, 0]], [[2, 0], [6, 5]], [[2, 0]], [[-3, 0]], [[6, 0], [-10, 2], [10, 3], [-10, 7]], [[-9, 0], [15, 1], [5, 2], [-5, 3], [15, 4], [-6, 5], [5, 7]], [[-13, 0], [15, 1], [10, 2], [-10, 3], [15, 4], [-9, 5], [10, 7]], [[2, 0]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[-4, 0]], [[6, 0], [9, 5]], [[-4, 0], [-6, 5]], [[2, 0]], [[6, 0]], [[-3, 0], [-9, 5]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[11, 0], [-15, 1], [-5, 2], [5, 3], [-15, 4], [9, 5], [-5, 7]], [[2, 0], [6, 5]], [[-3, 0]], [[-3, 0]], [[-4, 0]], [[6, 0], [9, 5]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[-3, 0]], [[6, 0]], [[-4, 0], [-6, 5]], [[2, 0], [6, 5]], [[-4, 0], [-6, 5]], [[-4, 0], [-6, 5]], [[-3, 0], [-9, 5]], [[-4, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-3, 0], [-9, 5]], [[2, 0], [6, 5]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[12, 0], [-15, 1], [-10, 2], [10, 3], [-15, 4], [6, 5], [-10, 7]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[6, 0], [9, 5]], [[2, 0]], [[6, 0]], [[-3, 0]], [[-4, 0], [10, 2], [-10, 3], [10, 7]], [[-4, 0]], [[-4, 0], [-6, 5]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[2, 0]], [[2, 0], [6, 5]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[2, 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]]]}
-
id: 5852833
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 115, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48v4', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0], [36, 5]], [[-24, 0], [-36, 5]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0], [-20, 2], [20, 3], [-20, 7]], [[8, 0]], [[-12, 0], [20, 2], [-20, 3], [20, 7]], [[-12, 0]], [[-12, 0]], [[8, 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]], [[-3, 0], [-9, 5]], [[6, 0], [9, 5]], [[-4, 0]], [[-4, 0], [10, 2], [-10, 3], [10, 7]], [[-4, 0]], [[6, 0], [-10, 2], [10, 3], [-10, 7]], [[-4, 0]], [[6, 0]], [[6, 0]], [[-4, 0]], [[-4, 0], [-6, 5]], [[2, 0]], [[-3, 0]], [[6, 0], [-10, 2], [10, 3], [-10, 7]], [[12, 0], [-15, 1], [-10, 2], [10, 3], [-15, 4], [6, 5], [-10, 7]], [[11, 0], [-15, 1], [-5, 2], [5, 3], [-15, 4], [9, 5], [-5, 7]], [[2, 0]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[-4, 0]], [[-3, 0], [-9, 5]], [[2, 0], [6, 5]], [[2, 0]], [[6, 0]], [[6, 0], [9, 5]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[-13, 0], [15, 1], [10, 2], [-10, 3], [15, 4], [-9, 5], [10, 7]], [[-4, 0], [-6, 5]], [[-3, 0]], [[-3, 0]], [[-4, 0]], [[-3, 0], [-9, 5]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[-3, 0]], [[6, 0]], [[2, 0], [6, 5]], [[-4, 0], [-6, 5]], [[2, 0], [6, 5]], [[2, 0], [6, 5]], [[6, 0], [9, 5]], [[-4, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[6, 0], [9, 5]], [[-4, 0], [-6, 5]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-9, 0], [15, 1], [5, 2], [-5, 3], [15, 4], [-6, 5], [5, 7]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0], [-9, 5]], [[2, 0]], [[6, 0]], [[-3, 0]], [[-4, 0], [10, 2], [-10, 3], [10, 7]], [[-4, 0]], [[2, 0], [6, 5]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[2, 0]], [[-4, 0], [-6, 5]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[2, 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]]]}
-
id: 5852834
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 116, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48w1', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0], [-36, 5]], [[12, 0], [36, 5]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-9, 0], [-6, 5]], [[-3, 0], [6, 5]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0], [-10, 5]], [[6, 0], [10, 5]], [[1, 0]], [[-8, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [-4, 5], [10, 7]], [[-3, 0]], [[2, 0], [-5, 5]], [[-4, 0]], [[-4, 0], [-6, 5]], [[2, 0], [6, 5]], [[-3, 0]], [[2, 0]], [[11, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [10, 5], [-5, 7]], [[6, 0], [4, 5]], [[1, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [4, 5], [5, 7]], [[2, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [-10, 7]], [[1, 0], [5, 5]], [[2, 0], [-4, 5]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 5]], [[-3, 0], [1, 5]], [[2, 0], [5, 5]], [[2, 0], [5, 5]], [[-4, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [5, 7]], [[-4, 0], [-1, 5]], [[2, 0]], [[-3, 0], [-5, 5]], [[1, 0]], [[-4, 0], [-1, 5]], [[2, 0], [-4, 5]], [[6, 0], [9, 5]], [[1, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-1, 5], [-5, 7]], [[-3, 0], [1, 5]], [[-9, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-10, 5], [5, 7]], [[1, 0]], [[-13, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [-5, 5], [10, 7]], [[-3, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 7]], [[12, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [5, 5], [-10, 7]], [[-3, 0]], [[6, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [-5, 7]], [[-3, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [10, 7]], [[2, 0], [1, 5]], [[-3, 0], [-9, 5]], [[7, 0]], [[7, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[7, 0], [5, 5]], [[-3, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 5], [5, 7]], [[-8, 0]], [[2, 0], [6, 5]], [[2, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 7]], [[-3, 0]], [[-3, 0]], [[-8, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[1, 0], [-1, 5]], [[2, 0], [5, 5]], [[-4, 0], [-5, 5]], [[-3, 0], [-5, 5]], [[-4, 0]], [[1, 0]], [[6, 0], [4, 5]], [[2, 0]], [[2, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 5], [-5, 7]], [[7, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [1, 5], [-10, 7]], [[2, 0]], [[-3, 0], [-5, 5]], [[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]]]}
-
id: 5852835
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 117, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48w2', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0], [36, 5]], [[-24, 0], [-36, 5]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-3, 0], [6, 5]], [[-9, 0], [-6, 5]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[6, 0], [10, 5]], [[-4, 0], [-10, 5]], [[1, 0]], [[1, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [4, 5], [5, 7]], [[-3, 0]], [[7, 0], [5, 5]], [[-4, 0]], [[2, 0], [6, 5]], [[-4, 0], [-6, 5]], [[-3, 0]], [[2, 0]], [[-9, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-10, 5], [5, 7]], [[2, 0], [-4, 5]], [[-8, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [-4, 5], [10, 7]], [[-3, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 7]], [[-4, 0], [-5, 5]], [[6, 0], [4, 5]], [[2, 0]], [[2, 0]], [[2, 0], [6, 5]], [[-4, 0], [-1, 5]], [[-3, 0], [-5, 5]], [[-3, 0], [-5, 5]], [[6, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [-5, 7]], [[-3, 0], [1, 5]], [[2, 0]], [[2, 0], [5, 5]], [[1, 0]], [[-3, 0], [1, 5]], [[6, 0], [4, 5]], [[-3, 0], [-9, 5]], [[7, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [1, 5], [-10, 7]], [[-4, 0], [-1, 5]], [[11, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [10, 5], [-5, 7]], [[1, 0]], [[-3, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 5], [5, 7]], [[2, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [-10, 7]], [[2, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 5], [-5, 7]], [[-3, 0]], [[-4, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [5, 7]], [[2, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 7]], [[1, 0], [-1, 5]], [[6, 0], [9, 5]], [[7, 0]], [[-8, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[2, 0], [-5, 5]], [[-13, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [-5, 5], [10, 7]], [[-8, 0]], [[-4, 0], [-6, 5]], [[-3, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [10, 7]], [[-3, 0]], [[-3, 0]], [[7, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[2, 0], [1, 5]], [[-3, 0], [-5, 5]], [[1, 0], [5, 5]], [[2, 0], [5, 5]], [[-4, 0]], [[1, 0]], [[2, 0], [-4, 5]], [[2, 0]], [[12, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [5, 5], [-10, 7]], [[1, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-1, 5], [-5, 7]], [[2, 0]], [[2, 0], [5, 5]], [[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]]]}
-
id: 5852836
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 118, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48w3', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0], [-36, 5]], [[12, 0], [36, 5]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-9, 0], [-6, 5]], [[-3, 0], [6, 5]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0], [-10, 5]], [[6, 0], [10, 5]], [[1, 0]], [[7, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [1, 5], [-10, 7]], [[-3, 0]], [[2, 0], [-5, 5]], [[-4, 0]], [[-4, 0], [-6, 5]], [[2, 0], [6, 5]], [[-3, 0]], [[2, 0]], [[-4, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [5, 7]], [[6, 0], [4, 5]], [[1, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-1, 5], [-5, 7]], [[-13, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [-5, 5], [10, 7]], [[1, 0], [5, 5]], [[2, 0], [-4, 5]], [[2, 0]], [[2, 0]], [[-4, 0], [-6, 5]], [[-3, 0], [1, 5]], [[2, 0], [5, 5]], [[2, 0], [5, 5]], [[11, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [10, 5], [-5, 7]], [[-4, 0], [-1, 5]], [[2, 0]], [[-3, 0], [-5, 5]], [[1, 0]], [[-4, 0], [-1, 5]], [[2, 0], [-4, 5]], [[6, 0], [9, 5]], [[1, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [4, 5], [5, 7]], [[-3, 0], [1, 5]], [[6, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [-5, 7]], [[1, 0]], [[2, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [-10, 7]], [[-3, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 5], [5, 7]], [[-3, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [10, 7]], [[-3, 0]], [[-9, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-10, 5], [5, 7]], [[12, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [5, 5], [-10, 7]], [[2, 0], [1, 5]], [[-3, 0], [-9, 5]], [[7, 0]], [[-8, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[7, 0], [5, 5]], [[-3, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 7]], [[-8, 0]], [[2, 0], [6, 5]], [[2, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 5], [-5, 7]], [[-3, 0]], [[-3, 0]], [[7, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[1, 0], [-1, 5]], [[2, 0], [5, 5]], [[-4, 0], [-5, 5]], [[-3, 0], [-5, 5]], [[-4, 0]], [[1, 0]], [[6, 0], [4, 5]], [[2, 0]], [[2, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 7]], [[-8, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [-4, 5], [10, 7]], [[2, 0]], [[-3, 0], [-5, 5]], [[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]]]}
-
id: 5852837
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 119, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48w4', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0], [36, 5]], [[-24, 0], [-36, 5]], [[-24, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-3, 0], [6, 5]], [[-9, 0], [-6, 5]], [[6, 0]], [[-4, 0]], [[6, 0]], [[-4, 0]], [[6, 0]], [[6, 0], [10, 5]], [[-4, 0], [-10, 5]], [[1, 0]], [[1, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-1, 5], [-5, 7]], [[-3, 0]], [[7, 0], [5, 5]], [[-4, 0]], [[2, 0], [6, 5]], [[-4, 0], [-6, 5]], [[-3, 0]], [[2, 0]], [[6, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [-5, 7]], [[2, 0], [-4, 5]], [[7, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [1, 5], [-10, 7]], [[-3, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 5], [5, 7]], [[-4, 0], [-5, 5]], [[6, 0], [4, 5]], [[2, 0]], [[2, 0]], [[2, 0], [6, 5]], [[-4, 0], [-1, 5]], [[-3, 0], [-5, 5]], [[-3, 0], [-5, 5]], [[-9, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-10, 5], [5, 7]], [[-3, 0], [1, 5]], [[2, 0]], [[2, 0], [5, 5]], [[1, 0]], [[-3, 0], [1, 5]], [[6, 0], [4, 5]], [[-3, 0], [-9, 5]], [[-8, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [-4, 5], [10, 7]], [[-4, 0], [-1, 5]], [[-4, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [5, 7]], [[1, 0]], [[-3, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 7]], [[-13, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [-5, 5], [10, 7]], [[2, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 7]], [[-3, 0]], [[11, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [10, 5], [-5, 7]], [[2, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 5], [-5, 7]], [[1, 0], [-1, 5]], [[6, 0], [9, 5]], [[7, 0]], [[7, 0], [-10, 1], [-5, 2], [5, 3], [-10, 4], [5, 5], [-5, 7]], [[2, 0], [-5, 5]], [[2, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [-10, 7]], [[-8, 0]], [[-4, 0], [-6, 5]], [[12, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [5, 5], [-10, 7]], [[-3, 0]], [[-3, 0]], [[-8, 0], [10, 1], [5, 2], [-5, 3], [10, 4], [-5, 5], [5, 7]], [[2, 0], [1, 5]], [[-3, 0], [-5, 5]], [[1, 0], [5, 5]], [[2, 0], [5, 5]], [[-4, 0]], [[1, 0]], [[2, 0], [-4, 5]], [[2, 0]], [[-3, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [10, 7]], [[1, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [4, 5], [5, 7]], [[2, 0]], [[2, 0], [5, 5]], [[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]]]}
-
id: 5852839
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 120, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48x1', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[18, 0]], [[-2, 0]], [[-2, 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]], [[-3, 0], [-15, 5]], [[12, 0], [15, 5]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[-10, 0]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[10, -5]], [[10, 5]], [[10, 5]], [[-3, 0], [-5, 5]], [[-7, 0]], [[-7, 0], [-5, 5]], [[3, 0], [-6, 2], [6, 3], [-6, 7]], [[-3, 0]], [[-3, 0]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[6, 1], [6, 4], [-3, 5]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[-3, 0], [-5, 5]], [[2, 0], [5, 5]], [[-3, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-2, 5], [3, 7]], [[-5, 0], [-10, 5]], [[2, 0], [5, 5]], [[-6, 6], [-6, -6]], [[9, 0], [-6, 1], [-6, 2], [6, 3], [-6, 4], [3, 5], [-6, 7]], [[-3, 0]], [[2, 0], [5, 5]], [[5, 0], [-3, 1], [-6, 2], [6, 3], [-3, 4], [-1, 5], [-6, 7]], [[-4, 0], [3, 1], [6, 2], [-6, 3], [3, 4], [-4, 5], [6, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[2, 0], [5, 5]], [[-3, 0], [6, 1], [6, 2], [-6, 3], [6, 4], [-3, 5], [6, 7]], [[3, 0], [-3, 1], [3, 2], [-3, 3], [-3, 4], [4, 5], [3, 7]], [[7, 0], [-9, 2], [9, 3], [-9, 7]], [[-3, 0], [-5, 5]], [[2, 0], [5, 5]], [[2, 0]], [[2, 0], [5, 5]], [[-3, 0], [-5, 5]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[-2, 0], [9, 2], [-9, 3], [9, 7]], [[9, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [7, 5], [-3, 7]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [2, 5], [-6, 7]], [[3, 1], [3, 2], [-3, 3], [3, 4], [1, 5], [3, 7]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[6, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [4, 5], [-3, 7]], [[2, 0], [-5, 5]], [[2, 0]], [[-2, 0]], [[7, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-2, 0], [5, 5]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [-7, 5], [6, 7]], [[-2, 0]], [[-3, 0]], [[-1, 0], [3, 1], [3, 4], [-4, 5]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-11, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[7, 0], [5, 5]], [[-2, 0]], [[5, 0], [10, 5]], [[3, 0], [3, 1], [-3, 2], [3, 3], [3, 4], [1, 5], [-3, 7]], [[-3, 0], [6, 2], [-6, 3], [6, 7]], [[10, -5]], [[-3, 0], [-5, 5]], [[6, 0], [-6, 1], [-6, 4], [3, 5]], [[2, 0], [-3, 1], [-3, 4], [-1, 5]], [[-3, 0], [-5, 5]], [[-6, 3], [-6, -3]], [[-2, 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]]]}
-
id: 5852840
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 121, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48x2', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[18, 0]], [[-2, 0]], [[-2, 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]], [[12, 0], [15, 5]], [[-3, 0], [-15, 5]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[-10, 0]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[10, 5]], [[10, -5]], [[10, -5]], [[2, 0], [5, 5]], [[-7, 0]], [[-2, 0], [5, 5]], [[3, 0], [-6, 2], [6, 3], [-6, 7]], [[-3, 0]], [[-3, 0]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[9, 0], [-6, 1], [-6, 2], [6, 3], [-6, 4], [3, 5], [-6, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[2, 0], [5, 5]], [[-3, 0], [-5, 5]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [2, 5], [-6, 7]], [[5, 0], [10, 5]], [[-3, 0], [-5, 5]], [[-6, 6], [-6, -6]], [[6, 1], [6, 4], [-3, 5]], [[-3, 0]], [[-3, 0], [-5, 5]], [[3, 0], [3, 1], [-3, 2], [3, 3], [3, 4], [1, 5], [-3, 7]], [[3, 0], [-3, 1], [3, 2], [-3, 3], [-3, 4], [4, 5], [3, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[-3, 0], [-5, 5]], [[6, 0], [-6, 1], [-6, 4], [3, 5]], [[-4, 0], [3, 1], [6, 2], [-6, 3], [3, 4], [-4, 5], [6, 7]], [[7, 0], [-9, 2], [9, 3], [-9, 7]], [[2, 0], [5, 5]], [[-3, 0], [-5, 5]], [[2, 0]], [[-3, 0], [-5, 5]], [[2, 0], [5, 5]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[-2, 0], [9, 2], [-9, 3], [9, 7]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [-7, 5], [6, 7]], [[-3, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-2, 5], [3, 7]], [[2, 0], [-3, 1], [-3, 4], [-1, 5]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[-1, 0], [3, 1], [3, 4], [-4, 5]], [[7, 0], [5, 5]], [[2, 0]], [[-2, 0]], [[-11, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[-7, 0], [-5, 5]], [[9, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [7, 5], [-3, 7]], [[-2, 0]], [[-3, 0]], [[6, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [4, 5], [-3, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[7, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[2, 0], [-5, 5]], [[-2, 0]], [[-5, 0], [-10, 5]], [[5, 0], [-3, 1], [-6, 2], [6, 3], [-3, 4], [-1, 5], [-6, 7]], [[-3, 0], [6, 2], [-6, 3], [6, 7]], [[10, 5]], [[2, 0], [5, 5]], [[-3, 0], [6, 1], [6, 2], [-6, 3], [6, 4], [-3, 5], [6, 7]], [[3, 1], [3, 2], [-3, 3], [3, 4], [1, 5], [3, 7]], [[2, 0], [5, 5]], [[-6, 3], [-6, -3]], [[-2, 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]]]}
-
id: 5852841
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 122, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48x3', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[18, 0]], [[-2, 0]], [[-2, 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]], [[-3, 0], [-15, 5]], [[12, 0], [15, 5]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[-10, 0]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[10, -5]], [[10, 5]], [[10, 5]], [[-3, 0], [-5, 5]], [[-7, 0]], [[-7, 0], [-5, 5]], [[-3, 0], [6, 2], [-6, 3], [6, 7]], [[-3, 0]], [[-3, 0]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[6, 0], [-6, 1], [-6, 4], [3, 5]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[-3, 0], [-5, 5]], [[2, 0], [5, 5]], [[9, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [7, 5], [-3, 7]], [[-5, 0], [-10, 5]], [[2, 0], [5, 5]], [[-6, 3], [-6, -3]], [[-3, 0], [6, 1], [6, 2], [-6, 3], [6, 4], [-3, 5], [6, 7]], [[-3, 0]], [[2, 0], [5, 5]], [[-4, 0], [3, 1], [6, 2], [-6, 3], [3, 4], [-4, 5], [6, 7]], [[5, 0], [-3, 1], [-6, 2], [6, 3], [-3, 4], [-1, 5], [-6, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[2, 0], [5, 5]], [[9, 0], [-6, 1], [-6, 2], [6, 3], [-6, 4], [3, 5], [-6, 7]], [[3, 0], [3, 1], [-3, 2], [3, 3], [3, 4], [1, 5], [-3, 7]], [[-2, 0], [9, 2], [-9, 3], [9, 7]], [[-3, 0], [-5, 5]], [[2, 0], [5, 5]], [[2, 0]], [[2, 0], [5, 5]], [[-3, 0], [-5, 5]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[7, 0], [-9, 2], [9, 3], [-9, 7]], [[-3, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-2, 5], [3, 7]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [-7, 5], [6, 7]], [[6, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [4, 5], [-3, 7]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[3, 1], [3, 2], [-3, 3], [3, 4], [1, 5], [3, 7]], [[2, 0], [-5, 5]], [[2, 0]], [[-2, 0]], [[-11, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[-2, 0], [5, 5]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [2, 5], [-6, 7]], [[-2, 0]], [[-3, 0]], [[2, 0], [-3, 1], [-3, 4], [-1, 5]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[7, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[7, 0], [5, 5]], [[-2, 0]], [[5, 0], [10, 5]], [[3, 0], [-3, 1], [3, 2], [-3, 3], [-3, 4], [4, 5], [3, 7]], [[3, 0], [-6, 2], [6, 3], [-6, 7]], [[10, -5]], [[-3, 0], [-5, 5]], [[6, 1], [6, 4], [-3, 5]], [[-1, 0], [3, 1], [3, 4], [-4, 5]], [[-3, 0], [-5, 5]], [[-6, 6], [-6, -6]], [[-2, 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]]]}
-
id: 5852842
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 123, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48x4', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[8, 0]], [[-12, 0]], [[18, 0]], [[-2, 0]], [[-2, 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]], [[12, 0], [15, 5]], [[-3, 0], [-15, 5]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[-10, 0]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[10, 5]], [[10, -5]], [[10, -5]], [[2, 0], [5, 5]], [[-7, 0]], [[-2, 0], [5, 5]], [[-3, 0], [6, 2], [-6, 3], [6, 7]], [[-3, 0]], [[-3, 0]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[-3, 0], [6, 1], [6, 2], [-6, 3], [6, 4], [-3, 5], [6, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[2, 0], [5, 5]], [[-3, 0], [-5, 5]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [-7, 5], [6, 7]], [[5, 0], [10, 5]], [[-3, 0], [-5, 5]], [[-6, 3], [-6, -3]], [[6, 0], [-6, 1], [-6, 4], [3, 5]], [[-3, 0]], [[-3, 0], [-5, 5]], [[3, 0], [-3, 1], [3, 2], [-3, 3], [-3, 4], [4, 5], [3, 7]], [[3, 0], [3, 1], [-3, 2], [3, 3], [3, 4], [1, 5], [-3, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[-3, 0], [-5, 5]], [[6, 1], [6, 4], [-3, 5]], [[5, 0], [-3, 1], [-6, 2], [6, 3], [-3, 4], [-1, 5], [-6, 7]], [[-2, 0], [9, 2], [-9, 3], [9, 7]], [[2, 0], [5, 5]], [[-3, 0], [-5, 5]], [[2, 0]], [[-3, 0], [-5, 5]], [[2, 0], [5, 5]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[7, 0], [-9, 2], [9, 3], [-9, 7]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [2, 5], [-6, 7]], [[9, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [7, 5], [-3, 7]], [[-1, 0], [3, 1], [3, 4], [-4, 5]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[2, 0], [-3, 1], [-3, 4], [-1, 5]], [[7, 0], [5, 5]], [[2, 0]], [[-2, 0]], [[7, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-7, 0], [-5, 5]], [[-3, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-2, 5], [3, 7]], [[-2, 0]], [[-3, 0]], [[3, 1], [3, 2], [-3, 3], [3, 4], [1, 5], [3, 7]], [[-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-9, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-11, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[2, 0], [-5, 5]], [[-2, 0]], [[-5, 0], [-10, 5]], [[-4, 0], [3, 1], [6, 2], [-6, 3], [3, 4], [-4, 5], [6, 7]], [[3, 0], [-6, 2], [6, 3], [-6, 7]], [[10, 5]], [[2, 0], [5, 5]], [[9, 0], [-6, 1], [-6, 2], [6, 3], [-6, 4], [3, 5], [-6, 7]], [[6, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [4, 5], [-3, 7]], [[2, 0], [5, 5]], [[-6, 6], [-6, -6]], [[-2, 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]]]}
-
id: 5852843
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 124, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48y1', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0], [20, 2], [-20, 3], [20, 7]], [[8, 0]], [[8, 0], [-20, 2], [20, 3], [-20, 7]], [[-12, 0]], [[-12, 0]], [[8, 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]], [[-3, 0]], [[-3, 0]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[-6, 0], [2, 2], [-2, 3], [2, 7]], [[-10, 0]], [[-4, 0], [-2, 2], [2, 3], [-2, 7]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[0, 0]], [[0, 0]], [[5, 0]], [[2, 0]], [[-7, 0]], [[3, 0]], [[2, 0], [1, 2], [-1, 3], [1, 7]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[-7, 0], [3, 1], [7, 2], [-7, 3], [3, 4], [-9, 5], [7, 7]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-3, 0]], [[2, 0]], [[2, 0], [-3, 1], [-3, 4], [9, 5]], [[0, 0]], [[-3, 0]], [[4, 3], [4, -3]], [[5, 0], [-3, 1], [4, 2], [-4, 3], [-3, 4], [9, 5], [4, 7]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[2, 0]], [[6, 1], [6, 4], [-3, 5]], [[6, 0], [-6, 1], [-6, 4], [3, 5]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-3, 0]], [[6, 0], [3, 1], [-4, 2], [4, 3], [3, 4], [6, 5], [-4, 7]], [[-3, 0], [6, 1], [6, 2], [-6, 3], [6, 4], [-3, 5], [6, 7]], [[3, 0], [-6, 2], [6, 3], [-6, 7]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-3, 0], [6, 2], [-6, 3], [6, 7]], [[-1, 0], [3, 1], [3, 4], [6, 5]], [[-10, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-9, 5], [3, 7]], [[-13, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-12, 5], [3, 7]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-1, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [-3, 5], [-3, 7]], [[-3, 0]], [[2, 0]], [[3, 0]], [[5, 0], [-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[3, 0]], [[-4, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-6, 5], [-3, 7]], [[3, 0]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [3, 5], [6, 7]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-4, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-3, 0]], [[8, 0], [15, 5]], [[0, 0]], [[9, 0], [-6, 1], [-6, 2], [6, 3], [-6, 4], [3, 5], [-6, 7]], [[3, 0], [-1, 2], [1, 3], [-1, 7]], [[5, 0]], [[2, 0]], [[3, 0], [-3, 1], [-7, 2], [7, 3], [-3, 4], [-6, 5], [-7, 7]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [12, 5], [-6, 7]], [[2, 0]], [[4, 6], [4, -6]], [[-7, 0], [-15, 5]], [[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]]]}
-
id: 5852844
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 125, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48y2', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0], [20, 2], [-20, 3], [20, 7]], [[8, 0]], [[8, 0], [-20, 2], [20, 3], [-20, 7]], [[-12, 0]], [[-12, 0]], [[8, 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]], [[-3, 0]], [[-3, 0]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[-6, 0], [2, 2], [-2, 3], [2, 7]], [[-10, 0]], [[-4, 0], [-2, 2], [2, 3], [-2, 7]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[0, 0]], [[0, 0]], [[5, 0]], [[2, 0]], [[-7, 0]], [[3, 0]], [[2, 0], [1, 2], [-1, 3], [1, 7]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[5, 0], [-3, 1], [4, 2], [-4, 3], [-3, 4], [9, 5], [4, 7]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-3, 0]], [[2, 0]], [[-10, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-9, 5], [3, 7]], [[0, 0]], [[-3, 0]], [[4, 3], [4, -3]], [[-7, 0], [3, 1], [7, 2], [-7, 3], [3, 4], [-9, 5], [7, 7]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[2, 0]], [[9, 0], [-6, 1], [-6, 2], [6, 3], [-6, 4], [3, 5], [-6, 7]], [[-3, 0], [6, 1], [6, 2], [-6, 3], [6, 4], [-3, 5], [6, 7]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-3, 0]], [[3, 0], [-3, 1], [-7, 2], [7, 3], [-3, 4], [-6, 5], [-7, 7]], [[6, 0], [-6, 1], [-6, 4], [3, 5]], [[3, 0], [-6, 2], [6, 3], [-6, 7]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-3, 0], [6, 2], [-6, 3], [6, 7]], [[-4, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-6, 5], [-3, 7]], [[2, 0], [-3, 1], [-3, 4], [9, 5]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [12, 5], [-6, 7]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [3, 5], [6, 7]], [[-3, 0]], [[2, 0]], [[3, 0]], [[-4, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[3, 0]], [[-1, 0], [3, 1], [3, 4], [6, 5]], [[3, 0]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[-1, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [-3, 5], [-3, 7]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[5, 0], [-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-3, 0]], [[-7, 0], [-15, 5]], [[0, 0]], [[6, 1], [6, 4], [-3, 5]], [[3, 0], [-1, 2], [1, 3], [-1, 7]], [[5, 0]], [[2, 0]], [[6, 0], [3, 1], [-4, 2], [4, 3], [3, 4], [6, 5], [-4, 7]], [[-13, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-12, 5], [3, 7]], [[2, 0]], [[4, 6], [4, -6]], [[8, 0], [15, 5]], [[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]]]}
-
id: 5852845
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 126, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48y3', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0], [-20, 2], [20, 3], [-20, 7]], [[8, 0]], [[-12, 0], [20, 2], [-20, 3], [20, 7]], [[-12, 0]], [[-12, 0]], [[8, 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]], [[-3, 0]], [[-3, 0]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[-4, 0], [-2, 2], [2, 3], [-2, 7]], [[-10, 0]], [[-6, 0], [2, 2], [-2, 3], [2, 7]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[0, 0]], [[0, 0]], [[5, 0]], [[2, 0]], [[-7, 0]], [[3, 0]], [[3, 0], [-1, 2], [1, 3], [-1, 7]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[3, 0], [-3, 1], [-7, 2], [7, 3], [-3, 4], [-6, 5], [-7, 7]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-3, 0]], [[2, 0]], [[-1, 0], [3, 1], [3, 4], [6, 5]], [[0, 0]], [[-3, 0]], [[4, 6], [4, -6]], [[6, 0], [3, 1], [-4, 2], [4, 3], [3, 4], [6, 5], [-4, 7]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[2, 0]], [[6, 0], [-6, 1], [-6, 4], [3, 5]], [[6, 1], [6, 4], [-3, 5]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-3, 0]], [[5, 0], [-3, 1], [4, 2], [-4, 3], [-3, 4], [9, 5], [4, 7]], [[9, 0], [-6, 1], [-6, 2], [6, 3], [-6, 4], [3, 5], [-6, 7]], [[-3, 0], [6, 2], [-6, 3], [6, 7]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[3, 0], [-6, 2], [6, 3], [-6, 7]], [[2, 0], [-3, 1], [-3, 4], [9, 5]], [[-4, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-6, 5], [-3, 7]], [[-1, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [-3, 5], [-3, 7]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-13, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-12, 5], [3, 7]], [[-3, 0]], [[2, 0]], [[3, 0]], [[-4, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[3, 0]], [[-10, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-9, 5], [3, 7]], [[3, 0]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [12, 5], [-6, 7]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[5, 0], [-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[-3, 0]], [[8, 0], [15, 5]], [[0, 0]], [[-3, 0], [6, 1], [6, 2], [-6, 3], [6, 4], [-3, 5], [6, 7]], [[2, 0], [1, 2], [-1, 3], [1, 7]], [[5, 0]], [[2, 0]], [[-7, 0], [3, 1], [7, 2], [-7, 3], [3, 4], [-9, 5], [7, 7]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [3, 5], [6, 7]], [[2, 0]], [[4, 3], [4, -3]], [[-7, 0], [-15, 5]], [[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]]]}
-
id: 5852846
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 127, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48y4', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0], [-20, 2], [20, 3], [-20, 7]], [[8, 0]], [[-12, 0], [20, 2], [-20, 3], [20, 7]], [[-12, 0]], [[-12, 0]], [[8, 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]], [[-3, 0]], [[-3, 0]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[-4, 0], [-2, 2], [2, 3], [-2, 7]], [[-10, 0]], [[-6, 0], [2, 2], [-2, 3], [2, 7]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[0, 0]], [[0, 0]], [[5, 0]], [[2, 0]], [[-7, 0]], [[3, 0]], [[3, 0], [-1, 2], [1, 3], [-1, 7]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[6, 0], [3, 1], [-4, 2], [4, 3], [3, 4], [6, 5], [-4, 7]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-3, 0]], [[2, 0]], [[-4, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-6, 5], [-3, 7]], [[0, 0]], [[-3, 0]], [[4, 6], [4, -6]], [[3, 0], [-3, 1], [-7, 2], [7, 3], [-3, 4], [-6, 5], [-7, 7]], [[2, 0], [-5, 2], [5, 3], [-5, 7]], [[2, 0]], [[-3, 0], [6, 1], [6, 2], [-6, 3], [6, 4], [-3, 5], [6, 7]], [[9, 0], [-6, 1], [-6, 2], [6, 3], [-6, 4], [3, 5], [-6, 7]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-3, 0]], [[-7, 0], [3, 1], [7, 2], [-7, 3], [3, 4], [-9, 5], [7, 7]], [[6, 1], [6, 4], [-3, 5]], [[-3, 0], [6, 2], [-6, 3], [6, 7]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[3, 0], [-6, 2], [6, 3], [-6, 7]], [[-10, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-9, 5], [3, 7]], [[-1, 0], [3, 1], [3, 4], [6, 5]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [3, 5], [6, 7]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [12, 5], [-6, 7]], [[-3, 0]], [[2, 0]], [[3, 0]], [[5, 0], [-6, 1], [-3, 2], [3, 3], [-6, 4], [3, 5], [-3, 7]], [[3, 0]], [[2, 0], [-3, 1], [-3, 4], [9, 5]], [[3, 0]], [[-3, 0], [5, 2], [-5, 3], [5, 7]], [[-13, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-12, 5], [3, 7]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-4, 0], [6, 1], [3, 2], [-3, 3], [6, 4], [-3, 5], [3, 7]], [[-3, 0]], [[-7, 0], [-15, 5]], [[0, 0]], [[6, 0], [-6, 1], [-6, 4], [3, 5]], [[2, 0], [1, 2], [-1, 3], [1, 7]], [[5, 0]], [[2, 0]], [[5, 0], [-3, 1], [4, 2], [-4, 3], [-3, 4], [9, 5], [4, 7]], [[-1, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [-3, 5], [-3, 7]], [[2, 0]], [[4, 3], [4, -3]], [[8, 0], [15, 5]], [[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]]]}
-
id: 5852847
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 128, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48z1', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-18, 0], [-15, 5]], [[-3, 0], [15, 5]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[0, 0]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[10, 5]], [[10, -5]], [[-5, 5]], [[-3, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 7]], [[3, 0]], [[-7, 0], [-5, 5]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[2, 0]], [[2, 0]], [[-6, 3], [-6, -3]], [[2, 0], [-3, 1], [-3, 4], [9, 5]], [[-7, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [-5, 5], [4, 7]], [[2, 0], [5, 5]], [[2, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [-10, 7]], [[1, 0], [-2, 1], [-4, 2], [4, 3], [-2, 4], [1, 5], [-4, 7]], [[-5, 0], [-10, 5]], [[-3, 0], [-5, 5]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[-10, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-9, 5], [3, 7]], [[2, 0]], [[7, 0]], [[-3, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-2, 5], [3, 7]], [[9, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [7, 5], [-3, 7]], [[2, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [-4, 7]], [[-3, 0], [-5, 5]], [[-4, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-6, 5], [-3, 7]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [-7, 5], [6, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[7, 0]], [[-3, 0], [-5, 5]], [[-3, 0]], [[-13, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [-5, 5], [10, 7]], [[2, 0], [5, 5]], [[3, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [5, 5], [-1, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[-5, 0], [2, 1], [4, 2], [-4, 3], [2, 4], [-1, 5], [4, 7]], [[-2, 0], [2, 1], [-2, 2], [2, 3], [2, 4], [-1, 5], [-2, 7]], [[2, 0], [1, 1], [-4, 2], [4, 3], [1, 4], [-3, 5], [-4, 7]], [[-6, 6], [-6, -6]], [[-3, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [1, 7]], [[-1, 0], [-1, 1], [4, 2], [-4, 3], [-1, 4], [-2, 5], [4, 7]], [[2, 0], [-5, 5]], [[-3, 0]], [[-2, 0]], [[1, 0], [-4, 1], [-2, 2], [2, 3], [-4, 4], [2, 5], [-2, 7]], [[-2, 0], [5, 5]], [[-2, 0], [-2, 1], [2, 2], [-2, 3], [-2, 4], [1, 5], [2, 7]], [[-2, 0]], [[2, 0]], [[1, 1], [5, 2], [-5, 3], [1, 4], [2, 5], [5, 7]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[-5, 0], [4, 1], [2, 2], [-2, 3], [4, 4], [-2, 5], [2, 7]], [[7, 0], [5, 5]], [[8, 0], [5, 5]], [[5, 0], [10, 5]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [2, 5], [-6, 7]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-5, -5]], [[2, 0], [5, 5]], [[-1, 0], [3, 1], [3, 4], [6, 5]], [[6, 0], [-1, 1], [-5, 2], [5, 3], [-1, 4], [3, 5], [-5, 7]], [[-3, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 5], [5, 7]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[3, 0], [-5, 5]], [[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]]]}
-
id: 5852848
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 129, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48z2', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-3, 0], [15, 5]], [[-18, 0], [-15, 5]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[0, 0]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[10, -5]], [[10, 5]], [[-5, -5]], [[2, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [-10, 7]], [[3, 0]], [[-2, 0], [5, 5]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[2, 0]], [[2, 0]], [[-6, 3], [-6, -3]], [[-10, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-9, 5], [3, 7]], [[3, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [5, 5], [-1, 7]], [[-3, 0], [-5, 5]], [[-3, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 7]], [[-2, 0], [2, 1], [-2, 2], [2, 3], [2, 4], [-1, 5], [-2, 7]], [[5, 0], [10, 5]], [[2, 0], [5, 5]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[2, 0], [-3, 1], [-3, 4], [9, 5]], [[2, 0]], [[7, 0]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [2, 5], [-6, 7]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [-7, 5], [6, 7]], [[-3, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [1, 7]], [[2, 0], [5, 5]], [[-1, 0], [3, 1], [3, 4], [6, 5]], [[9, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [7, 5], [-3, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[7, 0]], [[2, 0], [5, 5]], [[-3, 0]], [[-3, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 5], [5, 7]], [[-3, 0], [-5, 5]], [[-7, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [-5, 5], [4, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[-2, 0], [-2, 1], [2, 2], [-2, 3], [-2, 4], [1, 5], [2, 7]], [[1, 0], [-2, 1], [-4, 2], [4, 3], [-2, 4], [1, 5], [-4, 7]], [[6, 0], [-1, 1], [-5, 2], [5, 3], [-1, 4], [3, 5], [-5, 7]], [[-6, 6], [-6, -6]], [[2, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [-4, 7]], [[1, 1], [5, 2], [-5, 3], [1, 4], [2, 5], [5, 7]], [[7, 0], [5, 5]], [[-3, 0]], [[-2, 0]], [[-5, 0], [4, 1], [2, 2], [-2, 3], [4, 4], [-2, 5], [2, 7]], [[-7, 0], [-5, 5]], [[-5, 0], [2, 1], [4, 2], [-4, 3], [2, 4], [-1, 5], [4, 7]], [[-2, 0]], [[2, 0]], [[-1, 0], [-1, 1], [4, 2], [-4, 3], [-1, 4], [-2, 5], [4, 7]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[1, 0], [-4, 1], [-2, 2], [2, 3], [-4, 4], [2, 5], [-2, 7]], [[2, 0], [-5, 5]], [[3, 0], [-5, 5]], [[-5, 0], [-10, 5]], [[-3, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-2, 5], [3, 7]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[-5, 5]], [[-3, 0], [-5, 5]], [[-4, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-6, 5], [-3, 7]], [[2, 0], [1, 1], [-4, 2], [4, 3], [1, 4], [-3, 5], [-4, 7]], [[-13, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [-5, 5], [10, 7]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[8, 0], [5, 5]], [[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]]]}
-
id: 5852850
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 130, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48z3', 'nt': [360, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-18, 0], [-15, 5]], [[-3, 0], [15, 5]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[0, 0]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[10, 5]], [[10, -5]], [[-5, 5]], [[-3, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 5], [5, 7]], [[3, 0]], [[-7, 0], [-5, 5]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[2, 0]], [[2, 0]], [[-6, 6], [-6, -6]], [[-1, 0], [3, 1], [3, 4], [6, 5]], [[2, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [-4, 7]], [[2, 0], [5, 5]], [[-13, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [-5, 5], [10, 7]], [[-5, 0], [2, 1], [4, 2], [-4, 3], [2, 4], [-1, 5], [4, 7]], [[-5, 0], [-10, 5]], [[-3, 0], [-5, 5]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[-4, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-6, 5], [-3, 7]], [[2, 0]], [[7, 0]], [[9, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [7, 5], [-3, 7]], [[-3, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-2, 5], [3, 7]], [[-7, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [-5, 5], [4, 7]], [[-3, 0], [-5, 5]], [[-10, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-9, 5], [3, 7]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [2, 5], [-6, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[7, 0]], [[-3, 0], [-5, 5]], [[-3, 0]], [[2, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [-10, 7]], [[2, 0], [5, 5]], [[-3, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [1, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[1, 0], [-2, 1], [-4, 2], [4, 3], [-2, 4], [1, 5], [-4, 7]], [[-2, 0], [-2, 1], [2, 2], [-2, 3], [-2, 4], [1, 5], [2, 7]], [[-1, 0], [-1, 1], [4, 2], [-4, 3], [-1, 4], [-2, 5], [4, 7]], [[-6, 3], [-6, -3]], [[3, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [5, 5], [-1, 7]], [[2, 0], [1, 1], [-4, 2], [4, 3], [1, 4], [-3, 5], [-4, 7]], [[2, 0], [-5, 5]], [[-3, 0]], [[-2, 0]], [[-5, 0], [4, 1], [2, 2], [-2, 3], [4, 4], [-2, 5], [2, 7]], [[-2, 0], [5, 5]], [[-2, 0], [2, 1], [-2, 2], [2, 3], [2, 4], [-1, 5], [-2, 7]], [[-2, 0]], [[2, 0]], [[6, 0], [-1, 1], [-5, 2], [5, 3], [-1, 4], [3, 5], [-5, 7]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[1, 0], [-4, 1], [-2, 2], [2, 3], [-4, 4], [2, 5], [-2, 7]], [[7, 0], [5, 5]], [[8, 0], [5, 5]], [[5, 0], [10, 5]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [-7, 5], [6, 7]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-5, -5]], [[2, 0], [5, 5]], [[2, 0], [-3, 1], [-3, 4], [9, 5]], [[1, 1], [5, 2], [-5, 3], [1, 4], [2, 5], [5, 7]], [[-3, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 7]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[3, 0], [-5, 5]], [[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]]]}
-
id: 5852851
{'center': '162000.a1.a1', 'center_index': 162000, 'center_order': 1, 'counter': 131, 'cyclotomic_n': 15, 'dim': 48, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '162000.x', 'group_counter': 24, 'group_order': 162000, 'image': None, 'image_isoclass': '162000.x', 'image_order': 162000, 'indicator': 0, 'kernel': '162000.a1.a1', 'kernel_order': 1, 'label': '162000.x.48z4', 'nt': [360, 4], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-12, 0]], [[8, 0]], [[3, 0]], [[-2, 0]], [[-2, 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]], [[-3, 0], [15, 5]], [[-18, 0], [-15, 5]], [[6, 0], [-12, 2], [12, 3], [-12, 7]], [[8, 0], [-6, 2], [6, 3], [-6, 7]], [[0, 0]], [[2, 0], [6, 2], [-6, 3], [6, 7]], [[-6, 0], [12, 2], [-12, 3], [12, 7]], [[10, -5]], [[10, 5]], [[-5, -5]], [[-13, 0], [5, 1], [10, 2], [-10, 3], [5, 4], [-5, 5], [10, 7]], [[3, 0]], [[-2, 0], [5, 5]], [[-1, 0], [-3, 2], [3, 3], [-3, 7]], [[2, 0]], [[2, 0]], [[-6, 6], [-6, -6]], [[-4, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-6, 5], [-3, 7]], [[-3, 0], [5, 1], [1, 2], [-1, 3], [5, 4], [1, 7]], [[-3, 0], [-5, 5]], [[-3, 0], [-5, 1], [5, 2], [-5, 3], [-5, 4], [5, 5], [5, 7]], [[-2, 0], [-2, 1], [2, 2], [-2, 3], [-2, 4], [1, 5], [2, 7]], [[5, 0], [10, 5]], [[2, 0], [5, 5]], [[2, 0], [-3, 2], [3, 3], [-3, 7]], [[-1, 0], [3, 1], [3, 4], [6, 5]], [[2, 0]], [[7, 0]], [[-7, 0], [9, 1], [6, 2], [-6, 3], [9, 4], [-7, 5], [6, 7]], [[8, 0], [-9, 1], [-6, 2], [6, 3], [-9, 4], [2, 5], [-6, 7]], [[3, 0], [-5, 1], [-1, 2], [1, 3], [-5, 4], [5, 5], [-1, 7]], [[2, 0], [5, 5]], [[2, 0], [-3, 1], [-3, 4], [9, 5]], [[-3, 0], [9, 1], [3, 2], [-3, 3], [9, 4], [-2, 5], [3, 7]], [[1, 0], [3, 2], [-3, 3], [3, 7]], [[7, 0]], [[2, 0], [5, 5]], [[-3, 0]], [[-3, 0], [5, 1], [-5, 2], [5, 3], [5, 4], [-5, 7]], [[-3, 0], [-5, 5]], [[2, 0], [-5, 1], [-4, 2], [4, 3], [-5, 4], [-4, 7]], [[4, 0], [-3, 2], [3, 3], [-3, 7]], [[-2, 0], [2, 1], [-2, 2], [2, 3], [2, 4], [-1, 5], [-2, 7]], [[-5, 0], [2, 1], [4, 2], [-4, 3], [2, 4], [-1, 5], [4, 7]], [[1, 1], [5, 2], [-5, 3], [1, 4], [2, 5], [5, 7]], [[-6, 3], [-6, -3]], [[-7, 0], [5, 1], [4, 2], [-4, 3], [5, 4], [-5, 5], [4, 7]], [[6, 0], [-1, 1], [-5, 2], [5, 3], [-1, 4], [3, 5], [-5, 7]], [[7, 0], [5, 5]], [[-3, 0]], [[-2, 0]], [[1, 0], [-4, 1], [-2, 2], [2, 3], [-4, 4], [2, 5], [-2, 7]], [[-7, 0], [-5, 5]], [[1, 0], [-2, 1], [-4, 2], [4, 3], [-2, 4], [1, 5], [-4, 7]], [[-2, 0]], [[2, 0]], [[2, 0], [1, 1], [-4, 2], [4, 3], [1, 4], [-3, 5], [-4, 7]], [[12, 0], [-12, 1], [-6, 2], [6, 3], [-12, 4], [6, 5], [-6, 7]], [[-6, 0], [12, 1], [6, 2], [-6, 3], [12, 4], [-6, 5], [6, 7]], [[-5, 0], [4, 1], [2, 2], [-2, 3], [4, 4], [-2, 5], [2, 7]], [[2, 0], [-5, 5]], [[3, 0], [-5, 5]], [[-5, 0], [-10, 5]], [[9, 0], [-9, 1], [-3, 2], [3, 3], [-9, 4], [7, 5], [-3, 7]], [[-4, 0], [3, 2], [-3, 3], [3, 7]], [[-5, 5]], [[-3, 0], [-5, 5]], [[-10, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-9, 5], [3, 7]], [[-1, 0], [-1, 1], [4, 2], [-4, 3], [-1, 4], [-2, 5], [4, 7]], [[2, 0], [-5, 1], [-10, 2], [10, 3], [-5, 4], [-10, 7]], [[-1, 0], [3, 2], [-3, 3], [3, 7]], [[8, 0], [5, 5]], [[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]]]}
-
gps_subgroup_search • Show schema
Hide schema
-
id: 62909710
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 162000, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '162000.x.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162000.x', 'subgroup_hash': 242777464014375236, 'subgroup_order': 162000, 'subgroup_tex': '(C_{15}^3.A_4):C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909821
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 81000, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '162000.x.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '81000.x', 'subgroup_hash': 8132680312133666275, 'subgroup_order': 81000, 'subgroup_tex': 'C_3^3:D_5\\wr C_3', 'supersolvable': False, 'sylow': 0}
-
id: 62909932
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27000, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8310010270916625164, 'subgroup_order': 54000, 'subgroup_tex': 'C_{15}^3.C_2.D_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910043
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 40500, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '162000.x.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '40500.j', 'subgroup_hash': 2409037888781003016, 'subgroup_order': 40500, 'subgroup_tex': 'C_{15}^3.A_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910154
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6750, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40500.e', 'subgroup_hash': 2319521874645173983, 'subgroup_order': 40500, 'subgroup_tex': 'C_{15}\\wr C_3:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910265
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 27000, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '162000.x.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1281477608004268863, 'subgroup_order': 27000, 'subgroup_tex': 'C_{15}^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 62910376
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6750, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 391794098320878042, 'subgroup_order': 27000, 'subgroup_tex': 'C_3\\times C_5^3.(C_2.S_3^2)', 'supersolvable': True, 'sylow': 0}
-
id: 62910487
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6750, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8760987325825591949, 'subgroup_order': 27000, 'subgroup_tex': 'C_{15}^3.C_4.C_2', 'supersolvable': False, 'sylow': 0}
-
id: 62910598
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6750, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20250.b', 'subgroup_hash': 8737408772808678176, 'subgroup_order': 20250, 'subgroup_tex': 'C_{15}\\wr C_3:C_2', 'supersolvable': False, 'sylow': 0}
-
id: 62909711
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 250, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4318764616594269022, 'subgroup_order': 18000, 'subgroup_tex': 'C_5^3.S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909722
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 13500, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '162000.x.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4517675616309311718, 'subgroup_order': 13500, 'subgroup_tex': 'C_{15}^3.C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909733
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6750, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6598887701956054265, 'subgroup_order': 13500, 'subgroup_tex': 'C_3\\times C_5^3:(C_2\\times C_3:S_3)', 'supersolvable': True, 'sylow': 0}
-
id: 62909744
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '13500.d', 'subgroup_hash': 5899386867227522166, 'subgroup_order': 13500, 'subgroup_tex': 'C_{15}^2:C_{15}:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909755
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 6750, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5638704007976315411, 'subgroup_order': 13500, 'subgroup_tex': 'C_3\\times C_5^3:(C_3\\times C_3:C_4)', 'supersolvable': True, 'sylow': 0}
-
id: 62909766
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 3375, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8866350144015090564, 'subgroup_order': 13500, 'subgroup_tex': '(C_3\\times C_{15}^2).C_{20}', 'supersolvable': False, 'sylow': 0}
-
id: 62909777
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 3375, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7343951838369534593, 'subgroup_order': 13500, 'subgroup_tex': 'C_{15}^3.C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909788
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7508667018301004851, 'subgroup_order': 10800, 'subgroup_tex': '(C_3\\times C_{15}^2).C_2.D_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909799
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3375, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 15, 'label': '162000.x.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10125.a', 'subgroup_hash': 3765728509990489607, 'subgroup_order': 10125, 'subgroup_tex': 'C_{15}\\wr C_3', 'supersolvable': False, 'sylow': 0}
-
id: 62909810
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5689887894055609815, 'subgroup_order': 9000, 'subgroup_tex': 'C_3\\times C_5^3:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
-
id: 62909822
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2185498238548892811, 'subgroup_order': 9000, 'subgroup_tex': 'C_5^3.(C_2.S_3^2)', 'supersolvable': True, 'sylow': 0}
-
id: 62909833
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 250, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4058953828754847424, 'subgroup_order': 9000, 'subgroup_tex': 'C_5^3.C_3:S_3.C_2^2', 'supersolvable': False, 'sylow': 0}
-
id: 62909844
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 250, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 318099279106609719, 'subgroup_order': 9000, 'subgroup_tex': 'C_5^3.(C_2\\times S_3^2)', 'supersolvable': True, 'sylow': 0}
-
id: 62909855
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8100.q', 'subgroup_hash': 6163077415364916282, 'subgroup_order': 8100, 'subgroup_tex': 'C_{15}^2:C_3:C_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 62909866
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 6750, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '162000.x.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 969231122711952127, 'subgroup_order': 6750, 'subgroup_tex': 'C_3^3\\times C_5^2:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909877
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6750.b', 'subgroup_hash': 4747043094101760884, 'subgroup_order': 6750, 'subgroup_tex': '(C_5\\times C_{15}^2):C_6', 'supersolvable': False, 'sylow': 0}
-
id: 62909888
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6750.c', 'subgroup_hash': 7527631992402363360, 'subgroup_order': 6750, 'subgroup_tex': '(C_5\\times C_{15}^2).C_6', 'supersolvable': False, 'sylow': 0}
-
id: 62909899
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 3375, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1045482819749329843, 'subgroup_order': 6750, 'subgroup_tex': 'C_5\\times C_{15}\\times C_3:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909910
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3375, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7854367860781212545, 'subgroup_order': 6750, 'subgroup_tex': 'C_3\\times C_5^3:(C_3:S_3)', 'supersolvable': True, 'sylow': 0}
-
id: 62909921
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 250, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.27.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6000.bm', 'subgroup_hash': 7537202592292727862, 'subgroup_order': 6000, 'subgroup_tex': 'D_5^3.S_3', 'supersolvable': False, 'sylow': 0}
-
id: 62909933
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 250, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.27.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6334953065901057743, 'subgroup_order': 6000, 'subgroup_tex': 'C_5^3.C_6.D_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909944
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1889078786952235251, 'subgroup_order': 5400, 'subgroup_tex': 'C_3\\times C_5^2:(C_2.S_3^2)', 'supersolvable': True, 'sylow': 0}
-
id: 62909955
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6384283711531276956, 'subgroup_order': 5400, 'subgroup_tex': '(C_3\\times C_{15}^2).C_4.C_2', 'supersolvable': False, 'sylow': 0}
-
id: 62909966
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1454057301655894320, 'subgroup_order': 5400, 'subgroup_tex': 'C_3\\times C_5^2:(C_2.S_3^2)', 'supersolvable': True, 'sylow': 0}
-
id: 62909977
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2860243016396393442, 'subgroup_order': 5400, 'subgroup_tex': '(C_3\\times C_{15}^2).C_4.C_2', 'supersolvable': False, 'sylow': 0}
-
id: 62909988
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.30.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5917481437303169950, 'subgroup_order': 5400, 'subgroup_tex': 'C_{15}^2.C_6.C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909999
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3579612522681884059, 'subgroup_order': 4500, 'subgroup_tex': 'C_3\\times C_5^3:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910010
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3579612522681884059, 'subgroup_order': 4500, 'subgroup_tex': 'C_3\\times C_5^3:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910021
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2218901054626342950, 'subgroup_order': 4500, 'subgroup_tex': 'C_5^3:(C_2\\times C_3:S_3)', 'supersolvable': True, 'sylow': 0}
-
id: 62910032
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 250, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4543783095038794422, 'subgroup_order': 4500, 'subgroup_tex': 'C_5^3:(C_3\\times C_3:C_4)', 'supersolvable': True, 'sylow': 0}
-
id: 62910044
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4500.l', 'subgroup_hash': 4257863390704883839, 'subgroup_order': 4500, 'subgroup_tex': 'C_5\\wr C_3:C_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 62910055
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 250, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2051760747210064277, 'subgroup_order': 4500, 'subgroup_tex': 'C_3^2\\times C_5:(C_5:F_5)', 'supersolvable': True, 'sylow': 0}
-
id: 62910066
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 250, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4543783095038794422, 'subgroup_order': 4500, 'subgroup_tex': 'C_3\\times C_5^3:(C_3:C_4)', 'supersolvable': True, 'sylow': 0}
-
id: 62910077
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 250, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4543783095038794422, 'subgroup_order': 4500, 'subgroup_tex': 'C_5^3:(C_3\\times C_3:C_4)', 'supersolvable': True, 'sylow': 0}
-
id: 62910088
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 125, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6107335677675402871, 'subgroup_order': 4500, 'subgroup_tex': 'C_5^3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910099
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 125, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3016507979176022446, 'subgroup_order': 4500, 'subgroup_tex': 'C_5^3:(C_3:S_3.C_2)', 'supersolvable': False, 'sylow': 0}
-
id: 62910110
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 125, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6892203781633570860, 'subgroup_order': 4500, 'subgroup_tex': 'C_5^3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910121
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 125, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1389103232168575925, 'subgroup_order': 4500, 'subgroup_tex': 'C_5^3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910132
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4050.i', 'subgroup_hash': 1647273969934886050, 'subgroup_order': 4050, 'subgroup_tex': '(C_3\\times C_{15}^2):C_6', 'supersolvable': False, 'sylow': 0}
-
id: 62910143
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.45.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3600.cd', 'subgroup_hash': 5836885831044729660, 'subgroup_order': 3600, 'subgroup_tex': 'D_{15}^2:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910155
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': True, 'core_order': 3375, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '162000.x.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4:C_4', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S', 'D3', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2654368139746726960, 'subgroup_order': 3375, 'subgroup_tex': 'C_{15}^3', 'supersolvable': True, 'sylow': 0}
-
id: 62910166
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3375.a', 'subgroup_hash': 5944683378990376072, 'subgroup_order': 3375, 'subgroup_tex': 'C_{15}^2:C_{15}', 'supersolvable': False, 'sylow': 0}
-
id: 62910177
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3375.b', 'subgroup_hash': 6087309594989841362, 'subgroup_order': 3375, 'subgroup_tex': 'C_{15}^2.C_{15}', 'supersolvable': False, 'sylow': 0}
-
id: 62910188
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1098391311860348903, 'subgroup_order': 3000, 'subgroup_tex': 'C_3\\times C_5^3:(C_2\\times C_4)', 'supersolvable': True, 'sylow': 0}
-
id: 62910199
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 250, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8325417776300898914, 'subgroup_order': 3000, 'subgroup_tex': 'C_5^3:(C_2\\times C_3:C_4)', 'supersolvable': True, 'sylow': 0}
-
id: 62910210
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2581784598994232741, 'subgroup_order': 3000, 'subgroup_tex': 'C_5^3:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
-
id: 62910221
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 250, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3000.bv', 'subgroup_hash': 3666142396557707404, 'subgroup_order': 3000, 'subgroup_tex': 'D_5\\wr C_3', 'supersolvable': False, 'sylow': 0}
-
id: 62910232
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 250, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7945856957154518028, 'subgroup_order': 3000, 'subgroup_tex': 'C_5^3:(C_2^2\\times S_3)', 'supersolvable': True, 'sylow': 0}
-
id: 62910243
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6119636961237253897, 'subgroup_order': 2700, 'subgroup_tex': 'C_3\\times C_5^2:(C_2\\times C_3:S_3)', 'supersolvable': True, 'sylow': 0}
-
id: 62910254
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4180421001276880279, 'subgroup_order': 2700, 'subgroup_tex': 'C_3\\times C_5^2:(C_2\\times C_3:S_3)', 'supersolvable': True, 'sylow': 0}
-
id: 62910266
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4180421001276880279, 'subgroup_order': 2700, 'subgroup_tex': 'C_3\\times C_5^2:(C_2\\times C_3:S_3)', 'supersolvable': True, 'sylow': 0}
-
id: 62910277
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4180421001276880279, 'subgroup_order': 2700, 'subgroup_tex': 'C_3\\times C_5^2:(C_2\\times C_3:S_3)', 'supersolvable': True, 'sylow': 0}
-
id: 62910288
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2700.n', 'subgroup_hash': 3729736992199670331, 'subgroup_order': 2700, 'subgroup_tex': 'C_{15}^2:C_3:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910299
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6734059552211618364, 'subgroup_order': 2700, 'subgroup_tex': 'C_3\\times C_5^2:(C_3\\times C_3:C_4)', 'supersolvable': True, 'sylow': 0}
-
id: 62910310
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.f2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.f2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5794616430244295535, 'subgroup_order': 2700, 'subgroup_tex': 'C_3\\times C_5^2:(C_3\\times C_3:C_4)', 'supersolvable': True, 'sylow': 0}
-
id: 62910321
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5794616430244295535, 'subgroup_order': 2700, 'subgroup_tex': 'C_3\\times C_5^2:(C_3\\times C_3:C_4)', 'supersolvable': True, 'sylow': 0}
-
id: 62910332
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5794616430244295535, 'subgroup_order': 2700, 'subgroup_tex': 'C_3\\times C_5^2:(C_3\\times C_3:C_4)', 'supersolvable': True, 'sylow': 0}
-
id: 62910343
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5794616430244295535, 'subgroup_order': 2700, 'subgroup_tex': 'C_3\\times C_5^2:(C_3\\times C_3:C_4)', 'supersolvable': True, 'sylow': 0}
-
id: 62910354
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 27, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6282106534731023206, 'subgroup_order': 2700, 'subgroup_tex': 'C_5^2:(C_3^2:(C_3:C_4))', 'supersolvable': False, 'sylow': 0}
-
id: 62910365
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 27, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6157870383183080893, 'subgroup_order': 2700, 'subgroup_tex': 'C_5\\times C_5:(C_3^2:(C_3:C_4))', 'supersolvable': False, 'sylow': 0}
-
id: 62910377
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 27, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3917386642520365629, 'subgroup_order': 2700, 'subgroup_tex': 'C_5^2:(C_3^2:(C_3:C_4))', 'supersolvable': False, 'sylow': 0}
-
id: 62910388
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 27, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1451403804787500198, 'subgroup_order': 2700, 'subgroup_tex': 'C_5^2:(C_3^3:C_2^2)', 'supersolvable': True, 'sylow': 0}
-
id: 62910399
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 27, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6062335415848751334, 'subgroup_order': 2700, 'subgroup_tex': 'C_5^2:(C_3^3:C_2^2)', 'supersolvable': True, 'sylow': 0}
-
id: 62910410
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.60.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6062335415848751334, 'subgroup_order': 2700, 'subgroup_tex': 'C_5^2:(C_3^3:C_2^2)', 'supersolvable': True, 'sylow': 0}
-
id: 62910421
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 250, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1569054153411924802, 'subgroup_order': 2250, 'subgroup_tex': 'C_3^2\\times C_5^2:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910432
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2250.g', 'subgroup_hash': 3638640786514561450, 'subgroup_order': 2250, 'subgroup_tex': 'C_3\\times C_5^3:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 62910443
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2250.h', 'subgroup_hash': 5160734154559563270, 'subgroup_order': 2250, 'subgroup_tex': 'C_5^3:C_{18}', 'supersolvable': False, 'sylow': 0}
-
id: 62910454
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 250, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1569054153411924802, 'subgroup_order': 2250, 'subgroup_tex': 'C_3^2\\times C_5^2:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910465
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 250, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1569054153411924802, 'subgroup_order': 2250, 'subgroup_tex': 'C_3^2\\times C_5^2:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910476
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 125, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4539966168627826690, 'subgroup_order': 2250, 'subgroup_tex': 'C_5\\times C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910488
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 125, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4539966168627826690, 'subgroup_order': 2250, 'subgroup_tex': 'C_5\\times C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910499
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 125, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7003233357594768111, 'subgroup_order': 2250, 'subgroup_tex': 'C_5^2\\times C_3:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910510
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3031100145575243473, 'subgroup_order': 2250, 'subgroup_tex': 'C_3\\times C_5^3:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910521
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3031100145575243473, 'subgroup_order': 2250, 'subgroup_tex': 'C_3\\times C_5^3:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910532
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6402835584638580274, 'subgroup_order': 2250, 'subgroup_tex': 'C_5^3:(C_3:S_3)', 'supersolvable': True, 'sylow': 0}
-
id: 62910543
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.75.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 75, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.fi', 'subgroup_hash': 8107110896495812077, 'subgroup_order': 2160, 'subgroup_tex': '(D_5\\times C_3^3).D_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910554
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 27, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2025.d', 'subgroup_hash': 7403812059239877369, 'subgroup_order': 2025, 'subgroup_tex': 'C_{15}^2.C_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 62910565
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 250, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '162000.x.81.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2000.905', 'subgroup_hash': 905, 'subgroup_order': 2000, 'subgroup_tex': 'D_5^2:F_5', 'supersolvable': False, 'sylow': 0}
-
id: 62910576
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.90.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.607', 'subgroup_hash': 607, 'subgroup_order': 1800, 'subgroup_tex': 'S_3\\times C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910587
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.90.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.630', 'subgroup_hash': 630, 'subgroup_order': 1800, 'subgroup_tex': 'C_{15}:(S_3\\times F_5)', 'supersolvable': True, 'sylow': 0}
-
id: 62910599
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.90.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.649', 'subgroup_hash': 649, 'subgroup_order': 1800, 'subgroup_tex': 'C_{15}^2:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
-
id: 62910610
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.90.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.609', 'subgroup_hash': 609, 'subgroup_order': 1800, 'subgroup_tex': 'C_3\\times D_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910621
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.90.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.610', 'subgroup_hash': 610, 'subgroup_order': 1800, 'subgroup_tex': 'C_3\\times D_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910632
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.90.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.681', 'subgroup_hash': 681, 'subgroup_order': 1800, 'subgroup_tex': 'D_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62910643
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.90.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.632', 'subgroup_hash': 632, 'subgroup_order': 1800, 'subgroup_tex': 'C_{15}:(S_3\\times F_5)', 'supersolvable': True, 'sylow': 0}
-
id: 62910654
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.90.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.646', 'subgroup_hash': 646, 'subgroup_order': 1800, 'subgroup_tex': 'C_{15}^2:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
-
id: 62910665
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.90.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.679', 'subgroup_hash': 679, 'subgroup_order': 1800, 'subgroup_tex': 'C_{15}^2:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 62910676
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.100.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1620.88', 'subgroup_hash': 88, 'subgroup_order': 1620, 'subgroup_tex': '(C_5\\times \\He_3):C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910687
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.153', 'subgroup_hash': 153, 'subgroup_order': 1500, 'subgroup_tex': 'C_{15}:D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910689
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.162', 'subgroup_hash': 162, 'subgroup_order': 1500, 'subgroup_tex': 'C_{15}:D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909712
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.162', 'subgroup_hash': 162, 'subgroup_order': 1500, 'subgroup_tex': 'C_{15}:D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909713
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 250, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.139', 'subgroup_hash': 139, 'subgroup_order': 1500, 'subgroup_tex': 'C_5^3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62909714
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 250, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.139', 'subgroup_hash': 139, 'subgroup_order': 1500, 'subgroup_tex': 'C_5^3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62909715
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 250, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.139', 'subgroup_hash': 139, 'subgroup_order': 1500, 'subgroup_tex': 'C_5^3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62909716
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 250, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.108.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.148', 'subgroup_hash': 148, 'subgroup_order': 1500, 'subgroup_tex': '(C_5\\times C_{15}):F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909717
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.108.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.115', 'subgroup_hash': 115, 'subgroup_order': 1500, 'subgroup_tex': 'C_5\\wr C_3:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909718
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 125, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.108.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.146', 'subgroup_hash': 146, 'subgroup_order': 1500, 'subgroup_tex': 'C_5\\times C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909719
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 125, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.108.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.157', 'subgroup_hash': 157, 'subgroup_order': 1500, 'subgroup_tex': 'C_5^2:D_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62909720
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 125, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.108.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.158', 'subgroup_hash': 158, 'subgroup_order': 1500, 'subgroup_tex': 'C_{15}:D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909721
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 125, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.108.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.123', 'subgroup_hash': 123, 'subgroup_order': 1500, 'subgroup_tex': 'C_5^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909723
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 125, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.108.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.163', 'subgroup_hash': 163, 'subgroup_order': 1500, 'subgroup_tex': 'C_5^2:D_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62909724
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.51', 'subgroup_hash': 51, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 62909725
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.50', 'subgroup_hash': 50, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2.C_6', 'supersolvable': False, 'sylow': 0}
-
id: 62909726
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.102', 'subgroup_hash': 102, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909727
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.102', 'subgroup_hash': 102, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909728
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.102', 'subgroup_hash': 102, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909729
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.102', 'subgroup_hash': 102, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909730
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.102', 'subgroup_hash': 102, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909731
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 27, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.106', 'subgroup_hash': 106, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909732
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 27, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.107', 'subgroup_hash': 107, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909734
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 27, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.107', 'subgroup_hash': 107, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909735
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 27, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.107', 'subgroup_hash': 107, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909736
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 27, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.107', 'subgroup_hash': 107, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909737
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 27, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.107', 'subgroup_hash': 107, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909738
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 27, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.107', 'subgroup_hash': 107, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909739
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 27, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.120.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1350.108', 'subgroup_hash': 108, 'subgroup_order': 1350, 'subgroup_tex': 'C_{15}^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909740
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '162000.x.125.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '125.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 125, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3086', 'subgroup_hash': 3086, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times C_6).S_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909741
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.135.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '135.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 135, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1200.607', 'subgroup_hash': 607, 'subgroup_order': 1200, 'subgroup_tex': '(C_5\\times C_{10}).D_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 62909742
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 125, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1125.14', 'subgroup_hash': 14, 'subgroup_order': 1125, 'subgroup_tex': 'C_5\\times C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909743
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1125.13', 'subgroup_hash': 13, 'subgroup_order': 1125, 'subgroup_tex': 'C_5^3:C_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 62909745
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1125.11', 'subgroup_hash': 11, 'subgroup_order': 1125, 'subgroup_tex': 'C_5^2:C_{45}', 'supersolvable': False, 'sylow': 0}
-
id: 62909746
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 125, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1125.14', 'subgroup_hash': 14, 'subgroup_order': 1125, 'subgroup_tex': 'C_5\\times C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909747
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 125, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1125.14', 'subgroup_hash': 14, 'subgroup_order': 1125, 'subgroup_tex': 'C_5\\times C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909748
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.150.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.504', 'subgroup_hash': 504, 'subgroup_order': 1080, 'subgroup_tex': 'C_{15}:(S_3\\times C_{12})', 'supersolvable': True, 'sylow': 0}
-
id: 62909749
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.150.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.513', 'subgroup_hash': 513, 'subgroup_order': 1080, 'subgroup_tex': 'C_3^3:C_4\\times D_5', 'supersolvable': False, 'sylow': 0}
-
id: 62909750
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.150.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.504', 'subgroup_hash': 504, 'subgroup_order': 1080, 'subgroup_tex': 'C_{15}:(S_3\\times C_{12})', 'supersolvable': True, 'sylow': 0}
-
id: 62909751
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.150.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.512', 'subgroup_hash': 512, 'subgroup_order': 1080, 'subgroup_tex': '(D_5\\times C_3^3):C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909752
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.150.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.537', 'subgroup_hash': 537, 'subgroup_order': 1080, 'subgroup_tex': 'D_5\\times C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909753
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.162.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1000.170', 'subgroup_hash': 170, 'subgroup_order': 1000, 'subgroup_tex': 'C_5^3:(C_2\\times C_4)', 'supersolvable': True, 'sylow': 0}
-
id: 62909754
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 250, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.162.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1000.177', 'subgroup_hash': 177, 'subgroup_order': 1000, 'subgroup_tex': 'D_5.D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909756
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 250, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.162.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1000.183', 'subgroup_hash': 183, 'subgroup_order': 1000, 'subgroup_tex': 'D_5^3', 'supersolvable': True, 'sylow': 0}
-
id: 62909757
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.125', 'subgroup_hash': 125, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909758
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.125', 'subgroup_hash': 125, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909759
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.129', 'subgroup_hash': 129, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909760
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.127', 'subgroup_hash': 127, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909761
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.127', 'subgroup_hash': 127, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909762
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.127', 'subgroup_hash': 127, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909763
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.127', 'subgroup_hash': 127, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909764
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.127', 'subgroup_hash': 127, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909765
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.127', 'subgroup_hash': 127, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909767
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.127', 'subgroup_hash': 127, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909768
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.127', 'subgroup_hash': 127, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909769
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.131', 'subgroup_hash': 131, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909770
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.131', 'subgroup_hash': 131, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909771
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.131', 'subgroup_hash': 131, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909772
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.109', 'subgroup_hash': 109, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909773
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909774
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909775
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909776
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909778
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909779
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909780
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.89', 'subgroup_hash': 89, 'subgroup_order': 900, 'subgroup_tex': 'C_5^2:C_3:C_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 62909781
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.105', 'subgroup_hash': 105, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909782
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.106', 'subgroup_hash': 106, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909783
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.106', 'subgroup_hash': 106, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909784
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.106', 'subgroup_hash': 106, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909785
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.106', 'subgroup_hash': 106, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909786
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909787
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.109', 'subgroup_hash': 109, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909789
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909790
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909791
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909792
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.109', 'subgroup_hash': 109, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909793
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bg2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bg2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909794
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909795
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909796
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.110', 'subgroup_hash': 110, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909797
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.118', 'subgroup_hash': 118, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909798
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.133', 'subgroup_hash': 133, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}:D_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62909800
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.134', 'subgroup_hash': 134, 'subgroup_order': 900, 'subgroup_tex': 'C_5^2:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909801
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.137', 'subgroup_hash': 137, 'subgroup_order': 900, 'subgroup_tex': 'D_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909802
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.117', 'subgroup_hash': 117, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909803
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.121', 'subgroup_hash': 121, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}^2:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909804
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.133', 'subgroup_hash': 133, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}:D_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62909805
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.138', 'subgroup_hash': 138, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}:D_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62909806
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.138', 'subgroup_hash': 138, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}:D_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62909807
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.180.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.137', 'subgroup_hash': 137, 'subgroup_order': 900, 'subgroup_tex': 'D_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909808
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.200.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '810.10', 'subgroup_hash': 10, 'subgroup_order': 810, 'subgroup_tex': 'C_3\\wr C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909809
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 250, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '750.34', 'subgroup_hash': 34, 'subgroup_order': 750, 'subgroup_tex': 'C_5^3:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909811
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 250, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '750.34', 'subgroup_hash': 34, 'subgroup_order': 750, 'subgroup_tex': 'C_5^3:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909812
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 250, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '750.34', 'subgroup_hash': 34, 'subgroup_order': 750, 'subgroup_tex': 'C_5^3:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909813
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '750.30', 'subgroup_hash': 30, 'subgroup_order': 750, 'subgroup_tex': 'C_5^3:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 62909814
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 125, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '750.32', 'subgroup_hash': 32, 'subgroup_order': 750, 'subgroup_tex': 'C_5^2:C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62909815
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 125, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.216.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '750.36', 'subgroup_hash': 36, 'subgroup_order': 750, 'subgroup_tex': 'C_5^2\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909816
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 125, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.216.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '750.36', 'subgroup_hash': 36, 'subgroup_order': 750, 'subgroup_tex': 'C_5^2\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909817
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.216.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '750.33', 'subgroup_hash': 33, 'subgroup_order': 750, 'subgroup_tex': 'C_5^2:C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62909818
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.216.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '750.37', 'subgroup_hash': 37, 'subgroup_order': 750, 'subgroup_tex': 'C_5^2:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909819
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.216.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '750.37', 'subgroup_hash': 37, 'subgroup_order': 750, 'subgroup_tex': 'C_5^2:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909820
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.225.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '225.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 225, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.774', 'subgroup_hash': 774, 'subgroup_order': 720, 'subgroup_tex': 'S_3^2:F_5', 'supersolvable': False, 'sylow': 0}
-
id: 62909823
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '675.12', 'subgroup_hash': 12, 'subgroup_order': 675, 'subgroup_tex': 'C_{15}^2:C_3', 'supersolvable': False, 'sylow': 0}
-
id: 62909824
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '675.11', 'subgroup_hash': 11, 'subgroup_order': 675, 'subgroup_tex': 'C_{15}^2.C_3', 'supersolvable': False, 'sylow': 0}
-
id: 62909825
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 27, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '675.17', 'subgroup_hash': 17, 'subgroup_order': 675, 'subgroup_tex': 'C_3\\times C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909826
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 27, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '675.17', 'subgroup_hash': 17, 'subgroup_order': 675, 'subgroup_tex': 'C_3\\times C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909827
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 27, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.240.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '675.17', 'subgroup_hash': 17, 'subgroup_order': 675, 'subgroup_tex': 'C_3\\times C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909828
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 27, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.240.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '675.17', 'subgroup_hash': 17, 'subgroup_order': 675, 'subgroup_tex': 'C_3\\times C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909829
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 27, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.240.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '675.17', 'subgroup_hash': 17, 'subgroup_order': 675, 'subgroup_tex': 'C_3\\times C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909830
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.250.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '250.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 250, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.706', 'subgroup_hash': 706, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909831
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.270.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.186', 'subgroup_hash': 186, 'subgroup_order': 600, 'subgroup_tex': 'C_{30}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909832
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.270.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.107', 'subgroup_hash': 107, 'subgroup_order': 600, 'subgroup_tex': 'C_{30}.D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909834
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.270.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.161', 'subgroup_hash': 161, 'subgroup_order': 600, 'subgroup_tex': 'S_3\\times C_5:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909835
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.270.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.157', 'subgroup_hash': 157, 'subgroup_order': 600, 'subgroup_tex': 'D_5^2.C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62909836
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.270.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.166', 'subgroup_hash': 166, 'subgroup_order': 600, 'subgroup_tex': 'D_5^2.S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62909837
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.270.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.163', 'subgroup_hash': 163, 'subgroup_order': 600, 'subgroup_tex': 'D_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909838
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.270.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.164', 'subgroup_hash': 164, 'subgroup_order': 600, 'subgroup_tex': 'D_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909839
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.270.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.174', 'subgroup_hash': 174, 'subgroup_order': 600, 'subgroup_tex': 'S_3\\times D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909840
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.270.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.196', 'subgroup_hash': 196, 'subgroup_order': 600, 'subgroup_tex': 'C_{30}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909841
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.100', 'subgroup_hash': 100, 'subgroup_order': 540, 'subgroup_tex': 'C_3^3:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909842
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.100', 'subgroup_hash': 100, 'subgroup_order': 540, 'subgroup_tex': 'C_3^3:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909843
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.100', 'subgroup_hash': 100, 'subgroup_order': 540, 'subgroup_tex': 'C_3^3:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909845
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.100', 'subgroup_hash': 100, 'subgroup_order': 540, 'subgroup_tex': 'C_3^3:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909846
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.40', 'subgroup_hash': 40, 'subgroup_order': 540, 'subgroup_tex': '\\He_3:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909847
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.90', 'subgroup_hash': 90, 'subgroup_order': 540, 'subgroup_tex': 'C_3^3:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909848
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.90', 'subgroup_hash': 90, 'subgroup_order': 540, 'subgroup_tex': 'C_3^3:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909849
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.90', 'subgroup_hash': 90, 'subgroup_order': 540, 'subgroup_tex': 'C_3^3:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909850
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.h2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.h2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.90', 'subgroup_hash': 90, 'subgroup_order': 540, 'subgroup_tex': 'C_3^3:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909851
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.90', 'subgroup_hash': 90, 'subgroup_order': 540, 'subgroup_tex': 'C_3^3:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909852
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 27, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.96', 'subgroup_hash': 96, 'subgroup_order': 540, 'subgroup_tex': 'C_3^3:C_{20}', 'supersolvable': False, 'sylow': 0}
-
id: 62909853
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 27, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.98', 'subgroup_hash': 98, 'subgroup_order': 540, 'subgroup_tex': '(C_3^2\\times C_{15}):C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909854
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 27, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.109', 'subgroup_hash': 109, 'subgroup_order': 540, 'subgroup_tex': 'C_{15}:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909856
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 27, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.97', 'subgroup_hash': 97, 'subgroup_order': 540, 'subgroup_tex': 'C_3^3:F_5', 'supersolvable': False, 'sylow': 0}
-
id: 62909857
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 27, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.110', 'subgroup_hash': 110, 'subgroup_order': 540, 'subgroup_tex': 'C_{15}:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909858
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.300.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.110', 'subgroup_hash': 110, 'subgroup_order': 540, 'subgroup_tex': 'C_{15}:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909859
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.324.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '500.51', 'subgroup_hash': 51, 'subgroup_order': 500, 'subgroup_tex': 'C_5:D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909860
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 250, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.324.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '500.49', 'subgroup_hash': 49, 'subgroup_order': 500, 'subgroup_tex': 'C_5^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62909861
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 125, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.324.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '500.42', 'subgroup_hash': 42, 'subgroup_order': 500, 'subgroup_tex': 'C_5^2:C_{20}', 'supersolvable': True, 'sylow': 0}
-
id: 62909862
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 125, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.324.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '500.50', 'subgroup_hash': 50, 'subgroup_order': 500, 'subgroup_tex': 'C_5\\times D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909863
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 125, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.324.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '500.52', 'subgroup_hash': 52, 'subgroup_order': 500, 'subgroup_tex': 'C_5:D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909864
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909865
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909867
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909868
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909869
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909870
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909871
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909872
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909873
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909874
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.22', 'subgroup_hash': 22, 'subgroup_order': 450, 'subgroup_tex': 'C_3\\times C_5^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 62909875
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.12', 'subgroup_hash': 12, 'subgroup_order': 450, 'subgroup_tex': 'C_5^2:C_{18}', 'supersolvable': False, 'sylow': 0}
-
id: 62909876
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909878
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909879
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909880
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909881
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909882
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909883
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909884
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909885
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909886
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909887
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909889
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909890
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909891
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909892
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909893
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909894
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909895
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909896
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909897
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909898
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909900
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.27', 'subgroup_hash': 27, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909901
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.28', 'subgroup_hash': 28, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}:C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62909902
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.28', 'subgroup_hash': 28, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}:C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62909903
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.31', 'subgroup_hash': 31, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62909904
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909905
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909906
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909907
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909908
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909909
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909911
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909912
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909913
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.32', 'subgroup_hash': 32, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909914
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.32', 'subgroup_hash': 32, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909915
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.32', 'subgroup_hash': 32, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909916
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909917
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909918
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909919
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909920
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909922
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909923
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909924
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.29', 'subgroup_hash': 29, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909925
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.32', 'subgroup_hash': 32, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909926
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.32', 'subgroup_hash': 32, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909927
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.32', 'subgroup_hash': 32, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909928
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.30', 'subgroup_hash': 30, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909929
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.30', 'subgroup_hash': 30, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909930
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.360.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.33', 'subgroup_hash': 33, 'subgroup_order': 450, 'subgroup_tex': 'C_{15}:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909931
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.375.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '375.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 375, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.579', 'subgroup_hash': 579, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
-
id: 62909934
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 27, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.400.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '405.7', 'subgroup_hash': 7, 'subgroup_order': 405, 'subgroup_tex': 'C_3^3:C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909935
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.405.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '405.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 405, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '400.129', 'subgroup_hash': 129, 'subgroup_order': 400, 'subgroup_tex': 'D_5^2:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909936
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 125, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '375.7', 'subgroup_hash': 7, 'subgroup_order': 375, 'subgroup_tex': 'C_5^2\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909937
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 125, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.432.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '375.7', 'subgroup_hash': 7, 'subgroup_order': 375, 'subgroup_tex': 'C_5^2\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909938
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 125, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.432.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '375.7', 'subgroup_hash': 7, 'subgroup_order': 375, 'subgroup_tex': 'C_5^2\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62909939
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.432.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '375.6', 'subgroup_hash': 6, 'subgroup_order': 375, 'subgroup_tex': 'C_5\\wr C_3', 'supersolvable': False, 'sylow': 0}
-
id: 62909940
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.450.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.126', 'subgroup_hash': 126, 'subgroup_order': 360, 'subgroup_tex': 'D_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62909941
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.450.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.126', 'subgroup_hash': 126, 'subgroup_order': 360, 'subgroup_tex': 'D_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62909942
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.450.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.129', 'subgroup_hash': 129, 'subgroup_order': 360, 'subgroup_tex': 'D_5.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909943
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.450.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.130', 'subgroup_hash': 130, 'subgroup_order': 360, 'subgroup_tex': 'C_3^2:C_4\\times D_5', 'supersolvable': False, 'sylow': 0}
-
id: 62909945
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.450.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.126', 'subgroup_hash': 126, 'subgroup_order': 360, 'subgroup_tex': 'D_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62909946
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.450.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.137', 'subgroup_hash': 137, 'subgroup_order': 360, 'subgroup_tex': 'D_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909947
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.450.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.129', 'subgroup_hash': 129, 'subgroup_order': 360, 'subgroup_tex': 'D_5.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909948
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.450.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.131', 'subgroup_hash': 131, 'subgroup_order': 360, 'subgroup_tex': '(C_3^2\\times D_5):C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909949
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.450.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.137', 'subgroup_hash': 137, 'subgroup_order': 360, 'subgroup_tex': 'D_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909950
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.500.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '500.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.13', 'subgroup_hash': 13, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62909951
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.500.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '500.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.160', 'subgroup_hash': 160, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909952
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.45', 'subgroup_hash': 45, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909953
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.38', 'subgroup_hash': 38, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909954
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.38', 'subgroup_hash': 38, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909956
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.36', 'subgroup_hash': 36, 'subgroup_order': 300, 'subgroup_tex': 'C_3\\times D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909957
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.36', 'subgroup_hash': 36, 'subgroup_order': 300, 'subgroup_tex': 'C_3\\times D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909958
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.36', 'subgroup_hash': 36, 'subgroup_order': 300, 'subgroup_tex': 'C_3\\times D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62909959
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.40', 'subgroup_hash': 40, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909960
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.40', 'subgroup_hash': 40, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909961
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.40', 'subgroup_hash': 40, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909962
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.40', 'subgroup_hash': 40, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909963
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.40', 'subgroup_hash': 40, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909964
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.40', 'subgroup_hash': 40, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909965
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.40', 'subgroup_hash': 40, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909967
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.40', 'subgroup_hash': 40, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909968
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.30', 'subgroup_hash': 30, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909969
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909970
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909971
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909972
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909973
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909974
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909975
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.30', 'subgroup_hash': 30, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909976
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.v2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.v2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909978
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909979
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909980
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909981
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.30', 'subgroup_hash': 30, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909982
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909983
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909984
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909985
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909986
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.35', 'subgroup_hash': 35, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909987
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.34', 'subgroup_hash': 34, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909989
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.35', 'subgroup_hash': 35, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909990
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.35', 'subgroup_hash': 35, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909991
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.35', 'subgroup_hash': 35, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909992
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.23', 'subgroup_hash': 23, 'subgroup_order': 300, 'subgroup_tex': 'C_5^2:C_3:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62909993
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.19', 'subgroup_hash': 19, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:C_{20}', 'supersolvable': True, 'sylow': 0}
-
id: 62909994
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.32', 'subgroup_hash': 32, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:C_{20}', 'supersolvable': True, 'sylow': 0}
-
id: 62909995
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.33', 'subgroup_hash': 33, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62909996
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.37', 'subgroup_hash': 37, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62909997
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.47', 'subgroup_hash': 47, 'subgroup_order': 300, 'subgroup_tex': 'C_5\\times D_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62909998
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.37', 'subgroup_hash': 37, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910000
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.39', 'subgroup_hash': 39, 'subgroup_order': 300, 'subgroup_tex': 'D_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910001
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.40', 'subgroup_hash': 40, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910002
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.40', 'subgroup_hash': 40, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910003
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.540.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.39', 'subgroup_hash': 39, 'subgroup_order': 300, 'subgroup_tex': 'D_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910004
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.6', 'subgroup_hash': 6, 'subgroup_order': 270, 'subgroup_tex': 'D_5\\times \\He_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910005
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.7', 'subgroup_hash': 7, 'subgroup_order': 270, 'subgroup_tex': 'C_{45}:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910006
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.23', 'subgroup_hash': 23, 'subgroup_order': 270, 'subgroup_tex': 'D_5\\times C_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 62910007
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.23', 'subgroup_hash': 23, 'subgroup_order': 270, 'subgroup_tex': 'D_5\\times C_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 62910008
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.23', 'subgroup_hash': 23, 'subgroup_order': 270, 'subgroup_tex': 'D_5\\times C_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 62910009
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.23', 'subgroup_hash': 23, 'subgroup_order': 270, 'subgroup_tex': 'D_5\\times C_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 62910011
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.23', 'subgroup_hash': 23, 'subgroup_order': 270, 'subgroup_tex': 'D_5\\times C_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 62910012
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 27, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.26', 'subgroup_hash': 26, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62910013
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 27, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.26', 'subgroup_hash': 26, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62910014
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 27, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.26', 'subgroup_hash': 26, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62910015
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 27, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.27', 'subgroup_hash': 27, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910016
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 27, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.26', 'subgroup_hash': 26, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62910017
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 27, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.27', 'subgroup_hash': 27, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910018
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 27, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.27', 'subgroup_hash': 27, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910019
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 27, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.600.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '270.27', 'subgroup_hash': 27, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910020
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 250, 'counter': 379, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '162000.x.648.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '648.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '648.704', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 704, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^3:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '250.14', 'subgroup_hash': 14, 'subgroup_order': 250, 'subgroup_tex': 'C_5^3:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62910022
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 125, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.648.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '250.12', 'subgroup_hash': 12, 'subgroup_order': 250, 'subgroup_tex': 'D_5\\times C_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910023
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.648.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '250.13', 'subgroup_hash': 13, 'subgroup_order': 250, 'subgroup_tex': 'C_5^2:C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910024
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.675.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '675.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 675, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.96', 'subgroup_hash': 96, 'subgroup_order': 240, 'subgroup_tex': 'D_{30}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910025
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910026
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910027
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910028
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910029
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910030
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910031
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910033
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910034
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910035
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.5', 'subgroup_hash': 5, 'subgroup_order': 225, 'subgroup_tex': 'C_5^2:C_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 62910036
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.3', 'subgroup_hash': 3, 'subgroup_order': 225, 'subgroup_tex': 'C_5^2:C_9', 'supersolvable': False, 'sylow': 0}
-
id: 62910037
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910038
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910039
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910040
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910041
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910042
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910045
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910046
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910047
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910048
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910049
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910050
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910051
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910052
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910053
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910054
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910056
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910057
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910058
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910059
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910060
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910061
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.720.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '225.6', 'subgroup_hash': 6, 'subgroup_order': 225, 'subgroup_tex': 'C_{15}^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910062
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.750.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '750.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 750, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.120', 'subgroup_hash': 120, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910063
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.750.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '750.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 750, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910064
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.750.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '750.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 750, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910065
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.810.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.48', 'subgroup_hash': 48, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910067
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.810.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.23', 'subgroup_hash': 23, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}.D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910068
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.810.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.42', 'subgroup_hash': 42, 'subgroup_order': 200, 'subgroup_tex': 'D_5:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910069
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.810.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.41', 'subgroup_hash': 41, 'subgroup_order': 200, 'subgroup_tex': 'D_5\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910070
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.810.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '810.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.49', 'subgroup_hash': 49, 'subgroup_order': 200, 'subgroup_tex': 'D_5\\times D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910071
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910072
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910073
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910074
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910075
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910076
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910078
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910079
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910080
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.27', 'subgroup_hash': 27, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910081
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.27', 'subgroup_hash': 27, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910082
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.27', 'subgroup_hash': 27, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910083
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910084
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910085
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.27', 'subgroup_hash': 27, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910086
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910087
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910089
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910090
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910091
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910092
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910093
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910094
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910095
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.20', 'subgroup_hash': 20, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910096
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.20', 'subgroup_hash': 20, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910097
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.20', 'subgroup_hash': 20, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910098
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.20', 'subgroup_hash': 20, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910100
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.20', 'subgroup_hash': 20, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910101
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910102
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910103
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910104
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910105
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910106
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910107
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910108
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910109
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bi2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bi2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910111
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910112
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910113
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.23', 'subgroup_hash': 23, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2:C_{20}', 'supersolvable': False, 'sylow': 0}
-
id: 62910114
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.24', 'subgroup_hash': 24, 'subgroup_order': 180, 'subgroup_tex': '(C_3\\times C_{15}):C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910115
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910116
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.29', 'subgroup_hash': 29, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910117
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.30', 'subgroup_hash': 30, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910118
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.25', 'subgroup_hash': 25, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2:F_5', 'supersolvable': False, 'sylow': 0}
-
id: 62910119
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.29', 'subgroup_hash': 29, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910120
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.30', 'subgroup_hash': 30, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910122
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.900.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.29', 'subgroup_hash': 29, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910123
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1000.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1000.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.28', 'subgroup_hash': 28, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910124
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910125
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910126
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910127
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910128
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910129
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910130
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910131
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910133
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910134
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910135
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910136
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910137
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910138
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910139
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910140
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910141
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910142
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910144
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910145
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910146
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910147
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910148
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910149
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910150
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910151
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910152
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910153
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910156
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910157
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910158
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910159
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.6', 'subgroup_hash': 6, 'subgroup_order': 150, 'subgroup_tex': 'C_5^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 62910160
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.13', 'subgroup_hash': 13, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62910161
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.10', 'subgroup_hash': 10, 'subgroup_order': 150, 'subgroup_tex': 'S_3\\times C_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910162
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.10', 'subgroup_hash': 10, 'subgroup_order': 150, 'subgroup_tex': 'S_3\\times C_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910163
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910164
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910165
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910167
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910168
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910169
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910170
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910171
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910172
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910173
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910174
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910175
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910176
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910178
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910179
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910180
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910181
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910182
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910183
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910184
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910185
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910186
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910187
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910189
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.12', 'subgroup_hash': 12, 'subgroup_order': 150, 'subgroup_tex': 'C_5:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910190
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1080.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.12', 'subgroup_hash': 12, 'subgroup_order': 150, 'subgroup_tex': 'C_5:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910191
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1125.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1125.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1125, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.115', 'subgroup_hash': 115, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910192
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1200.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1200.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '135.3', 'subgroup_hash': 3, 'subgroup_order': 135, 'subgroup_tex': 'C_5\\times \\He_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910193
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1200.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1200.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '135.4', 'subgroup_hash': 4, 'subgroup_order': 135, 'subgroup_tex': 'C_9:C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910194
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 27, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1200.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1200.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '135.5', 'subgroup_hash': 5, 'subgroup_order': 135, 'subgroup_tex': 'C_3^2\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910195
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 27, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1200.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1200.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '135.5', 'subgroup_hash': 5, 'subgroup_order': 135, 'subgroup_tex': 'C_3^2\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910196
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 27, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1200.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1200.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '135.5', 'subgroup_hash': 5, 'subgroup_order': 135, 'subgroup_tex': 'C_3^2\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910197
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 27, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1200.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1200.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '135.5', 'subgroup_hash': 5, 'subgroup_order': 135, 'subgroup_tex': 'C_3^2\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910198
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 27, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1200.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1200.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '135.5', 'subgroup_hash': 5, 'subgroup_order': 135, 'subgroup_tex': 'C_3^2\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910200
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': True, 'core_order': 125, 'counter': 540, 'cyclic': False, 'direct': False, 'hall': 5, 'label': '162000.x.1296.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1296.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1296.3086', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3086, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1296, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_3^2\\times C_6).S_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '125.5', 'subgroup_hash': 5, 'subgroup_order': 125, 'subgroup_tex': 'C_5^3', 'supersolvable': True, 'sylow': 5}
-
id: 62910201
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1350.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1350.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1350, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910202
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1350.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1350.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1350, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.8', 'subgroup_hash': 8, 'subgroup_order': 120, 'subgroup_tex': 'C_6.D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910203
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1350.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1350.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1350, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910204
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1350.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1350.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1350, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910205
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1350.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1350.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1350, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910206
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1350.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1350.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1350, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.41', 'subgroup_hash': 41, 'subgroup_order': 120, 'subgroup_tex': 'C_{30}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910207
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1350.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1350.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1350, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910208
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1350.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1350.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1350, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910209
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1350.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1350.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1350, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910211
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1500.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1500.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910212
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1500.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1500.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.11', 'subgroup_hash': 11, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910213
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1500.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1500.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910214
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 27, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1500.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1500.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910215
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 27, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1500.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1500.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910216
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1500.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1500.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910217
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910218
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910219
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910220
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910222
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910223
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.e2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.e2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910224
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910225
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910226
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910227
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.6', 'subgroup_hash': 6, 'subgroup_order': 100, 'subgroup_tex': 'C_5:C_{20}', 'supersolvable': True, 'sylow': 0}
-
id: 62910228
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.9', 'subgroup_hash': 9, 'subgroup_order': 100, 'subgroup_tex': 'C_5\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910229
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.10', 'subgroup_hash': 10, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910230
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.14', 'subgroup_hash': 14, 'subgroup_order': 100, 'subgroup_tex': 'C_5\\times D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910231
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910233
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1620.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1620.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910234
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910235
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910236
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910237
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910238
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910239
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910240
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910241
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910242
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910244
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910245
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.2', 'subgroup_hash': 2, 'subgroup_order': 90, 'subgroup_tex': 'C_9\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910246
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910247
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910248
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910249
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910250
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910251
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910252
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910253
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910255
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910256
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910257
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910258
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910259
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910260
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910261
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910262
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910263
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910264
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910267
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910268
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910269
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910270
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910271
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910272
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910273
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910274
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910275
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910276
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910278
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910279
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910280
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910281
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910282
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910283
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910284
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910285
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.9', 'subgroup_hash': 9, 'subgroup_order': 90, 'subgroup_tex': 'C_3:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910286
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910287
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910289
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910290
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910291
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910292
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910293
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910294
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910295
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910296
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910297
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910298
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.9', 'subgroup_hash': 9, 'subgroup_order': 90, 'subgroup_tex': 'C_3:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910300
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.9', 'subgroup_hash': 9, 'subgroup_order': 90, 'subgroup_tex': 'C_3:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910301
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.1800.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.9', 'subgroup_hash': 9, 'subgroup_order': 90, 'subgroup_tex': 'C_3:D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910302
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 27, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '162000.x.2000.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2000.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.7', 'subgroup_hash': 7, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\wr C_3', 'supersolvable': True, 'sylow': 3}
-
id: 62910303
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2025.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2025.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2025, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.34', 'subgroup_hash': 34, 'subgroup_order': 80, 'subgroup_tex': 'D_{10}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910304
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910305
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910306
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910307
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910308
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910309
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910311
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910312
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910313
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910314
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910315
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910316
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910317
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910318
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910319
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6750, 'characteristic': False, 'core_order': 1, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910320
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910322
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910323
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910324
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910325
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910326
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910327
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910328
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910329
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910330
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910331
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910333
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910334
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910335
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910336
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910337
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910338
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2160.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.2', 'subgroup_hash': 2, 'subgroup_order': 75, 'subgroup_tex': 'C_5^2:C_3', 'supersolvable': False, 'sylow': 0}
-
id: 62910339
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2250.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2250.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2250, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910340
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2250.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2250.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2250, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910341
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2250.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2250.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2250, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910342
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2250.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2250.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2250, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910344
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910345
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910346
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910347
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910348
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910349
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910350
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910351
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910352
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910353
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910355
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910356
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910357
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910358
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910359
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910360
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910361
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910362
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910363
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910364
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910366
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910367
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910368
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910369
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910370
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.x2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.x2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910371
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910372
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910373
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910374
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910375
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910378
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910379
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910380
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910381
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910382
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910383
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910384
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910385
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
-
id: 62910386
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.3', 'subgroup_hash': 3, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910387
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910389
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910390
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910391
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910392
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62910393
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910394
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910395
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.2700.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2700.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62910396
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3000.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3000.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910397
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3000.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3000.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910398
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3000.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3000.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910400
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 27, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3000.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3000.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910401
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 27, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3000.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3000.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910402
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910403
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910404
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910405
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910406
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3240.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910407
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3240.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910408
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3240.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910409
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3240.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910411
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3240.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910412
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3240.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910413
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3240.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910414
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3240.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910415
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3240.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3240.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910416
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3375.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3375.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3375, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910417
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3375.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3375.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3375, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910418
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910419
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910420
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910422
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910423
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910424
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910425
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910426
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910427
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910428
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 1, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910429
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 1, 'counter': 747, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.3600.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.1', 'subgroup_hash': 1, 'subgroup_order': 45, 'subgroup_tex': 'C_{45}', 'supersolvable': True, 'sylow': 0}
-
id: 62910430
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910431
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910433
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910434
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910435
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910436
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910437
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910438
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910439
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910440
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910441
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910442
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910444
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910445
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910446
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910447
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910448
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910449
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910450
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910451
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910452
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910453
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.3600.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910455
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4050.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4050.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4050, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910456
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4050.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4050.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4050, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910457
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4050.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4050.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4050, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910458
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4050.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4050.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4050, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910459
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4050.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4050.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4050, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910460
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4500.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4500.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910461
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4500.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4500.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910462
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4500.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4500.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910463
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4500.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4500.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910464
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4500.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4500.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910466
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4500.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4500.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910467
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4500.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4500.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910468
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4500.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4500.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910469
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4500.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4500.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910470
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4500.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4500.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910471
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4500.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4500.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910472
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.4500.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4500.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910473
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910474
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910475
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910477
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910478
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910479
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910480
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910481
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910482
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910483
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910484
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910485
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910486
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910489
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910490
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910491
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910492
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910493
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910494
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910495
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910496
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910497
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910498
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910500
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910501
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910502
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910503
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910504
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910505
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910506
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910507
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910508
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910509
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 819, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62910511
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 820, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62910512
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 821, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62910513
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910514
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910515
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910516
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910517
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910518
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910519
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910520
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910522
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910523
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910524
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910525
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 833, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 62910526
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910527
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910528
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910529
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910530
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910531
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910533
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910534
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910535
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910536
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910537
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910538
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910539
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.5400.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5400.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910540
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6750, 'characteristic': True, 'core_order': 27, 'counter': 847, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '162000.x.6000.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '6000.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6000.bm', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7537202592292727862, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 6000, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_5^3.S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 62910541
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6000.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6000.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910542
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6000.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6000.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910544
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910545
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6480.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910546
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6750, 'characteristic': False, 'core_order': 1, 'counter': 852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6480.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910547
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6480.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910548
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6480.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910549
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6750.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6750.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6750, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910550
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6750.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6750.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6750, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910551
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6750.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6750.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6750, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910552
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6750.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6750.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6750, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910553
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.6750.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6750.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6750, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910555
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8100.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910556
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8100.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910557
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8100.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910558
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8100.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910559
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8100.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910560
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8100.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910561
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8100.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910562
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.g2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8100.g2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910563
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8100.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910564
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 869, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.8100.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8100.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
-
id: 62910566
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8100.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910567
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8100.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910568
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8100.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910569
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8100.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910570
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.8100.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8100.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910571
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.9000.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9000.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910572
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.9000.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9000.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910573
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 877, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.9000.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9000.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
-
id: 62910574
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.9000.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9000.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910575
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.9000.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9000.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910577
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 300, 'characteristic': False, 'core_order': 1, 'counter': 880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.9000.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9000.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910578
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.9000.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9000.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910579
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.9000.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9000.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910580
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.9000.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9000.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910581
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.9000.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9000.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910582
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.9000.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9000.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910583
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 886, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '162000.x.10125.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10125.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10125, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 2}
-
id: 62910584
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 887, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910585
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 888, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910586
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10125, 'characteristic': False, 'core_order': 1, 'counter': 889, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910588
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 890, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910589
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 891, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910590
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 892, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910591
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 893, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910592
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 894, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910593
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 895, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910594
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6750, 'characteristic': False, 'core_order': 1, 'counter': 896, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910595
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6750, 'characteristic': False, 'core_order': 1, 'counter': 897, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910596
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6750, 'characteristic': False, 'core_order': 1, 'counter': 898, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910597
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 899, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910600
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 900, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910601
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6750, 'characteristic': False, 'core_order': 1, 'counter': 901, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910602
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 902, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910603
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 903, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910604
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 904, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910605
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 905, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910606
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 906, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910607
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 907, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910608
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 908, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910609
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 909, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910611
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 910, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910612
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 911, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910613
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 912, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910614
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 913, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910615
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 914, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910616
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 915, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910617
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 916, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910618
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 917, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910619
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 1, 'counter': 918, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.10800.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 62910620
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.13500.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '13500.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910622
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.13500.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '13500.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910623
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.13500.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '13500.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910624
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 922, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.13500.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '13500.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910625
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 923, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.13500.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '13500.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910626
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 924, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.13500.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '13500.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 62910627
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.13500.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '13500.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910628
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.13500.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '13500.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910629
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.13500.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '13500.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910630
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.13500.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '13500.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910631
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.13500.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '13500.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910633
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.13500.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '13500.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 62910634
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.13500.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '13500.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910635
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.16200.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16200.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910636
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.16200.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16200.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910637
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.16200.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16200.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910638
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.16200.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16200.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910639
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.16200.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16200.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910640
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 300, 'characteristic': False, 'core_order': 1, 'counter': 937, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.16200.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16200.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910641
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 300, 'characteristic': False, 'core_order': 1, 'counter': 938, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.16200.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16200.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910642
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 939, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.16200.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16200.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910644
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 300, 'characteristic': False, 'core_order': 1, 'counter': 940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.16200.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16200.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910645
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 941, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.16200.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16200.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 62910646
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.16200.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16200.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910647
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.16200.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16200.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910648
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.16200.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16200.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910649
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6750, 'characteristic': False, 'core_order': 1, 'counter': 945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.18000.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18000.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910650
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.18000.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18000.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910651
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 947, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.18000.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18000.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
-
id: 62910652
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 13500, 'characteristic': False, 'core_order': 1, 'counter': 948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.18000.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18000.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910653
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6750, 'characteristic': False, 'core_order': 1, 'counter': 949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.18000.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18000.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910655
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.20250.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20250.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20250, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910656
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.20250.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20250.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20250, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910657
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.20250.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20250.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20250, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 62910658
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 953, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.27000.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27000.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910659
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 954, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.27000.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27000.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910660
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 955, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.27000.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27000.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910661
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 956, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.27000.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27000.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910662
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 600, 'characteristic': False, 'core_order': 1, 'counter': 957, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.27000.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27000.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910663
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 300, 'characteristic': False, 'core_order': 1, 'counter': 958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.27000.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27000.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910664
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 300, 'characteristic': False, 'core_order': 1, 'counter': 959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.27000.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27000.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910666
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 960, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.27000.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27000.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 62910667
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.27000.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27000.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910668
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.27000.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27000.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910669
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 13500, 'characteristic': False, 'core_order': 1, 'counter': 963, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.32400.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32400.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910670
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 13500, 'characteristic': False, 'core_order': 1, 'counter': 964, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.32400.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32400.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910671
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 10125, 'characteristic': False, 'core_order': 1, 'counter': 965, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.32400.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32400.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910672
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6750, 'characteristic': False, 'core_order': 1, 'counter': 966, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.32400.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32400.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910673
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3375, 'characteristic': False, 'core_order': 1, 'counter': 967, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.32400.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32400.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
-
id: 62910674
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.40500.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40500.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910675
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 969, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.40500.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40500.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910677
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 970, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.40500.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40500.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 62910678
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.40500.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40500.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910679
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.x.40500.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40500.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 62910680
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 40500, 'characteristic': False, 'core_order': 1, 'counter': 973, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.54000.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54000.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910681
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27000, 'characteristic': False, 'core_order': 1, 'counter': 974, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.54000.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54000.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910682
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 13500, 'characteristic': False, 'core_order': 1, 'counter': 975, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.54000.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54000.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910683
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 976, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.54000.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54000.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
-
id: 62910684
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': False, 'core_order': 1, 'counter': 977, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.81000.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81000.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62910685
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1200, 'characteristic': False, 'core_order': 1, 'counter': 978, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.81000.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81000.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62910686
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 979, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '162000.x.81000.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81000.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 62910688
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '162000.x', 'ambient_counter': 24, 'ambient_order': 162000, 'ambient_tex': '(C_{15}^3.A_4):C_4', 'central': True, 'central_factor': False, 'centralizer_order': 162000, 'characteristic': True, 'core_order': 1, 'counter': 980, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '162000.x.162000.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162000.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '162000.x', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 242777464014375236, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 162000, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_{15}^3.A_4):C_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D4', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
-
gps_subgroup_data • Show schema
Hide schema
-
id: 62909710
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': ['162000.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '4.b1.a1', '27.a1.a1', '125.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [129744, 32400, 108000, 2, 480, 65100, 7200, 1, 82888, 75240, 66960], 'label': '162000.x.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '162000.x'}
-
id: 62909711
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.b1.a1', '18.c1.a1', '18.d1.a1', '45.a1.a1', '81.a1.a1', '225.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [32400, 2160, 125640, 108000, 119340, 97344, 7201, 2, 108480], 'label': '162000.x.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909712
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.c1.a1', '54.c1.a1'], 'contains': ['216.c1.a1', '216.g1.a1', '216.j1.a1', '324.a1.a1', '540.c1.a1', '540.k1.a1', '540.l1.a1', '540.m1.a1', '540.n1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10862, 32400, 54480, 97344, 119340, 66960], 'label': '162000.x.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909713
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.e1.a1', '36.f1.a1'], 'contains': ['216.a1.a1', '324.b1.a1', '540.o1.a1', '540.p1.a1', '540.q1.a1', '540.r1.a1', '540.s1.a1', '540.t1.a1', '540.u1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10503, 32400, 10862, 97344, 112080, 99360], 'label': '162000.x.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.f1.a1', 'old_label': '108.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.a1', 'subgroup_fusion': None, 'weyl_group': '500.49'}
-
id: 62909714
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.g1.a1', '54.a1.a1'], 'contains': ['216.b1.a1', '324.b1.a1', '540.v1.a1', '540.v2.a1', '540.w1.a1', '540.x1.a1', '540.y1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10503, 32400, 10862, 97344, 7200, 99360], 'label': '162000.x.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '108.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1000.170'}
-
id: 62909715
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.h1.a1', '54.c1.a1'], 'contains': ['216.c1.a1', '324.b1.a1', '540.z1.a1', '540.ba1.a1', '540.bb1.a1', '540.bc1.a1', '540.bd1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10503, 32400, 10862, 97344, 108480, 99360], 'label': '162000.x.108.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '108.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1000.170'}
-
id: 62909716
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.g1.a1', '36.h1.a1', '54.c1.a1'], 'contains': ['216.c1.a1', '324.b1.a1', '540.be1.a1', '540.bf1.a1', '540.bg1.a1', '540.bh1.a1', '540.bi1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10503, 32400, 54480, 97344, 10862, 99360], 'label': '162000.x.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '108.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909717
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '36.e1.a1'], 'contains': ['216.d1.a1', '324.b1.a1', '540.bj1.a1', '2700.bj1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [75483, 66960, 25768, 32400, 10862, 32544], 'label': '162000.x.108.h1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1.a1', 'old_label': '108.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1500.115'}
-
id: 62909718
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '54.b1.a1'], 'contains': ['216.e1.a1', '324.c1.a1', '540.bk1.a1', '540.bl1.a1', '540.bm1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 2160, 2, 7200, 32400, 97344], 'label': '162000.x.108.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1.a1', 'old_label': '108.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.a1', 'subgroup_fusion': None, 'weyl_group': '600.166'}
-
id: 62909719
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '36.k1.a1', '54.e1.a1'], 'contains': ['216.e1.a1', '216.f1.a1', '216.i1.a1', '324.d1.a1', '540.bn1.a1', '540.bo1.a1', '540.bq1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [17642, 32400, 66960, 480, 11340, 97344], 'label': '162000.x.108.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1.a1', 'old_label': '108.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.a1', 'subgroup_fusion': None, 'weyl_group': '600.174'}
-
id: 62909720
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '54.e1.a1'], 'contains': ['216.f1.a1', '216.h1.a1', '324.d1.a1', '540.bp1.a1', '540.br1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [17882, 32400, 66960, 7200, 11100, 97344], 'label': '162000.x.108.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '108.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1200.607'}
-
id: 62909721
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '54.d1.a1'], 'contains': ['324.e1.a1', '432.d1.a1', '13500.l1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [83128, 32400, 14040, 8784, 3300, 131760], 'label': '162000.x.108.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6000.bm'}
-
id: 62909722
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': ['13500.h1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['24.e1.a1', '36.l1.a1', '60.o1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [11100, 108000, 66960, 480, 97344, 32400, 125640, 7200], 'label': '162000.x.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': '12.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '162000.x'}
-
id: 62909723
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '54.e1.a1'], 'contains': ['216.h1.a1', '216.i1.a1', '324.e1.a1', '540.bs1.a1', '540.bt1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [119340, 32400, 480, 97344, 125640, 66960], 'label': '162000.x.108.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '108.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909724
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.a1.a1', '60.e1.a1'], 'contains': ['240.a1.a1', '360.i1.a1', '360.j1.a1', '3000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [10862, 66960, 61200, 58080, 25768, 32544], 'label': '162000.x.120.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2700.o'}
-
id: 62909725
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '40.a1.a1'], 'contains': ['240.b1.a1', '360.i1.a1', '360.k1.a1', '3000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': None, 'generators': [10862, 66960, 61200, 58080, 25288, 32544], 'label': '162000.x.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.a1.a1', 'old_label': '120.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1350.51'}
-
id: 62909726
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.b1.a1'], 'contains': ['240.c1.a1', '360.a1.a1', '360.l1.a1', '360.m1.a1', '360.y1.a1', '360.z1.a1', '600.c1.a1', '600.d1.a1', '600.g1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 2160, 7200, 108000, 480, 97344], 'label': '162000.x.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '120.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.a1', 'subgroup_fusion': None, 'weyl_group': '200.41'}
-
id: 62909727
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.c1.a1', '60.f1.a1', '60.f2.a1'], 'contains': ['240.d1.a1', '360.b1.a1', '360.c1.a1', '360.n1.a1', '360.o1.a1', '360.p1.a1', '360.ba1.a1', '360.bb1.a1', '600.c1.a1', '600.e1.a1', '600.f1.a1', '600.g1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 66960, 7200, 108000, 480, 144], 'label': '162000.x.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '120.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62909728
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.a1.a1', '60.d1.a1', '60.g1.a1'], 'contains': ['240.e1.a1', '360.d1.a1', '360.q1.a1', '360.r1.a1', '360.bc1.a1', '360.bd1.a1', '600.c1.a1', '600.d1.a1', '600.f1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [10862, 32400, 7200, 108000, 480, 97344], 'label': '162000.x.120.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.a1', 'subgroup_fusion': None, 'weyl_group': '400.129'}
-
id: 62909729
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.h1.a1'], 'contains': ['240.f1.a1', '360.e1.a1', '360.f1.a1', '360.g1.a1', '360.s1.a1', '360.t1.a1', '360.u1.a1', '360.v1.a1', '360.be1.a1', '360.bf1.a1', '600.d1.a1', '600.e1.a1', '600.f1.a1', '600.g1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 66960, 7200, 108000, 480, 97344], 'label': '162000.x.120.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '120.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909730
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.a1.a1', '60.i1.a1'], 'contains': ['240.g1.a1', '360.h1.a1', '360.i1.a1', '360.w1.a1', '360.x1.a1', '360.bg1.a1', '600.f1.a1', '600.g1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [10862, 66960, 61200, 108000, 7680, 32544], 'label': '162000.x.120.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '120.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.g1.a1', 'subgroup_fusion': None, 'weyl_group': '300.23'}
-
id: 62909731
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '60.a1.a1', '60.j1.a1', '60.m1.a1'], 'contains': ['240.e1.a1', '360.bh1.a1', '360.bi1.a1', '360.bj1.a1', '600.h1.a1', '600.i1.a1', '600.j1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [2, 108000, 97344, 32400, 7200, 480], 'label': '162000.x.120.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.h1.a1', 'subgroup_fusion': None, 'weyl_group': '144.115'}
-
id: 62909732
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '60.b1.a1', '60.k1.a1', '60.l1.a1'], 'contains': ['240.c1.a1', '360.bk1.a1', '360.bo1.a1', '360.bs1.a1', '600.i1.a1', '600.k1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2, 2160, 97344, 480, 7200, 108000], 'label': '162000.x.120.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '120.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.i1.a1', 'subgroup_fusion': None, 'weyl_group': '360.131'}
-
id: 62909733
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.e1.a1', '36.a1.a1', '36.b1.a1', '36.c1.a1', '60.a1.a1', '60.b1.a1', '60.c1.a1', '60.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 108000, 2160, 7200, 97344, 32400, 11100, 480], 'label': '162000.x.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909734
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '60.c1.a1'], 'contains': ['240.d1.a1', '360.bl1.a1', '360.bm1.a1', '360.bp1.a1', '360.bt1.a1', '600.j1.a1', '600.k1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2, 2160, 32544, 480, 7200, 108000], 'label': '162000.x.120.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '120.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.a1', 'subgroup_fusion': None, 'weyl_group': '360.129'}
-
id: 62909735
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '60.d1.a1', '60.m1.a1', '60.n1.a1'], 'contains': ['240.e1.a1', '360.bn1.a1', '360.bq1.a1', '360.br1.a1', '360.bu1.a1', '600.h1.a1', '600.k1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2, 2160, 32400, 480, 7200, 108000], 'label': '162000.x.120.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '120.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.k1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62909736
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '60.b1.a1'], 'contains': ['240.c1.a1', '360.bv1.a1', '360.bz1.a1', '360.cd1.a1', '600.l1.a1', '600.n1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [11100, 97344, 2160, 480, 7200, 108000], 'label': '162000.x.120.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '120.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.l1.a1', 'subgroup_fusion': None, 'weyl_group': '360.130'}
-
id: 62909737
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '60.c1.a1'], 'contains': ['240.d1.a1', '360.bw1.a1', '360.bx1.a1', '360.ca1.a1', '360.ce1.a1', '600.l1.a1', '600.o1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [11100, 32544, 2160, 480, 7200, 108000], 'label': '162000.x.120.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '120.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.m1.a1', 'subgroup_fusion': None, 'weyl_group': '360.129'}
-
id: 62909738
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '60.d1.a1', '60.m1.a1', '60.o1.a1'], 'contains': ['240.e1.a1', '360.by1.a1', '360.cb1.a1', '360.cc1.a1', '360.cf1.a1', '600.l1.a1', '600.m1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [11100, 32400, 66960, 480, 7200, 108000], 'label': '162000.x.120.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1.a1', 'old_label': '120.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.n1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62909739
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '60.a1.a1', '60.n1.a1', '60.o1.a1'], 'contains': ['240.e1.a1', '360.cg1.a1', '360.ch1.a1', '360.ci1.a1', '600.m1.a1', '600.n1.a1', '600.o1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [11100, 32400, 480, 108000, 7200, 97344], 'label': '162000.x.120.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62909740
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '125.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['250.a1.a1', '375.a1.a1', '500.a1.a1', '3375.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': None, 'generators': [1, 125640, 480, 2, 119340, 108000, 7200, 161488], 'label': '162000.x.125.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '125.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '125.a1.a1', 'subgroup_fusion': None, 'weyl_group': '648.704'}
-
id: 62909741
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '135.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '27.b1.a1'], 'contains': ['270.a1.a1', '270.b1.a1', '270.i1.a1', '405.a1.a1', '3375.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 135, 'diagramx': None, 'generators': [108001, 97344, 108482, 119340, 125640, 32400, 7200], 'label': '162000.x.135.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1.a1', 'old_label': '135.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '135.a1.a1', 'subgroup_fusion': None, 'weyl_group': '600.170'}
-
id: 62909742
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '144.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '72.a1.a1'], 'contains': ['432.a1.a1', '432.c1.a1', '720.a1.a1', '720.b1.a1', '720.c1.a1', '720.d1.a1', '720.e1.a1', '720.f1.a1', '720.g1.a1', '720.h1.a1', '720.i1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [115680, 97344, 66960, 61200, 32400], 'label': '162000.x.144.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '144.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.1'}
-
id: 62909743
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '72.b1.a1'], 'contains': ['432.a1.a1', '432.d1.a1', '720.j1.a1', '3600.j1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25768, 32400, 32544, 58080, 66960], 'label': '162000.x.144.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '144.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '900.90'}
-
id: 62909744
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['24.b1.a1', '36.d1.a1', '36.e1.a1', '60.e1.a1', '300.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [75483, 32400, 32544, 25768, 58080, 66960, 10862, 61200], 'label': '162000.x.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '12.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '13500.e'}
-
id: 62909745
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '72.c1.a1'], 'contains': ['432.a1.a1', '720.k1.a1', '3600.k1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25288, 58080, 32544, 32400, 66960], 'label': '162000.x.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '144.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '450.22'}
-
id: 62909746
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.d1.a1', '72.f1.a1', '72.i1.a1'], 'contains': ['432.a1.a1', '432.b1.a1', '432.c1.a1', '720.l1.a1', '720.m1.a1', '720.n1.a1', '720.o1.a1', '720.p1.a1', '720.q1.a1', '720.r1.a1', '720.s1.a1', '720.t1.a1', '720.u1.a1', '720.v1.a1', '720.w1.a1', '720.x1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 97344, 66960, 61200, 32400], 'label': '162000.x.144.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '144.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62909747
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.e1.a1', '72.g1.a1', '72.h1.a1', '72.j1.a1', '72.k1.a1'], 'contains': ['432.b1.a1', '432.c1.a1', '720.y1.a1', '720.z1.a1', '720.ba1.a1', '720.bb1.a1', '720.bc1.a1', '720.bd1.a1', '720.be1.a1', '720.bf1.a1', '720.bg1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [480, 97344, 66960, 7200, 32400], 'label': '162000.x.144.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
-
id: 62909748
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '150.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.c1.a1'], 'contains': ['300.c1.a1', '300.h1.a1', '300.h2.a1', '450.a1.a1', '450.b1.a1', '450.c1.a1', '750.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10503, 108000, 7200, 10862, 11100, 32544, 54480], 'label': '162000.x.150.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '150.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.a1.a1', 'subgroup_fusion': None, 'weyl_group': '360.129'}
-
id: 62909749
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '150.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '30.d1.a1'], 'contains': ['300.b1.a1', '300.j1.a1', '300.k1.a1', '450.d1.a1', '750.b1.a1', '1350.b1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [1, 108000, 2, 108480, 11100, 97344, 7200], 'label': '162000.x.150.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.a1', 'old_label': '150.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1080.513'}
-
id: 62909750
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '150.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1', '75.a1.a1'], 'contains': ['300.d1.a1', '300.f1.a1', '450.e1.a1', '450.g1.a1', '750.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [10503, 108000, 7200, 10862, 11100, 2160, 54480], 'label': '162000.x.150.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '150.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.c1.a1', 'subgroup_fusion': None, 'weyl_group': '720.774'}
-
id: 62909751
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '150.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.a1', '75.a1.a1'], 'contains': ['300.d1.a1', '300.m1.a1', '450.h1.a1', '750.b1.a1', '1350.f1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [1, 108000, 2, 108480, 11100, 2160, 7200], 'label': '162000.x.150.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '150.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2160.fi'}
-
id: 62909752
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '150.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.a1', '75.a1.a1'], 'contains': ['300.a1.a1', '300.d1.a1', '300.l1.a1', '300.n1.a1', '300.o1.a1', '450.f1.a1', '450.i1.a1', '750.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [17642, 108000, 125640, 480, 7140, 32400, 7200], 'label': '162000.x.150.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '150.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2160.fi'}
-
id: 62909753
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.c1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.b1.a1', '810.a1.a1', '810.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [64263, 32400, 10862, 97344, 11100, 99360], 'label': '162000.x.162.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '162.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2000.905'}
-
id: 62909754
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '54.b1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.c1.a1', '810.b1.a1', '810.d1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1, 32400, 2, 97344, 10860, 2160], 'label': '162000.x.162.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2000.905'}
-
id: 62909755
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '36.d1.a1', '36.f1.a1', '36.g1.a1', '36.h1.a1', '60.f1.a1', '60.f2.a1', '60.g1.a1', '60.h1.a1', '60.i1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10503, 54480, 99360, 108000, 97344, 32400, 7200, 10862], 'label': '162000.x.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909756
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.d1.a1', '54.e1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.d1.a1', '324.e1.a1', '810.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [108242, 32400, 125640, 97344, 119100, 2160], 'label': '162000.x.162.c1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6000.bm'}
-
id: 62909757
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.a1.a1', '90.a1.a1'], 'contains': ['360.r1.a1', '360.bh1.a1', '360.cg1.a1', '540.a1.a1', '540.c1.a1', '900.a1.a1', '900.b1.a1', '900.c1.a1', '900.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10862, 32400, 7200, 54480, 119340, 97344], 'label': '162000.x.180.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.a1.a1', 'subgroup_fusion': None, 'weyl_group': '600.161'}
-
id: 62909758
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.a1.a1', '90.i1.a1'], 'contains': ['360.bc1.a1', '360.bi1.a1', '360.ch1.a1', '540.a1.a1', '540.b1.a1', '900.e1.a1', '900.f1.a1', '900.g1.a1', '900.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 32400, 7200, 480, 11340, 97344], 'label': '162000.x.180.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '180.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.b1.a1', 'subgroup_fusion': None, 'weyl_group': '600.174'}
-
id: 62909777
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.d1.a1', '24.e1.a1', '36.i1.a1', '36.k1.a1', '60.m1.a1', '60.n1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [17402, 7200, 97344, 66960, 108000, 32400, 11100, 480], 'label': '162000.x.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909759
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.a1.a1', '90.b1.a1', '90.c1.a1', '90.f1.a1'], 'contains': ['360.bd1.a1', '360.bj1.a1', '360.ci1.a1', '540.b1.a1', '540.c1.a1', '900.i1.a1', '900.j1.a1', '900.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [2, 32400, 108480, 108000, 119340, 97344], 'label': '162000.x.180.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '180.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62909760
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.b1.a1'], 'contains': ['360.l1.a1', '360.bk1.a1', '360.bv1.a1', '540.d1.a1', '540.k1.a1', '900.b1.a1', '900.l1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10862, 2160, 7200, 54480, 119340, 97344], 'label': '162000.x.180.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.d1.a1', 'old_label': '180.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.d1.a1', 'subgroup_fusion': None, 'weyl_group': '300.40'}
-
id: 62909761
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.c1.a1', '90.d1.a1'], 'contains': ['360.o1.a1', '360.bl1.a1', '360.bw1.a1', '540.e1.a1', '540.l1.a1', '900.c1.a1', '900.l1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10862, 2160, 7200, 54480, 119340, 129744], 'label': '162000.x.180.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.d1.a1', 'old_label': '180.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.e1.a1', 'subgroup_fusion': None, 'weyl_group': '600.163'}
-
id: 62909762
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.c1.a1', '90.e1.a1'], 'contains': ['360.p1.a1', '360.bm1.a1', '360.bx1.a1', '540.e1.a1', '540.m1.a1', '900.d1.a1', '900.l1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10862, 2160, 7200, 54480, 119340, 32544], 'label': '162000.x.180.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1.a1', 'old_label': '180.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.f1.a1', 'subgroup_fusion': None, 'weyl_group': '600.164'}
-
id: 62909763
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.d1.a1'], 'contains': ['360.q1.a1', '360.bn1.a1', '360.by1.a1', '540.f1.a1', '540.n1.a1', '900.a1.a1', '900.l1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10862, 32400, 7200, 54480, 119340, 66960], 'label': '162000.x.180.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.g1.a1', 'old_label': '180.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.g1.a1', 'subgroup_fusion': None, 'weyl_group': '300.40'}
-
id: 62909764
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.b1.a1'], 'contains': ['360.y1.a1', '360.bo1.a1', '360.bz1.a1', '540.d1.a1', '540.g1.a1', '900.g1.a1', '900.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [2, 2160, 7200, 480, 11340, 97344], 'label': '162000.x.180.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.h1.a1', 'old_label': '180.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.h1.a1', 'subgroup_fusion': None, 'weyl_group': '300.40'}
-
id: 62909765
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.c1.a1'], 'contains': ['360.ba1.a1', '360.bp1.a1', '360.ca1.a1', '540.e1.a1', '540.h1.a1', '900.h1.a1', '900.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [2, 2160, 7200, 480, 11340, 32544], 'label': '162000.x.180.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.i1.a1', 'old_label': '180.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.i1.a1', 'subgroup_fusion': None, 'weyl_group': '300.40'}
-
id: 62909766
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['24.d1.a1', '36.j1.a1', '60.j1.a1', '60.k1.a1', '60.l1.a1', '108.i1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 7200, 97344, 2, 108000, 2160, 32400, 108480], 'label': '162000.x.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909767
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.d1.a1', '90.i1.a1'], 'contains': ['360.bc1.a1', '360.bq1.a1', '360.cb1.a1', '540.f1.a1', '540.j1.a1', '900.f1.a1', '900.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 32400, 7200, 480, 11340, 2160], 'label': '162000.x.180.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '180.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.j1.a1', 'subgroup_fusion': None, 'weyl_group': '600.196'}
-
id: 62909768
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.d1.a1', '90.f1.a1'], 'contains': ['360.bd1.a1', '360.br1.a1', '360.cc1.a1', '540.f1.a1', '540.i1.a1', '900.e1.a1', '900.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 2160, 7200, 480, 11340, 144], 'label': '162000.x.180.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1.a1', 'old_label': '180.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.k1.a1', 'subgroup_fusion': None, 'weyl_group': '600.174'}
-
id: 62909769
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.b1.a1', '90.h1.a1'], 'contains': ['360.z1.a1', '360.bs1.a1', '360.cd1.a1', '540.g1.a1', '540.k1.a1', '900.j1.a1', '900.n1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [2, 2160, 108480, 108000, 119340, 97344], 'label': '162000.x.180.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '180.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.646'}
-
id: 62909770
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.c1.a1', '90.g1.a1'], 'contains': ['360.bb1.a1', '360.bt1.a1', '360.ce1.a1', '540.h1.a1', '540.l1.a1', '540.m1.a1', '900.k1.a1', '900.n1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 2160, 108480, 108000, 119340, 32544], 'label': '162000.x.180.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '180.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.632'}
-
id: 62909771
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.d1.a1', '90.i1.a1'], 'contains': ['360.bc1.a1', '360.bu1.a1', '360.cf1.a1', '540.i1.a1', '540.j1.a1', '540.n1.a1', '900.i1.a1', '900.n1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [2, 32400, 108480, 108000, 119340, 2160], 'label': '162000.x.180.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1.a1', 'old_label': '180.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.679'}
-
id: 62909772
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '60.f1.a1'], 'contains': ['360.b1.a1', '540.o1.a1', '540.bf1.a1', '900.o1.a1', '900.p1.a1', '900.q1.a1', '900.s1.a1', '900.t1.a1', '900.u1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 2160, 10862, 54480, 61200, 32544], 'label': '162000.x.180.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.f1.a1', 'old_label': '180.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.o1.a1', 'subgroup_fusion': None, 'weyl_group': '300.34'}
-
id: 62909773
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '60.f2.a1'], 'contains': ['360.c1.a1', '540.p1.a1', '540.be1.a1', '900.o1.a1', '900.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 2160, 10862, 54480, 61200, 129744], 'label': '162000.x.180.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.f2.a1', 'old_label': '180.p1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.p1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62909774
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '60.g1.a1'], 'contains': ['360.d1.a1', '540.q1.a1', '540.bg1.a1', '900.r1.a1', '900.s1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 32400, 10862, 54480, 61200, 97344], 'label': '162000.x.180.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.g1.a1', 'old_label': '180.q1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.q1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62909775
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '60.h1.a1'], 'contains': ['360.e1.a1', '540.r1.a1', '540.bh1.a1', '900.p1.a1', '900.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 34560, 10862, 54480, 61200, 129744], 'label': '162000.x.180.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '180.r1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.r1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62909776
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '60.h1.a1'], 'contains': ['360.f1.a1', '540.s1.a1', '540.bh1.a1', '900.q1.a1', '900.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 131760, 10862, 54480, 61200, 129744], 'label': '162000.x.180.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '180.s1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.s1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62909778
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '60.i1.a1'], 'contains': ['360.h1.a1', '540.u1.a1', '540.bi1.a1', '900.r1.a1', '900.u1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 99360, 10862, 54480, 61200, 129744], 'label': '162000.x.180.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '180.t1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.t1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62909779
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '60.e1.a1', '60.i1.a1'], 'contains': ['360.i1.a1', '540.t1.a1', '540.bi1.a1', '900.r1.a1', '900.t1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 66960, 10862, 54480, 61200, 129744], 'label': '162000.x.180.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '180.u1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.u1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62909780
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '60.e1.a1'], 'contains': ['360.j1.a1', '540.t1.a1', '540.bj1.a1', '4500.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [75483, 66960, 10862, 25768, 58080, 138384], 'label': '162000.x.180.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.v1.a1', 'old_label': '180.v1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.v1.a1', 'subgroup_fusion': None, 'weyl_group': '300.23'}
-
id: 62909781
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '60.f1.a1', '90.d1.a1'], 'contains': ['360.o1.a1', '540.o1.a1', '540.v1.a1', '540.z1.a1', '900.w1.a1', '900.x1.a1', '900.y1.a1', '900.ba1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10503, 2160, 7200, 10862, 108480, 32544], 'label': '162000.x.180.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.d1.a1', 'old_label': '180.w1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.w1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62909782
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '60.f2.a1', '90.e1.a1'], 'contains': ['360.p1.a1', '540.p1.a1', '540.v2.a1', '540.ba1.a1', '900.w1.a1', '900.z1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10503, 2160, 7200, 10862, 108480, 129744], 'label': '162000.x.180.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1.a1', 'old_label': '180.x1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.x1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62909783
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '60.g1.a1', '90.a1.a1'], 'contains': ['360.r1.a1', '540.q1.a1', '540.w1.a1', '540.bb1.a1', '900.y1.a1', '900.z1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10503, 32400, 7200, 10862, 108480, 97344], 'label': '162000.x.180.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.y1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.y1.a1', 'subgroup_fusion': None, 'weyl_group': '200.48'}
-
id: 62909784
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '60.h1.a1'], 'contains': ['360.t1.a1', '540.r1.a1', '540.s1.a1', '540.x1.a1', '540.bc1.a1', '900.x1.a1', '900.z1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 131760, 7200, 10862, 108480, 129744], 'label': '162000.x.180.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.z1.a1', 'old_label': '180.z1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.z1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909785
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '60.i1.a1'], 'contains': ['360.x1.a1', '540.t1.a1', '540.u1.a1', '540.y1.a1', '540.bd1.a1', '900.z1.a1', '900.ba1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 66960, 7200, 10862, 108480, 129744], 'label': '162000.x.180.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.ba1.a1', 'old_label': '180.ba1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909786
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '60.f2.a1', '90.d1.a1'], 'contains': ['360.o1.a1', '540.v2.a1', '540.be1.a1', '900.bb1.a1', '900.bd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10503, 2160, 10862, 54480, 7200, 129744], 'label': '162000.x.180.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '180.bb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '600.163'}
-
id: 62909787
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '60.f1.a1', '90.e1.a1'], 'contains': ['360.p1.a1', '540.v1.a1', '540.bf1.a1', '900.bb1.a1', '900.bc1.a1', '900.be1.a1', '900.bf1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10503, 2160, 10862, 54480, 7200, 32544], 'label': '162000.x.180.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '180.bc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '600.164'}
-
id: 62909788
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.e1.a1', '45.a1.a1', '135.a1.a1', '375.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [32400, 97344, 125640, 7200, 119340, 108000, 1, 2, 108480], 'label': '162000.x.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909789
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '60.g1.a1', '90.a1.a1'], 'contains': ['360.r1.a1', '540.w1.a1', '540.bg1.a1', '900.bd1.a1', '900.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10503, 32400, 10862, 54480, 7200, 97344], 'label': '162000.x.180.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '180.bd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '600.161'}
-
id: 62909790
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '60.h1.a1'], 'contains': ['360.v1.a1', '540.x1.a1', '540.bh1.a1', '900.bc1.a1', '900.bd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 131760, 10862, 54480, 7200, 129744], 'label': '162000.x.180.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '180.be1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.be1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62909791
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '60.i1.a1'], 'contains': ['360.w1.a1', '540.y1.a1', '540.bi1.a1', '900.bd1.a1', '900.bf1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 66960, 10862, 54480, 7200, 129744], 'label': '162000.x.180.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '180.bf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62909792
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '60.f1.a1', '90.g1.a1'], 'contains': ['360.bb1.a1', '540.z1.a1', '540.bf1.a1', '900.bg1.a1', '900.bh1.a1', '900.bi1.a1', '900.bj1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10503, 2160, 10862, 54480, 108000, 32544], 'label': '162000.x.180.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '180.bg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '600.164'}
-
id: 62909793
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bg2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '60.f2.a1', '90.g1.a1'], 'contains': ['360.bb1.a1', '540.ba1.a1', '540.be1.a1', '900.bg1.a1', '900.bi2.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10503, 2160, 10862, 54480, 108000, 129744], 'label': '162000.x.180.bg2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '180.bg2.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bg2.a1', 'subgroup_fusion': None, 'weyl_group': '600.163'}
-
id: 62909794
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '60.g1.a1', '90.b1.a1'], 'contains': ['360.bd1.a1', '540.bb1.a1', '540.bg1.a1', '900.bi1.a1', '900.bi2.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10503, 32400, 10862, 54480, 108000, 97344], 'label': '162000.x.180.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '180.bh1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '600.161'}
-
id: 62909795
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '60.h1.a1'], 'contains': ['360.bf1.a1', '540.bc1.a1', '540.bh1.a1', '900.bh1.a1', '900.bi2.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 131760, 10862, 54480, 108000, 129744], 'label': '162000.x.180.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '180.bi1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62909796
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '60.i1.a1'], 'contains': ['360.bg1.a1', '540.bd1.a1', '540.bi1.a1', '900.bi2.a1', '900.bj1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 66960, 10862, 54480, 108000, 129744], 'label': '162000.x.180.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '180.bj1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62909797
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.a1', '60.j1.a1', '90.c1.a1'], 'contains': ['360.bj1.a1', '900.bl1.a1', '900.bm1.a1', '1620.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [1, 97344, 2, 108480, 32400, 108000], 'label': '162000.x.180.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '180.bk1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '360.130'}
-
id: 62909798
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '60.m1.a1', '90.i1.a1'], 'contains': ['360.bi1.a1', '360.bq1.a1', '360.cf1.a1', '540.bn1.a1', '540.bo1.a1', '900.bk1.a1', '900.bo1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [17642, 32400, 66960, 480, 119340, 108000], 'label': '162000.x.180.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '180.bl1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62909799
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.a1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '80.a1.a1', '400.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [29128, 32544, 32400, 61200, 108000, 66960, 58080], 'label': '162000.x.16.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2700.o'}
-
id: 62909800
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '60.m1.a1', '90.f1.a1'], 'contains': ['360.bj1.a1', '360.br1.a1', '360.cc1.a1', '540.bn1.a1', '540.bp1.a1', '900.bn1.a1', '900.bp1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [17642, 144, 2160, 480, 11340, 7200], 'label': '162000.x.180.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1.a1', 'old_label': '180.bm1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62909801
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '60.n1.a1', '90.f1.a1'], 'contains': ['360.br1.a1', '360.ci1.a1', '540.bq1.a1', '900.bo1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [17642, 32400, 480, 108000, 119340, 97344], 'label': '162000.x.180.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '180.bn1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62909802
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.a1', '60.k1.a1', '90.h1.a1'], 'contains': ['360.bs1.a1', '900.bl1.a1', '900.bq1.a1', '1620.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [1, 2160, 2, 108480, 64944, 108000], 'label': '162000.x.180.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.h1.a1', 'old_label': '180.bo1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '360.131'}
-
id: 62909803
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.a1', '60.l1.a1', '90.h1.a1'], 'contains': ['360.bs1.a1', '900.bm1.a1', '900.bq1.a1', '1620.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 2160, 108480, 108000, 2, 97344], 'label': '162000.x.180.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '180.bp1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.646'}
-
id: 62909804
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '60.m1.a1', '90.i1.a1'], 'contains': ['360.bi1.a1', '360.bu1.a1', '360.cb1.a1', '540.bo1.a1', '540.bp1.a1', '900.bn1.a1', '900.br1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [17642, 32400, 66960, 480, 11340, 7200], 'label': '162000.x.180.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '180.bq1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62909805
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '60.n1.a1', '90.i1.a1'], 'contains': ['360.bq1.a1', '360.bu1.a1', '360.ch1.a1', '540.bq1.a1', '540.br1.a1', '900.bp1.a1', '900.br1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [17642, 32400, 480, 7200, 11340, 97344], 'label': '162000.x.180.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '180.br1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.br1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.679'}
-
id: 62909806
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '60.o1.a1', '90.i1.a1'], 'contains': ['360.cb1.a1', '360.cf1.a1', '360.ch1.a1', '540.bs1.a1', '540.bt1.a1', '900.bs1.a1', '900.bt1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [6660, 32400, 480, 7200, 125640, 144], 'label': '162000.x.180.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '180.bs1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.679'}
-
id: 62909807
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '180.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '60.o1.a1', '90.f1.a1'], 'contains': ['360.cc1.a1', '360.ci1.a1', '540.bt1.a1', '900.bt1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [6660, 2160, 480, 7200, 125640, 144], 'label': '162000.x.180.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.bt1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62909808
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '200.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '100.a1.a1'], 'contains': ['400.a1.a1', '600.a1.a1', '600.b1.a1', '600.e1.a1', '1000.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': None, 'generators': [10862, 136224, 108000, 61200, 83128, 58080], 'label': '162000.x.200.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '200.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.a1.a1', 'subgroup_fusion': None, 'weyl_group': '540.37'}
-
id: 62909809
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '72.d1.a1', '108.d1.a1'], 'contains': ['432.a1.a1', '648.a1.a1', '1080.a1.a1', '1080.b1.a1', '1080.c1.a1', '1080.d1.a1', '1080.e1.a1', '1080.f1.a1', '1080.g1.a1', '1080.h1.a1', '1080.i1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [10862, 97344, 66960, 61680, 32400], 'label': '162000.x.216.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '216.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1500.115'}
-
id: 62909810
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['36.a1.a1', '36.f1.a1', '36.g1.a1', '54.a1.a1', '54.c1.a1', '90.a1.a1', '90.d1.a1', '90.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [64263, 54480, 99360, 7200, 97344, 32400, 119340, 10862], 'label': '162000.x.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909811
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.e1.a1', '108.a1.a1', '108.b1.a1', '108.e1.a1'], 'contains': ['432.b1.a1', '648.a1.a1', '1080.j1.a1', '1080.k1.a1', '1080.l1.a1', '1080.m1.a1', '1080.n1.a1', '1080.o1.a1', '1080.p1.a1', '1080.q1.a1', '1080.r1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [10862, 97344, 66960, 480, 32400], 'label': '162000.x.216.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2000.905'}
-
id: 62909812
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.d1.a1', '72.e1.a1', '108.c1.a1', '108.f1.a1', '108.g1.a1'], 'contains': ['432.c1.a1', '648.a1.a1', '1080.s1.a1', '1080.t1.a1', '1080.u1.a1', '1080.v1.a1', '1080.w1.a1', '1080.x1.a1', '1080.y1.a1', '1080.z1.a1', '1080.ba1.a1', '1080.bb1.a1', '1080.bc1.a1', '1080.bd1.a1', '1080.be1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10862, 97344, 66960, 4080, 32400], 'label': '162000.x.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '216.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1000.170'}
-
id: 62909813
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.d1.a1', '72.b1.a1', '108.h1.a1'], 'contains': ['432.d1.a1', '648.a1.a1', '1080.bf1.a1', '5400.bf1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [10862, 97344, 99360, 83128, 32400], 'label': '162000.x.216.d1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1.a1', 'old_label': '216.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1500.115'}
-
id: 62909814
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '72.g1.a1', '108.a1.a1', '108.i1.a1', '108.j1.a1'], 'contains': ['432.b1.a1', '648.b1.a1', '1080.bg1.a1', '1080.bj1.a1', '1080.bk1.a1', '1080.bl1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [2, 97344, 32400, 7200, 2160], 'label': '162000.x.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '216.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': '80.34'}
-
id: 62909815
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '72.h1.a1', '108.b1.a1', '108.j1.a1', '108.k1.a1'], 'contains': ['432.b1.a1', '648.b1.a1', '1080.bh1.a1', '1080.bm1.a1', '1080.bn1.a1', '1080.bo1.a1', '1080.bp1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2, 32400, 480, 97344, 2160], 'label': '162000.x.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '216.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62909816
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '72.h1.a1', '108.c1.a1'], 'contains': ['432.c1.a1', '648.b1.a1', '1080.bi1.a1', '1080.bq1.a1', '1080.br1.a1', '1080.bs1.a1', '1080.bt1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [54482, 32400, 54480, 97344, 2160], 'label': '162000.x.216.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '216.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62909817
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '72.j1.a1', '108.a1.a1', '108.k1.a1', '108.m1.a1'], 'contains': ['432.b1.a1', '648.c1.a1', '1080.bu1.a1', '1080.bv1.a1', '1080.bw1.a1', '1080.cf1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [11100, 66960, 97344, 7200, 32400], 'label': '162000.x.216.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '216.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1.a1', 'subgroup_fusion': None, 'weyl_group': '400.129'}
-
id: 62909818
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '72.k1.a1', '108.b1.a1', '108.j1.a1', '108.m1.a1'], 'contains': ['432.b1.a1', '648.c1.a1', '1080.bx1.a1', '1080.by1.a1', '1080.bz1.a1', '1080.ca1.a1', '1080.cg1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [11340, 480, 97344, 66960, 32400], 'label': '162000.x.216.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '216.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1.a1', 'subgroup_fusion': None, 'weyl_group': '600.174'}
-
id: 62909819
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '72.k1.a1', '108.c1.a1'], 'contains': ['432.c1.a1', '648.c1.a1', '1080.cb1.a1', '1080.cc1.a1', '1080.cd1.a1', '1080.ce1.a1', '1080.ch1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119340, 54480, 97344, 66960, 32400], 'label': '162000.x.216.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '216.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.a1', 'subgroup_fusion': None, 'weyl_group': '600.161'}
-
id: 62909820
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '225.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '75.a1.a1'], 'contains': ['450.g1.a1', '450.h1.a1', '450.i1.a1', '1125.a1.a1', '2025.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': None, 'generators': [7201, 108000, 2, 119340, 125640, 2160, 108480], 'label': '162000.x.225.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '225.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '225.a1.a1', 'subgroup_fusion': None, 'weyl_group': '720.774'}
-
id: 62909821
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '8.a1.a1', '54.d1.a1', '250.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [66960, 32544, 29128, 61200, 14040, 108000, 2, 64860, 54480, 32400], 'label': '162000.x.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '162000.x'}
-
id: 62909822
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.h1.a1', '54.c1.a1', '90.b1.a1', '90.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [64263, 108000, 99360, 10862, 97344, 32400, 119340, 54480], 'label': '162000.x.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909823
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '80.a1.a1', '120.a1.a1'], 'contains': ['720.i1.a1', '720.j1.a1', '6000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25768, 58080, 4464, 61200, 66960], 'label': '162000.x.240.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '240.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2700.o'}
-
id: 62909824
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '80.a1.a1', '120.b1.a1'], 'contains': ['720.i1.a1', '720.k1.a1', '6000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25288, 58080, 4464, 61200, 66960], 'label': '162000.x.240.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '240.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1350.51'}
-
id: 62909825
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '120.c1.a1', '120.i1.a1', '120.l1.a1'], 'contains': ['720.a1.a1', '720.l1.a1', '720.m1.a1', '720.y1.a1', '720.z1.a1', '1200.c1.a1', '1200.d1.a1', '1200.g1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 108000, 97344, 7200, 2160], 'label': '162000.x.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '240.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62909826
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '120.d1.a1', '120.j1.a1', '120.m1.a1'], 'contains': ['720.b1.a1', '720.c1.a1', '720.n1.a1', '720.o1.a1', '720.p1.a1', '720.ba1.a1', '720.bb1.a1', '1200.c1.a1', '1200.e1.a1', '1200.f1.a1', '1200.g1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 108000, 144, 7200, 66960], 'label': '162000.x.240.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '240.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62909827
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '120.e1.a1', '120.h1.a1', '120.k1.a1', '120.n1.a1', '120.o1.a1'], 'contains': ['720.d1.a1', '720.q1.a1', '720.r1.a1', '720.bc1.a1', '720.bd1.a1', '1200.c1.a1', '1200.d1.a1', '1200.f1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [480, 108000, 97344, 7200, 32400], 'label': '162000.x.240.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '240.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
-
id: 62909828
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '120.f1.a1'], 'contains': ['720.e1.a1', '720.f1.a1', '720.g1.a1', '720.s1.a1', '720.t1.a1', '720.u1.a1', '720.v1.a1', '720.be1.a1', '720.bf1.a1', '1200.d1.a1', '1200.e1.a1', '1200.f1.a1', '1200.g1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 108000, 97344, 61200, 66960], 'label': '162000.x.240.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '240.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62909829
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '80.a1.a1', '120.g1.a1'], 'contains': ['720.h1.a1', '720.i1.a1', '720.w1.a1', '720.x1.a1', '720.bg1.a1', '1200.f1.a1', '1200.g1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [480, 108000, 32544, 115200, 66960], 'label': '162000.x.240.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '240.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.1'}
-
id: 62909830
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '250.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '125.a1.a1'], 'contains': ['500.b1.a1', '750.c1.a1', '1000.a1.a1', '6750.d1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': None, 'generators': [2, 7200, 480, 29128, 108000, 3300, 14040], 'label': '162000.x.250.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '250.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '250.a1.a1', 'subgroup_fusion': None, 'weyl_group': '648.704'}
-
id: 62909831
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '270.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '90.a1.a1', '135.a1.a1'], 'contains': ['540.a1.a1', '540.w1.a1', '810.a1.a1', '1350.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 135, 'diagramx': None, 'generators': [75001, 32400, 7200, 10862, 11100, 64944], 'label': '162000.x.270.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1.a1', 'old_label': '270.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.a1.a1', 'subgroup_fusion': None, 'weyl_group': '200.43'}
-
id: 62909832
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '270.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '54.b1.a1', '135.a1.a1'], 'contains': ['540.a1.a1', '540.bk1.a1', '810.b1.a1', '1350.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 135, 'diagramx': None, 'generators': [1, 32400, 2, 7200, 10860, 97344], 'label': '162000.x.270.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1.a1', 'old_label': '270.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.b1.a1', 'subgroup_fusion': None, 'weyl_group': '600.170'}
-
id: 62909833
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.j1.a1', '90.c1.a1', '90.h1.a1', '162.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 108000, 2160, 2, 97344, 32400, 119340, 108480], 'label': '162000.x.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909834
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '270.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '90.a1.a1', '90.b1.a1'], 'contains': ['540.c1.a1', '540.bb1.a1', '540.bg1.a1', '810.a1.a1', '1350.c1.a1', '1350.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [64263, 32400, 10862, 54480, 119340, 97344], 'label': '162000.x.270.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '270.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.c1.a1', 'subgroup_fusion': None, 'weyl_group': '600.161'}
-
id: 62909835
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '270.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '90.d1.a1', '90.e1.a1'], 'contains': ['540.e1.a1', '540.v1.a1', '540.v2.a1', '810.c1.a1', '1350.a1.a1', '1350.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [75001, 2160, 7200, 10862, 11100, 32544], 'label': '162000.x.270.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.d1.a1', 'old_label': '270.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.d1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62909836
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '270.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.a1', '54.b1.a1'], 'contains': ['540.d1.a1', '540.bl1.a1', '540.bm1.a1', '810.d1.a1', '1350.b1.a1', '1350.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [1, 2160, 2, 7200, 10860, 97344], 'label': '162000.x.270.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1.a1', 'old_label': '270.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.e1.a1', 'subgroup_fusion': None, 'weyl_group': '600.166'}
-
id: 62909837
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '270.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '90.d1.a1', '90.g1.a1'], 'contains': ['540.l1.a1', '540.z1.a1', '540.be1.a1', '810.c1.a1', '1350.c1.a1', '1350.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [64263, 2160, 10862, 54480, 119340, 129744], 'label': '162000.x.270.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.d1.a1', 'old_label': '270.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.f1.a1', 'subgroup_fusion': None, 'weyl_group': '600.163'}
-
id: 62909838
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '270.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '90.e1.a1', '90.g1.a1'], 'contains': ['540.m1.a1', '540.ba1.a1', '540.bf1.a1', '810.c1.a1', '1350.d1.a1', '1350.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [64263, 2160, 10862, 54480, 119340, 32544], 'label': '162000.x.270.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1.a1', 'old_label': '270.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.g1.a1', 'subgroup_fusion': None, 'weyl_group': '600.164'}
-
id: 62909839
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '270.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.e1.a1', '90.f1.a1', '90.i1.a1'], 'contains': ['540.b1.a1', '540.f1.a1', '540.i1.a1', '540.bn1.a1', '540.bp1.a1', '540.bq1.a1', '540.bt1.a1', '810.e1.a1', '1350.g1.a1', '1350.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [10862, 32400, 125640, 480, 119340, 97344], 'label': '162000.x.270.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.h1.a1', 'old_label': '270.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.h1.a1', 'subgroup_fusion': None, 'weyl_group': '600.174'}
-
id: 62909840
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '270.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.e1.a1', '90.i1.a1', '135.a1.a1'], 'contains': ['540.a1.a1', '540.j1.a1', '540.bo1.a1', '540.br1.a1', '540.bs1.a1', '810.e1.a1', '1350.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 135, 'diagramx': None, 'generators': [10862, 32400, 125640, 480, 119340, 66960], 'label': '162000.x.270.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1.a1', 'old_label': '270.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.i1.a1', 'subgroup_fusion': None, 'weyl_group': '600.170'}
-
id: 62909841
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '60.d1.a1', '150.e1.a1'], 'contains': ['600.c1.a1', '600.h1.a1', '600.m1.a1', '900.a1.a1', '900.e1.a1', '900.f1.a1', '900.i1.a1', '1500.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [2, 32400, 7200, 480, 11100, 108000], 'label': '162000.x.300.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.e1.a1', 'old_label': '300.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.a1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62909842
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '60.b1.a1', '150.b1.a1'], 'contains': ['600.d1.a1', '600.i1.a1', '600.n1.a1', '900.b1.a1', '900.g1.a1', '900.j1.a1', '1500.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [2, 97344, 7200, 480, 11100, 108000], 'label': '162000.x.300.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.a1', 'old_label': '300.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.b1.a1', 'subgroup_fusion': None, 'weyl_group': '360.130'}
-
id: 62909843
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '60.c1.a1', '150.a1.a1'], 'contains': ['600.f1.a1', '600.j1.a1', '600.o1.a1', '900.c1.a1', '900.d1.a1', '900.h1.a1', '900.k1.a1', '1500.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 32544, 7200, 480, 11100, 108000], 'label': '162000.x.300.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '300.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.c1.a1', 'subgroup_fusion': None, 'weyl_group': '360.129'}
-
id: 62909844
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '36.i1.a1', '36.k1.a1', '36.l1.a1', '54.e1.a1', '90.f1.a1', '90.i1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [21482, 7200, 2160, 125640, 144, 32400, 6660, 4080], 'label': '162000.x.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909845
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.c1.a1', '60.d1.a1', '150.c1.a1', '150.d1.a1', '150.e1.a1'], 'contains': ['600.c1.a1', '600.k1.a1', '600.l1.a1', '900.l1.a1', '900.m1.a1', '900.n1.a1', '1500.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [2, 2160, 7200, 480, 11100, 108000], 'label': '162000.x.300.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '300.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.d1.a1', 'subgroup_fusion': None, 'weyl_group': '720.774'}
-
id: 62909846
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '100.a1.a1'], 'contains': ['600.a1.a1', '900.p1.a1', '900.v1.a1', '1500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': None, 'generators': [75483, 58080, 25768, 61200, 10862, 136224], 'label': '162000.x.300.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '300.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.e1.a1', 'subgroup_fusion': None, 'weyl_group': '540.37'}
-
id: 62909847
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.a1', '60.f2.a1', '150.c1.a1'], 'contains': ['600.c1.a1', '900.o1.a1', '900.w1.a1', '900.bb1.a1', '900.bg1.a1', '1500.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10503, 2160, 108000, 10862, 7200, 54480], 'label': '162000.x.300.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '300.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.f1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62909848
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.a1', '60.h1.a1', '100.a1.a1'], 'contains': ['600.e1.a1', '900.p1.a1', '900.q1.a1', '900.x1.a1', '900.bc1.a1', '900.bh1.a1', '1500.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 39024, 108000, 10862, 7200, 54480], 'label': '162000.x.300.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '300.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.g1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62909849
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.a1', '60.g1.a1', '150.a1.a1'], 'contains': ['600.f1.a1', '900.s1.a1', '900.y1.a1', '900.be1.a1', '900.bi1.a1', '1500.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10503, 32544, 108000, 10862, 7200, 54480], 'label': '162000.x.300.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '300.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.h1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62909850
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.h2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f2.a1', '60.g1.a1', '60.h1.a1', '60.i1.a1', '150.a1.a1'], 'contains': ['600.f1.a1', '900.r1.a1', '900.z1.a1', '900.bd1.a1', '900.bi2.a1', '1500.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10503, 129744, 108000, 10862, 7200, 54480], 'label': '162000.x.300.h2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '300.h2.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.h2.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62909851
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.a1', '60.i1.a1'], 'contains': ['600.g1.a1', '900.t1.a1', '900.u1.a1', '900.ba1.a1', '900.bf1.a1', '900.bj1.a1', '1500.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 41184, 108000, 10862, 7200, 54480], 'label': '162000.x.300.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '300.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.i1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62909852
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.j1.a1', '60.k1.a1', '150.b1.a1'], 'contains': ['600.i1.a1', '900.bl1.a1', '1500.d1.a1', '2700.bk1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [1, 108000, 2, 108480, 64944, 7200], 'label': '162000.x.300.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.a1', 'old_label': '300.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.j1.a1', 'subgroup_fusion': None, 'weyl_group': '216.169'}
-
id: 62909853
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.j1.a1', '60.l1.a1', '150.b1.a1'], 'contains': ['600.i1.a1', '900.bm1.a1', '1500.d1.a1', '2700.bl1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [1, 97344, 108480, 7200, 2, 108000], 'label': '162000.x.300.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '300.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1080.513'}
-
id: 62909854
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.m1.a1', '150.e1.a1'], 'contains': ['600.h1.a1', '600.l1.a1', '900.bk1.a1', '900.bn1.a1', '1500.e1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [17402, 108000, 2160, 480, 11100, 7200], 'label': '162000.x.300.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '300.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.l1.a1', 'subgroup_fusion': None, 'weyl_group': '432.579'}
-
id: 62909855
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['40.a1.a1', '60.e1.a1', '60.i1.a1', '500.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [75483, 61200, 138384, 10862, 58080, 66960, 108000, 25768], 'label': '162000.x.20.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2700.o'}
-
id: 62909856
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.k1.a1', '60.l1.a1', '150.d1.a1'], 'contains': ['600.k1.a1', '900.bq1.a1', '1500.d1.a1', '2700.bn1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [1, 2160, 108480, 7200, 2, 108000], 'label': '162000.x.300.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '300.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1080.512'}
-
id: 62909857
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.m1.a1', '60.n1.a1', '150.e1.a1'], 'contains': ['600.h1.a1', '600.k1.a1', '600.m1.a1', '900.bo1.a1', '900.bp1.a1', '900.br1.a1', '1500.e1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [17402, 32400, 480, 7200, 11100, 108000], 'label': '162000.x.300.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1.a1', 'old_label': '300.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1080.537'}
-
id: 62909858
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '300.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.o1.a1', '150.e1.a1'], 'contains': ['600.l1.a1', '600.m1.a1', '900.bs1.a1', '900.bt1.a1', '1500.f1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [7140, 32400, 480, 7200, 125640, 108000], 'label': '162000.x.300.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '300.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2160.fi'}
-
id: 62909859
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.b1.a1', '108.c1.a1', '162.a1.a1', '162.b1.a1', '162.c1.a1'], 'contains': ['648.a1.a1', '648.b1.a1', '648.c1.a1', '1620.a1.a1', '1620.b1.a1', '1620.c1.a1', '1620.d1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [242, 97344, 2160, 11100, 32400], 'label': '162000.x.324.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '324.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2000.905'}
-
id: 62909860
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.a1', '108.e1.a1', '108.f1.a1', '108.g1.a1', '108.h1.a1', '162.a1.a1'], 'contains': ['648.a1.a1', '1620.e1.a1', '1620.e2.a1', '1620.f1.a1', '1620.g1.a1', '1620.h1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10503, 97344, 99360, 10862, 32400], 'label': '162000.x.324.b1.a1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '324.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1000.170'}
-
id: 62909861
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.a1', '108.i1.a1', '162.b1.a1'], 'contains': ['648.b1.a1', '1620.i1.a1', '1620.j1.a1', '1620.k1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 2, 97344, 32400, 2160], 'label': '162000.x.324.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.b1.a1', 'old_label': '324.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1.a1', 'subgroup_fusion': None, 'weyl_group': '200.41'}
-
id: 62909862
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '108.k1.a1', '162.c1.a1'], 'contains': ['648.b1.a1', '648.c1.a1', '1620.l1.a1', '1620.m1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [17882, 66960, 97344, 11100, 32400], 'label': '162000.x.324.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1.a1', 'subgroup_fusion': None, 'weyl_group': '400.129'}
-
id: 62909863
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.l1.a1', '108.m1.a1', '162.c1.a1'], 'contains': ['648.c1.a1', '1620.n1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [119100, 97344, 66960, 125640, 32400], 'label': '162000.x.324.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '324.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6000.bm'}
-
id: 62909864
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.c1.a1'], 'contains': ['720.a1.a1', '1080.a1.a1', '1080.s1.a1', '1080.t1.a1', '1800.a1.a1', '1800.b1.a1', '1800.g1.a1', '1800.h1.a1', '1800.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 61200, 97344, 115680, 2160], 'label': '162000.x.360.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.c1.a1', 'old_label': '360.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.a1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62909865
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.d1.a1', '180.o1.a1'], 'contains': ['720.b1.a1', '1080.b1.a1', '1080.v1.a1', '1080.w1.a1', '1800.a1.a1', '1800.c1.a1', '1800.d1.a1', '1800.f1.a1', '1800.g1.a1', '1800.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 61200, 32544, 54480, 2160], 'label': '162000.x.360.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.f1.a1', 'old_label': '360.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.b1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
-
id: 62909866
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.d1.a1'], 'contains': ['48.a1.a1', '72.a1.a1', '72.d1.a1', '72.e1.a1', '120.c1.a1', '120.d1.a1', '120.e1.a1', '120.f1.a1', '120.g1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [10862, 66960, 7200, 108000, 480, 32400, 97344], 'label': '162000.x.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.a1.a1', '648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6000.bm'}
-
id: 62909867
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.d1.a1', '180.p1.a1'], 'contains': ['720.c1.a1', '1080.c1.a1', '1080.u1.a1', '1080.w1.a1', '1800.a1.a1', '1800.d1.a1', '1800.e1.a1', '1800.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 61200, 144, 115680, 66960], 'label': '162000.x.360.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.f2.a1', 'old_label': '360.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.c1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909868
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.e1.a1', '180.q1.a1'], 'contains': ['720.d1.a1', '1080.d1.a1', '1080.x1.a1', '1080.y1.a1', '1800.a1.a1', '1800.b1.a1', '1800.e1.a1', '1800.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 61200, 97344, 54480, 32400], 'label': '162000.x.360.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.g1.a1', 'old_label': '360.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.d1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909869
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.f1.a1', '180.r1.a1'], 'contains': ['720.e1.a1', '1080.e1.a1', '1080.z1.a1', '1080.bc1.a1', '1800.b1.a1', '1800.c1.a1', '1800.e1.a1', '1800.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 61200, 6624, 4080, 131760], 'label': '162000.x.360.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '360.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.e1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909870
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.f1.a1', '180.s1.a1'], 'contains': ['720.f1.a1', '1080.g1.a1', '1080.z1.a1', '1080.bb1.a1', '1800.b1.a1', '1800.d1.a1', '1800.e1.a1', '1800.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 61200, 97344, 115680, 66960], 'label': '162000.x.360.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '360.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.f1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909871
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.f1.a1'], 'contains': ['720.g1.a1', '1080.f1.a1', '1080.ba1.a1', '1080.bb1.a1', '1080.bc1.a1', '1800.b1.a1', '1800.d1.a1', '1800.f1.a1', '1800.g1.a1', '1800.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 61200, 97344, 115680, 34560], 'label': '162000.x.360.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.f1.a1', 'old_label': '360.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.g1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62909872
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.g1.a1', '180.t1.a1'], 'contains': ['720.h1.a1', '1080.i1.a1', '1080.bd1.a1', '1080.be1.a1', '1800.e1.a1', '1800.f1.a1', '1800.h1.a1', '1800.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 61200, 32544, 115680, 66960], 'label': '162000.x.360.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '360.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.h1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909873
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.a1.a1', '120.b1.a1', '120.g1.a1', '180.u1.a1'], 'contains': ['720.i1.a1', '1080.h1.a1', '1080.bd1.a1', '1800.e1.a1', '1800.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [10862, 61200, 129744, 115680, 66960], 'label': '162000.x.360.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '360.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.i1.a1', 'subgroup_fusion': None, 'weyl_group': '300.23'}
-
id: 62909874
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '120.a1.a1', '180.v1.a1'], 'contains': ['720.j1.a1', '1080.h1.a1', '1080.bf1.a1', '9000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 58080, 32544, 25768, 66960], 'label': '162000.x.360.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.e1.a1', 'old_label': '360.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.j1.a1', 'subgroup_fusion': None, 'weyl_group': '900.90'}
-
id: 62909875
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '120.b1.a1'], 'contains': ['720.k1.a1', '1080.h1.a1', '9000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 58080, 32544, 25288, 66960], 'label': '162000.x.360.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.b1.a1', 'old_label': '360.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.k1.a1', 'subgroup_fusion': None, 'weyl_group': '450.22'}
-
id: 62909876
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.c1.a1', '180.d1.a1'], 'contains': ['720.l1.a1', '1080.a1.a1', '1080.j1.a1', '1080.s1.a1', '1800.l1.a1', '1800.n1.a1', '1800.v1.a1', '1800.x1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 61200, 144, 480, 131760], 'label': '162000.x.360.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '360.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.l1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
-
id: 62909877
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.c1.a1'], 'contains': ['48.b1.a1', '72.a1.a1', '72.b1.a1', '120.a1.a1', '600.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [10862, 99360, 61200, 58080, 25768, 32400, 97344], 'label': '162000.x.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '13500.e'}
-
id: 62909878
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.c1.a1'], 'contains': ['720.m1.a1', '1080.a1.a1', '1080.k1.a1', '1080.t1.a1', '1800.m1.a1', '1800.o1.a1', '1800.u1.a1', '1800.v1.a1', '1800.w1.a1', '1800.x1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 61200, 97344, 480, 2160], 'label': '162000.x.360.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.c1.a1', 'old_label': '360.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.m1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62909879
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.d1.a1'], 'contains': ['720.n1.a1', '1080.b1.a1', '1080.c1.a1', '1080.m1.a1', '1080.w1.a1', '1800.m1.a1', '1800.p1.a1', '1800.q1.a1', '1800.t1.a1', '1800.v1.a1', '1800.x1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 61200, 32544, 480, 2160], 'label': '162000.x.360.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.d1.a1', 'old_label': '360.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.n1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62909880
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.d1.a1', '180.e1.a1', '180.w1.a1', '180.bb1.a1'], 'contains': ['720.o1.a1', '1080.b1.a1', '1080.l1.a1', '1080.u1.a1', '1800.l1.a1', '1800.p1.a1', '1800.r1.a1', '1800.u1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 61200, 144, 480, 66960], 'label': '162000.x.360.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '360.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.o1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62909881
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.d1.a1', '180.f1.a1', '180.x1.a1', '180.bc1.a1'], 'contains': ['720.p1.a1', '1080.c1.a1', '1080.l1.a1', '1080.v1.a1', '1800.l1.a1', '1800.q1.a1', '1800.s1.a1', '1800.w1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 61200, 144, 480, 99360], 'label': '162000.x.360.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '360.p1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.p1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62909882
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.e1.a1', '180.g1.a1'], 'contains': ['720.q1.a1', '1080.d1.a1', '1080.n1.a1', '1080.y1.a1', '1800.l1.a1', '1800.m1.a1', '1800.o1.a1', '1800.t1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 61200, 97344, 480, 32400], 'label': '162000.x.360.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '360.q1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.q1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
-
id: 62909883
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.e1.a1', '180.a1.a1', '180.y1.a1', '180.bd1.a1'], 'contains': ['720.r1.a1', '1080.d1.a1', '1080.o1.a1', '1080.x1.a1', '1800.m1.a1', '1800.n1.a1', '1800.r1.a1', '1800.s1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 61200, 66960, 480, 32400], 'label': '162000.x.360.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '360.r1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.r1.a1', 'subgroup_fusion': None, 'weyl_group': '200.48'}
-
id: 62909884
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.f1.a1'], 'contains': ['720.s1.a1', '1080.e1.a1', '1080.f1.a1', '1080.p1.a1', '1080.bb1.a1', '1800.n1.a1', '1800.o1.a1', '1800.p1.a1', '1800.t1.a1', '1800.v1.a1', '1800.w1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 61200, 97344, 480, 34560], 'label': '162000.x.360.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.f1.a1', 'old_label': '360.s1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.s1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62909885
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.f1.a1', '180.z1.a1'], 'contains': ['720.t1.a1', '1080.e1.a1', '1080.g1.a1', '1080.q1.a1', '1080.ba1.a1', '1800.o1.a1', '1800.p1.a1', '1800.s1.a1', '1800.x1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 61200, 97344, 480, 99360], 'label': '162000.x.360.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '360.t1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.t1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909886
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.f1.a1'], 'contains': ['720.u1.a1', '1080.f1.a1', '1080.g1.a1', '1080.p1.a1', '1080.bc1.a1', '1800.n1.a1', '1800.o1.a1', '1800.q1.a1', '1800.t1.a1', '1800.u1.a1', '1800.x1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 61200, 97344, 480, 131760], 'label': '162000.x.360.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.f1.a1', 'old_label': '360.u1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.u1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62909887
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.f1.a1', '180.be1.a1'], 'contains': ['720.v1.a1', '1080.f1.a1', '1080.q1.a1', '1080.z1.a1', '1800.o1.a1', '1800.q1.a1', '1800.r1.a1', '1800.v1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 61200, 97344, 480, 66960], 'label': '162000.x.360.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '360.v1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.v1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909888
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['48.c1.a1', '72.a1.a1', '72.c1.a1', '120.b1.a1', '600.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [10862, 99360, 61200, 58080, 25288, 32400, 97344], 'label': '162000.x.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6750.b'}
-
id: 62909889
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.g1.a1', '180.bf1.a1'], 'contains': ['720.w1.a1', '1080.i1.a1', '1080.r1.a1', '1080.bd1.a1', '1800.r1.a1', '1800.t1.a1', '1800.w1.a1', '1800.x1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 61200, 32544, 480, 66960], 'label': '162000.x.360.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '360.w1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.w1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909890
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.g1.a1', '180.ba1.a1'], 'contains': ['720.x1.a1', '1080.h1.a1', '1080.i1.a1', '1080.r1.a1', '1080.be1.a1', '1800.s1.a1', '1800.t1.a1', '1800.u1.a1', '1800.v1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 61200, 129744, 480, 99360], 'label': '162000.x.360.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '360.x1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.x1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909891
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.c1.a1', '180.h1.a1'], 'contains': ['720.y1.a1', '1080.j1.a1', '1080.k1.a1', '1080.t1.a1', '1800.y1.a1', '1800.ba1.a1', '1800.bf1.a1', '1800.bg1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 7200, 97344, 480, 2160], 'label': '162000.x.360.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '360.y1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.y1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
-
id: 62909892
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.c1.a1', '180.l1.a1'], 'contains': ['720.z1.a1', '1080.k1.a1', '1080.s1.a1', '1800.z1.a1', '1800.bb1.a1', '1800.bf1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 7200, 41184, 480, 32400], 'label': '162000.x.360.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '360.z1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.z1.a1', 'subgroup_fusion': None, 'weyl_group': '200.41'}
-
id: 62909893
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.d1.a1', '180.i1.a1'], 'contains': ['720.ba1.a1', '1080.l1.a1', '1080.m1.a1', '1080.w1.a1', '1800.y1.a1', '1800.bc1.a1', '1800.bd1.a1', '1800.bf1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 7200, 144, 480, 66960], 'label': '162000.x.360.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.c1.a1', 'old_label': '360.ba1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
-
id: 62909894
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.d1.a1', '180.m1.a1', '180.bg1.a1', '180.bg2.a1'], 'contains': ['720.bb1.a1', '1080.m1.a1', '1080.u1.a1', '1080.v1.a1', '1800.z1.a1', '1800.bc1.a1', '1800.be1.a1', '1800.bg1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 7200, 69264, 480, 32400], 'label': '162000.x.360.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '360.bb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62909895
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.e1.a1', '180.b1.a1', '180.j1.a1', '180.n1.a1'], 'contains': ['720.bc1.a1', '1080.n1.a1', '1080.o1.a1', '1080.y1.a1', '1800.y1.a1', '1800.z1.a1', '1800.ba1.a1', '1800.bd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 7200, 97344, 480, 32400], 'label': '162000.x.360.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1.a1', 'old_label': '360.bc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '200.49'}
-
id: 62909896
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.e1.a1', '180.c1.a1', '180.k1.a1', '180.bh1.a1'], 'contains': ['720.bd1.a1', '1080.n1.a1', '1080.x1.a1', '1800.y1.a1', '1800.bb1.a1', '1800.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [10862, 7200, 144, 480, 2160], 'label': '162000.x.360.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '360.bd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '400.129'}
-
id: 62909897
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.f1.a1'], 'contains': ['720.be1.a1', '1080.p1.a1', '1080.q1.a1', '1080.bb1.a1', '1080.bc1.a1', '1800.ba1.a1', '1800.bb1.a1', '1800.bc1.a1', '1800.bd1.a1', '1800.bf1.a1', '1800.bg1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 7200, 97344, 480, 66960], 'label': '162000.x.360.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.f1.a1', 'old_label': '360.be1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.be1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62909898
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.f1.a1', '180.bi1.a1'], 'contains': ['720.bf1.a1', '1080.p1.a1', '1080.z1.a1', '1080.ba1.a1', '1800.ba1.a1', '1800.bc1.a1', '1800.be1.a1', '1800.bf1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 7200, 97344, 7680, 34560], 'label': '162000.x.360.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '360.bf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909899
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.e1.a1', '12.f1.a1'], 'contains': ['48.a1.a1', '72.f1.a1', '72.g1.a1', '72.h1.a1', '120.h1.a1', '120.i1.a1', '120.j1.a1', '120.k1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 108000, 97344, 32400, 7200, 2160, 480], 'label': '162000.x.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '720.774'}
-
id: 62909900
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.g1.a1', '180.bj1.a1'], 'contains': ['720.bg1.a1', '1080.r1.a1', '1080.bd1.a1', '1080.be1.a1', '1800.bd1.a1', '1800.be1.a1', '1800.bf1.a1', '1800.bg1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 7200, 32544, 7680, 66960], 'label': '162000.x.360.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '360.bg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909901
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '120.h1.a1', '180.a1.a1'], 'contains': ['720.r1.a1', '1080.bg1.a1', '1080.bi1.a1', '1800.bh1.a1', '1800.bi1.a1', '1800.bj1.a1', '1800.bk1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [54482, 97344, 32400, 7200, 54480], 'label': '162000.x.360.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.bh1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
-
id: 62909902
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '120.h1.a1', '180.b1.a1', '180.bl1.a1', '180.bq1.a1'], 'contains': ['720.bc1.a1', '1080.bg1.a1', '1080.bh1.a1', '1800.bl1.a1', '1800.bm1.a1', '1800.bn1.a1', '1800.bo1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 97344, 32400, 7200, 480], 'label': '162000.x.360.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '360.bi1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 62909903
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '120.h1.a1', '180.c1.a1', '180.bk1.a1', '180.bm1.a1'], 'contains': ['720.bd1.a1', '1080.bh1.a1', '1080.bi1.a1', '1800.bp1.a1', '1800.bq1.a1', '1800.br1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [2, 32400, 480, 97344, 108000], 'label': '162000.x.360.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '360.bj1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '144.115'}
-
id: 62909904
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '120.i1.a1', '180.d1.a1'], 'contains': ['720.l1.a1', '1080.bj1.a1', '1080.bq1.a1', '1800.bi1.a1', '1800.bs1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [54482, 97344, 54480, 7200, 2160], 'label': '162000.x.360.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '360.bk1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62909905
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '120.j1.a1', '180.e1.a1'], 'contains': ['720.o1.a1', '1080.bk1.a1', '1080.br1.a1', '1800.bj1.a1', '1800.bs1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [54482, 129744, 54480, 7200, 2160], 'label': '162000.x.360.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '360.bl1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62909906
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '120.j1.a1', '180.f1.a1'], 'contains': ['720.p1.a1', '1080.bk1.a1', '1080.bs1.a1', '1800.bk1.a1', '1800.bs1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [54482, 32544, 54480, 7200, 2160], 'label': '162000.x.360.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '360.bm1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62909907
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '120.k1.a1', '180.g1.a1'], 'contains': ['720.q1.a1', '1080.bl1.a1', '1080.bt1.a1', '1800.bh1.a1', '1800.bs1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [54482, 32400, 54480, 7200, 2160], 'label': '162000.x.360.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '360.bn1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62909908
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '120.i1.a1', '180.h1.a1'], 'contains': ['720.y1.a1', '1080.bj1.a1', '1080.bm1.a1', '1800.bn1.a1', '1800.bt1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2, 97344, 480, 7200, 2160], 'label': '162000.x.360.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '360.bo1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62909909
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '120.j1.a1', '180.i1.a1'], 'contains': ['720.ba1.a1', '1080.bk1.a1', '1080.bn1.a1', '1800.bo1.a1', '1800.bt1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2, 32544, 480, 7200, 2160], 'label': '162000.x.360.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '360.bp1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62909910
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.f1.a1'], 'contains': ['48.a1.a1', '72.i1.a1', '72.j1.a1', '72.k1.a1', '120.l1.a1', '120.m1.a1', '120.n1.a1', '120.o1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [11100, 97344, 66960, 480, 7200, 32400, 108000], 'label': '162000.x.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62909911
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '120.k1.a1', '180.j1.a1', '180.bl1.a1', '180.br1.a1'], 'contains': ['720.bc1.a1', '1080.bl1.a1', '1080.bp1.a1', '1800.bm1.a1', '1800.bt1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2, 32400, 480, 7200, 2160], 'label': '162000.x.360.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '360.bq1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62909912
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '120.k1.a1', '180.k1.a1', '180.bm1.a1', '180.bn1.a1'], 'contains': ['720.bd1.a1', '1080.bl1.a1', '1080.bo1.a1', '1800.bl1.a1', '1800.bt1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2, 144, 480, 7200, 2160], 'label': '162000.x.360.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '360.br1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.br1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62909913
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '120.i1.a1', '180.l1.a1', '180.bo1.a1', '180.bp1.a1'], 'contains': ['720.z1.a1', '1080.bm1.a1', '1080.bq1.a1', '1800.bq1.a1', '1800.bu1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2, 480, 108000, 97344, 2160], 'label': '162000.x.360.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '360.bs1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '360.131'}
-
id: 62909914
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '120.j1.a1', '180.m1.a1'], 'contains': ['720.bb1.a1', '1080.bn1.a1', '1080.br1.a1', '1080.bs1.a1', '1800.br1.a1', '1800.bu1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2, 480, 108000, 32544, 2160], 'label': '162000.x.360.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '360.bt1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '360.129'}
-
id: 62909915
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '120.k1.a1', '180.n1.a1', '180.bq1.a1', '180.br1.a1'], 'contains': ['720.bc1.a1', '1080.bo1.a1', '1080.bp1.a1', '1080.bt1.a1', '1800.bp1.a1', '1800.bu1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2, 480, 108000, 32400, 2160], 'label': '162000.x.360.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '360.bu1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62909916
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '120.l1.a1', '180.d1.a1'], 'contains': ['720.l1.a1', '1080.bu1.a1', '1080.cb1.a1', '1800.bv1.a1', '1800.bz1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [119340, 2160, 54480, 7200, 97344], 'label': '162000.x.360.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.d1.a1', 'old_label': '360.bv1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62909917
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '120.m1.a1', '180.e1.a1'], 'contains': ['720.o1.a1', '1080.bv1.a1', '1080.cc1.a1', '1800.bv1.a1', '1800.ca1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [119340, 2160, 54480, 7200, 129744], 'label': '162000.x.360.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.d1.a1', 'old_label': '360.bw1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62909918
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '120.m1.a1', '180.f1.a1'], 'contains': ['720.p1.a1', '1080.bv1.a1', '1080.cd1.a1', '1800.bv1.a1', '1800.cb1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [119340, 2160, 54480, 7200, 32544], 'label': '162000.x.360.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1.a1', 'old_label': '360.bx1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62909919
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '120.n1.a1', '180.g1.a1'], 'contains': ['720.q1.a1', '1080.bw1.a1', '1080.ce1.a1', '1800.bv1.a1', '1800.by1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [119340, 66960, 54480, 7200, 32400], 'label': '162000.x.360.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.g1.a1', 'old_label': '360.by1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.by1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62909920
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '120.l1.a1', '180.h1.a1'], 'contains': ['720.y1.a1', '1080.bu1.a1', '1080.bx1.a1', '1800.bw1.a1', '1800.ce1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [11340, 2160, 480, 7200, 97344], 'label': '162000.x.360.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.h1.a1', 'old_label': '360.bz1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62909921
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['54.d1.a1', '81.a1.a1', '108.h1.a1', '3375.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [115201, 125640, 99360, 107728, 129744, 32400, 108482, 119340], 'label': '162000.x.27.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6000.bm'}
-
id: 62909922
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '120.m1.a1', '180.i1.a1'], 'contains': ['720.ba1.a1', '1080.bv1.a1', '1080.by1.a1', '1800.bw1.a1', '1800.cf1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [11340, 2160, 480, 7200, 32544], 'label': '162000.x.360.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.i1.a1', 'old_label': '360.ca1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62909923
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '120.n1.a1', '180.j1.a1', '180.bq1.a1', '180.bs1.a1'], 'contains': ['720.bc1.a1', '1080.bw1.a1', '1080.ca1.a1', '1800.bw1.a1', '1800.cd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [11340, 66960, 480, 7200, 32400], 'label': '162000.x.360.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '360.cb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62909924
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '120.n1.a1', '180.k1.a1', '180.bm1.a1', '180.bt1.a1'], 'contains': ['720.bd1.a1', '1080.bw1.a1', '1080.bz1.a1', '1800.bw1.a1', '1800.cc1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [11340, 2160, 480, 7200, 144], 'label': '162000.x.360.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1.a1', 'old_label': '360.cc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62909925
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '120.l1.a1', '180.l1.a1'], 'contains': ['720.z1.a1', '1080.bx1.a1', '1080.cb1.a1', '1800.bx1.a1', '1800.ch1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [119340, 480, 108000, 2160, 97344], 'label': '162000.x.360.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '360.cd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '360.130'}
-
id: 62909926
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '120.m1.a1', '180.m1.a1'], 'contains': ['720.bb1.a1', '1080.by1.a1', '1080.cc1.a1', '1080.cd1.a1', '1800.bx1.a1', '1800.ci1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [119340, 480, 108000, 2160, 32544], 'label': '162000.x.360.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '360.ce1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '360.129'}
-
id: 62909927
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '120.n1.a1', '180.n1.a1', '180.bl1.a1', '180.bs1.a1'], 'contains': ['720.bc1.a1', '1080.bz1.a1', '1080.ca1.a1', '1080.ce1.a1', '1800.bx1.a1', '1800.cg1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [119340, 480, 108000, 66960, 32400], 'label': '162000.x.360.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1.a1', 'old_label': '360.cf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62909928
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '120.o1.a1', '180.a1.a1'], 'contains': ['720.r1.a1', '1080.cf1.a1', '1080.ch1.a1', '1800.by1.a1', '1800.bz1.a1', '1800.ca1.a1', '1800.cb1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119340, 54480, 97344, 7200, 32400], 'label': '162000.x.360.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '360.cg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '600.161'}
-
id: 62909929
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '120.o1.a1', '180.b1.a1', '180.br1.a1', '180.bs1.a1'], 'contains': ['720.bc1.a1', '1080.cf1.a1', '1080.cg1.a1', '1800.cc1.a1', '1800.cd1.a1', '1800.ce1.a1', '1800.cf1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [11340, 480, 97344, 7200, 32400], 'label': '162000.x.360.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '360.ch1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '600.174'}
-
id: 62909930
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '360.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '120.o1.a1', '180.c1.a1', '180.bn1.a1', '180.bt1.a1'], 'contains': ['720.bd1.a1', '1080.cg1.a1', '1080.ch1.a1', '1800.cg1.a1', '1800.ch1.a1', '1800.ci1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [119340, 108000, 97344, 480, 32400], 'label': '162000.x.360.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '360.ci1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62909931
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '375.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '75.a1.a1', '125.a1.a1'], 'contains': ['750.a1.a1', '750.b1.a1', '750.c1.a1', '1125.a1.a1', '3375.b1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': None, 'generators': [1, 7200, 108480, 125640, 108000, 2, 119340], 'label': '162000.x.375.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '375.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '375.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.158'}
-
id: 62909932
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '9.a1.a1', '15.a1.a1', '27.b1.a1', '75.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2160, 97344, 125640, 7200, 119340, 108000, 1, 2, 108480, 32400], 'label': '162000.x.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909933
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['54.a1.a1', '54.b1.a1', '54.e1.a1', '81.a1.a1', '135.a1.a1', '675.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [108001, 7200, 2160, 108482, 97344, 32400, 125640, 119340], 'label': '162000.x.27.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '27.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909934
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '400.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '200.a1.a1'], 'contains': ['1200.a1.a1', '1200.b1.a1', '1200.e1.a1', '2000.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': None, 'generators': [83128, 136224, 61200, 108000, 58080], 'label': '162000.x.400.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '400.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.8'}
-
id: 62909935
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '405.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1', '81.a1.a1', '135.a1.a1'], 'contains': ['810.a1.a1', '810.b1.a1', '810.e1.a1', '10125.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [115201, 32400, 108482, 119340, 125640, 97344], 'label': '162000.x.405.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '405.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '405.a1.a1', 'subgroup_fusion': None, 'weyl_group': '200.43'}
-
id: 62909936
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '144.d1.a1', '216.a1.a1'], 'contains': ['1296.a1.a1', '2160.a1.a1', '2160.b1.a1', '2160.c1.a1', '2160.d1.a1', '2160.e1.a1', '2160.f1.a1', '2160.g1.a1', '2160.h1.a1', '2160.i1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [61680, 66960, 32400, 97344], 'label': '162000.x.432.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '432.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.1'}
-
id: 62909937
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '144.e1.a1', '216.b1.a1', '216.e1.a1', '216.f1.a1', '216.h1.a1', '216.i1.a1'], 'contains': ['1296.a1.a1', '2160.j1.a1', '2160.k1.a1', '2160.l1.a1', '2160.m1.a1', '2160.n1.a1', '2160.o1.a1', '2160.p1.a1', '2160.q1.a1', '2160.r1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [480, 66960, 32400, 97344], 'label': '162000.x.432.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '432.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
-
id: 62909938
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.d1.a1', '144.e1.a1', '216.c1.a1', '216.g1.a1', '216.j1.a1'], 'contains': ['1296.a1.a1', '2160.s1.a1', '2160.t1.a1', '2160.u1.a1', '2160.v1.a1', '2160.w1.a1', '2160.x1.a1', '2160.y1.a1', '2160.z1.a1', '2160.ba1.a1', '2160.bb1.a1', '2160.bc1.a1', '2160.bd1.a1', '2160.be1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [4080, 66960, 32400, 97344], 'label': '162000.x.432.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '432.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62909939
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.l1.a1', '144.b1.a1', '216.d1.a1'], 'contains': ['1296.a1.a1', '2160.bf1.a1', '10800.bf1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [83128, 32544, 66960, 32400], 'label': '162000.x.432.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1.a1', 'old_label': '432.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1.a1', 'subgroup_fusion': None, 'weyl_group': '300.23'}
-
id: 62909940
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '450.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '90.d1.a1', '150.a1.a1'], 'contains': ['900.c1.a1', '900.y1.a1', '900.bd1.a1', '1350.a1.a1', '1350.c1.a1', '2250.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [64263, 129744, 7200, 10862, 119340, 54480], 'label': '162000.x.450.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.a1.a1', 'old_label': '450.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62909941
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '450.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '90.e1.a1', '150.a1.a1'], 'contains': ['900.d1.a1', '900.z1.a1', '900.be1.a1', '1350.a1.a1', '1350.d1.a1', '2250.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [64263, 32544, 7200, 10862, 119340, 54480], 'label': '162000.x.450.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '450.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.b1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62909942
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '450.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.b1.a1', '90.g1.a1', '150.a1.a1'], 'contains': ['900.k1.a1', '900.bi1.a1', '900.bi2.a1', '1350.c1.a1', '1350.d1.a1', '2250.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [64263, 32544, 10862, 54480, 119340, 108000], 'label': '162000.x.450.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '450.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.c1.a1', 'subgroup_fusion': None, 'weyl_group': '360.129'}
-
id: 62909943
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '450.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.c1.a1', '90.h1.a1', '150.b1.a1'], 'contains': ['900.j1.a1', '900.bl1.a1', '900.bm1.a1', '2250.c1.a1', '4050.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [1, 97344, 2, 108480, 119340, 108000], 'label': '162000.x.450.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.d1.a1', 'old_label': '450.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.d1.a1', 'subgroup_fusion': None, 'weyl_group': '360.130'}
-
id: 62909944
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.g1.a1', '90.a1.a1', '90.b1.a1', '150.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [10503, 54480, 97344, 7200, 108000, 32400, 11100, 10862], 'label': '162000.x.30.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62909945
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '450.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.d1.a1', '90.e1.a1', '150.c1.a1'], 'contains': ['900.l1.a1', '900.w1.a1', '900.bb1.a1', '1350.e1.a1', '1350.h1.a1', '2250.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [64263, 2160, 7200, 10862, 119340, 54480], 'label': '162000.x.450.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.e1.a1', 'old_label': '450.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.e1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62909946
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '450.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.f1.a1', '90.i1.a1', '150.e1.a1'], 'contains': ['900.e1.a1', '900.i1.a1', '900.m1.a1', '900.bn1.a1', '900.bo1.a1', '900.bp1.a1', '900.bt1.a1', '1350.g1.a1', '1350.i1.a1', '2250.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [21482, 144, 125640, 4080, 6660, 7200], 'label': '162000.x.450.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.f1.a1', 'old_label': '450.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.f1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62909947
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '450.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.g1.a1', '150.c1.a1', '225.a1.a1'], 'contains': ['900.n1.a1', '900.bg1.a1', '1350.h1.a1', '2250.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [64263, 2160, 10862, 54480, 119340, 108000], 'label': '162000.x.450.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '450.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.g1.a1', 'subgroup_fusion': None, 'weyl_group': '720.774'}
-
id: 62909948
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '450.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.h1.a1', '150.d1.a1', '225.a1.a1'], 'contains': ['900.n1.a1', '900.bq1.a1', '2250.c1.a1', '4050.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': None, 'generators': [1, 2160, 2, 108480, 119340, 108000], 'label': '162000.x.450.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '450.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.h1.a1', 'subgroup_fusion': None, 'weyl_group': '720.774'}
-
id: 62909949
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '450.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.i1.a1', '150.e1.a1', '225.a1.a1'], 'contains': ['900.f1.a1', '900.n1.a1', '900.bk1.a1', '900.br1.a1', '900.bs1.a1', '1350.i1.a1', '2250.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': None, 'generators': [21482, 32400, 125640, 4080, 6660, 7200], 'label': '162000.x.450.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '450.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.i1.a1', 'subgroup_fusion': None, 'weyl_group': '720.774'}
-
id: 62909950
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '500.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '100.a1.a1', '125.a1.a1'], 'contains': ['1000.a1.a1', '1500.b1.a1', '1500.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 500, 'diagramx': None, 'generators': [75483, 58080, 61200, 108000, 10862, 25768], 'label': '162000.x.500.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '500.a1.a1', 'old_label': '500.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '500.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
-
id: 62909951
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '500.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '250.a1.a1'], 'contains': ['1500.f1.a1', '2000.a1.a1', '13500.l1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': None, 'generators': [29128, 108000, 115200, 6660, 71640, 4080], 'label': '162000.x.500.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '500.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '500.b1.a1', 'subgroup_fusion': None, 'weyl_group': '648.704'}
-
id: 62909952
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '180.a1.a1', '180.b1.a1', '270.a1.a1', '270.b1.a1', '270.i1.a1'], 'contains': ['1080.o1.a1', '1080.bg1.a1', '1080.cf1.a1', '1620.a1.a1', '2700.a1.a1', '2700.b1.a1', '2700.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 135, 'diagramx': None, 'generators': [242, 7200, 97344, 11100, 32400], 'label': '162000.x.540.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1.a1', 'old_label': '540.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.a1.a1', 'subgroup_fusion': None, 'weyl_group': '200.43'}
-
id: 62909953
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '180.b1.a1', '180.c1.a1', '270.h1.a1'], 'contains': ['1080.n1.a1', '1080.bh1.a1', '1080.cg1.a1', '1620.a1.a1', '2700.d1.a1', '2700.e1.a1', '2700.f1.a1', '2700.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 480, 97344, 11340, 32400], 'label': '162000.x.540.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '540.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.b1.a1', 'subgroup_fusion': None, 'weyl_group': '600.174'}
-
id: 62910628
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '13500.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.bj1.a1', '2700.bj1.a1', '3375.a1.a1', '4500.e1.a1'], 'contains': ['27000.d1.a1', '40500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4500, 'diagramx': None, 'generators': [75483, 10862, 25768], 'label': '162000.x.13500.h1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4500.e1.a1', 'old_label': '13500.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13500.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62909954
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '180.a1.a1', '180.c1.a1', '270.c1.a1'], 'contains': ['1080.x1.a1', '1080.bi1.a1', '1080.ch1.a1', '1620.a1.a1', '2700.h1.a1', '2700.i1.a1', '2700.j1.a1', '2700.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10862, 54480, 97344, 119340, 32400], 'label': '162000.x.540.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '540.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.c1.a1', 'subgroup_fusion': None, 'weyl_group': '600.161'}
-
id: 62909955
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.j1.a1', '90.c1.a1', '150.b1.a1', '270.b1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [1, 7200, 97344, 2, 108000, 32400, 11100, 108480], 'label': '162000.x.30.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909956
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '180.d1.a1', '180.h1.a1', '270.e1.a1'], 'contains': ['1080.j1.a1', '1080.bj1.a1', '1080.bu1.a1', '1620.b1.a1', '2700.b1.a1', '2700.l1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [242, 7200, 97344, 11100, 2160], 'label': '162000.x.540.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1.a1', 'old_label': '540.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.d1.a1', 'subgroup_fusion': None, 'weyl_group': '200.41'}
-
id: 62909957
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '180.e1.a1', '180.f1.a1', '180.i1.a1', '270.d1.a1'], 'contains': ['1080.l1.a1', '1080.bk1.a1', '1080.bv1.a1', '1620.c1.a1', '2700.c1.a1', '2700.l1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [10862, 7200, 32544, 11100, 2160], 'label': '162000.x.540.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.d1.a1', 'old_label': '540.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.e1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62909958
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '180.g1.a1', '180.j1.a1', '180.k1.a1', '270.h1.a1'], 'contains': ['1080.n1.a1', '1080.bl1.a1', '1080.bw1.a1', '1620.d1.a1', '2700.a1.a1', '2700.l1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [242, 7200, 2160, 11100, 32400], 'label': '162000.x.540.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.h1.a1', 'old_label': '540.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.f1.a1', 'subgroup_fusion': None, 'weyl_group': '200.49'}
-
id: 62909959
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '180.h1.a1', '180.l1.a1'], 'contains': ['1080.k1.a1', '1080.bm1.a1', '1080.bx1.a1', '1620.b1.a1', '2700.f1.a1', '2700.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [2, 480, 97344, 11340, 2160], 'label': '162000.x.540.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.h1.a1', 'old_label': '540.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.g1.a1', 'subgroup_fusion': None, 'weyl_group': '300.40'}
-
id: 62909960
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '180.i1.a1', '180.m1.a1'], 'contains': ['1080.m1.a1', '1080.bn1.a1', '1080.by1.a1', '1620.c1.a1', '2700.g1.a1', '2700.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [2, 480, 32544, 11340, 2160], 'label': '162000.x.540.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.i1.a1', 'old_label': '540.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.h1.a1', 'subgroup_fusion': None, 'weyl_group': '300.40'}
-
id: 62909961
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '180.k1.a1', '180.n1.a1', '270.h1.a1'], 'contains': ['1080.n1.a1', '1080.bo1.a1', '1080.bz1.a1', '1620.d1.a1', '2700.d1.a1', '2700.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 480, 144, 11340, 2160], 'label': '162000.x.540.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1.a1', 'old_label': '540.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.i1.a1', 'subgroup_fusion': None, 'weyl_group': '600.174'}
-
id: 62909962
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '180.j1.a1', '180.n1.a1', '270.i1.a1'], 'contains': ['1080.o1.a1', '1080.bp1.a1', '1080.ca1.a1', '1620.d1.a1', '2700.e1.a1', '2700.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 480, 2160, 11340, 32400], 'label': '162000.x.540.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '540.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.j1.a1', 'subgroup_fusion': None, 'weyl_group': '300.40'}
-
id: 62909963
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '180.d1.a1', '180.l1.a1'], 'contains': ['1080.s1.a1', '1080.bq1.a1', '1080.cb1.a1', '1620.b1.a1', '2700.i1.a1', '2700.n1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10862, 54480, 97344, 119340, 2160], 'label': '162000.x.540.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.d1.a1', 'old_label': '540.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.k1.a1', 'subgroup_fusion': None, 'weyl_group': '300.40'}
-
id: 62909964
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '180.e1.a1', '180.m1.a1', '270.f1.a1'], 'contains': ['1080.u1.a1', '1080.br1.a1', '1080.cc1.a1', '1620.c1.a1', '2700.j1.a1', '2700.n1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10862, 54480, 129744, 119340, 2160], 'label': '162000.x.540.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.d1.a1', 'old_label': '540.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.l1.a1', 'subgroup_fusion': None, 'weyl_group': '600.163'}
-
id: 62909965
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '180.f1.a1', '180.m1.a1', '270.g1.a1'], 'contains': ['1080.v1.a1', '1080.bs1.a1', '1080.cd1.a1', '1620.c1.a1', '2700.k1.a1', '2700.n1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10862, 54480, 32544, 119340, 2160], 'label': '162000.x.540.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1.a1', 'old_label': '540.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.m1.a1', 'subgroup_fusion': None, 'weyl_group': '600.164'}
-
id: 62909966
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['60.c1.a1', '60.f1.a1', '60.f2.a1', '90.d1.a1', '90.e1.a1', '90.g1.a1', '150.a1.a1', '150.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10503, 54480, 32544, 7200, 108000, 2160, 11100, 10862], 'label': '162000.x.30.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '30.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.632'}
-
id: 62909967
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '180.g1.a1', '180.n1.a1'], 'contains': ['1080.y1.a1', '1080.bt1.a1', '1080.ce1.a1', '1620.d1.a1', '2700.h1.a1', '2700.n1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10862, 54480, 66960, 119340, 32400], 'label': '162000.x.540.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.g1.a1', 'old_label': '540.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.n1.a1', 'subgroup_fusion': None, 'weyl_group': '300.40'}
-
id: 62909968
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.a1', '180.o1.a1', '180.w1.a1'], 'contains': ['1080.b1.a1', '1620.e1.a1', '2700.o1.a1', '2700.p1.a1', '2700.q1.a1', '2700.r1.a1', '2700.t1.a1', '2700.u1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 10862, 32544, 112080, 2160], 'label': '162000.x.540.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.w1.a1', 'old_label': '540.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.o1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
-
id: 62909969
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.a1', '180.p1.a1', '180.x1.a1'], 'contains': ['1080.c1.a1', '1620.e2.a1', '2700.o1.a1', '2700.s1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 10862, 129744, 112080, 2160], 'label': '162000.x.540.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.x1.a1', 'old_label': '540.p1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.p1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909970
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.a1', '180.q1.a1', '180.y1.a1'], 'contains': ['1080.d1.a1', '1620.f1.a1', '2700.r1.a1', '2700.s1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 10862, 97344, 112080, 32400], 'label': '162000.x.540.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.y1.a1', 'old_label': '540.q1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.q1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909971
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.a1', '180.r1.a1', '180.z1.a1'], 'contains': ['1080.e1.a1', '1620.g1.a1', '2700.p1.a1', '2700.s1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 10862, 129744, 112080, 131760], 'label': '162000.x.540.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.z1.a1', 'old_label': '540.r1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.r1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909972
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.a1', '180.s1.a1', '180.z1.a1'], 'contains': ['1080.g1.a1', '1620.g1.a1', '2700.q1.a1', '2700.s1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 10862, 129744, 112080, 34560], 'label': '162000.x.540.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.z1.a1', 'old_label': '540.s1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.s1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909973
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.a1', '180.u1.a1', '180.v1.a1', '180.ba1.a1'], 'contains': ['1080.h1.a1', '1620.h1.a1', '2700.s1.a1', '2700.t1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 10862, 129744, 112080, 99360], 'label': '162000.x.540.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.ba1.a1', 'old_label': '540.t1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.t1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909974
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.a1', '180.t1.a1', '180.ba1.a1'], 'contains': ['1080.i1.a1', '1620.h1.a1', '2700.s1.a1', '2700.u1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 10862, 129744, 112080, 66960], 'label': '162000.x.540.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.ba1.a1', 'old_label': '540.u1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.u1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909975
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1.a1', '180.w1.a1', '180.bc1.a1', '270.d1.a1'], 'contains': ['1080.l1.a1', '1620.e1.a1', '2700.v1.a1', '2700.w1.a1', '2700.x1.a1', '2700.y1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10503, 10862, 32544, 7200, 2160], 'label': '162000.x.540.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.d1.a1', 'old_label': '540.v1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.v1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62909976
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.v2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1.a1', '180.x1.a1', '180.bb1.a1', '270.d1.a1'], 'contains': ['1080.l1.a1', '1620.e2.a1', '2700.v1.a1', '2700.x2.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10503, 10862, 129744, 7200, 2160], 'label': '162000.x.540.v2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1.a1', 'old_label': '540.v2.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.v2.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62909977
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['60.b1.a1', '60.k1.a1', '60.l1.a1', '90.h1.a1', '150.b1.a1', '150.d1.a1', '270.e1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [1, 7200, 97344, 2, 108000, 2160, 11100, 108480], 'label': '162000.x.30.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '30.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909978
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1.a1', '180.y1.a1', '180.bd1.a1', '270.a1.a1'], 'contains': ['1080.o1.a1', '1620.f1.a1', '2700.x1.a1', '2700.x2.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10503, 10862, 97344, 7200, 32400], 'label': '162000.x.540.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '540.w1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.w1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909979
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1.a1', '180.z1.a1', '180.be1.a1'], 'contains': ['1080.q1.a1', '1620.g1.a1', '2700.w1.a1', '2700.x2.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 10862, 129744, 7200, 131760], 'label': '162000.x.540.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.z1.a1', 'old_label': '540.x1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.x1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909980
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1.a1', '180.ba1.a1', '180.bf1.a1'], 'contains': ['1080.r1.a1', '1620.h1.a1', '2700.x2.a1', '2700.y1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 10862, 129744, 7200, 66960], 'label': '162000.x.540.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.ba1.a1', 'old_label': '540.y1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.y1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909981
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1.a1', '180.w1.a1', '180.bg1.a1', '270.f1.a1'], 'contains': ['1080.u1.a1', '1620.e1.a1', '2700.z1.a1', '2700.ba1.a1', '2700.bb1.a1', '2700.bd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10503, 10862, 32544, 108480, 2160], 'label': '162000.x.540.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.d1.a1', 'old_label': '540.z1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.z1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62909982
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1.a1', '180.x1.a1', '180.bg2.a1', '270.g1.a1'], 'contains': ['1080.v1.a1', '1620.e2.a1', '2700.z1.a1', '2700.bc1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10503, 10862, 129744, 108480, 2160], 'label': '162000.x.540.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1.a1', 'old_label': '540.ba1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62909983
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1.a1', '180.y1.a1', '180.bh1.a1', '270.c1.a1'], 'contains': ['1080.x1.a1', '1620.f1.a1', '2700.bb1.a1', '2700.bc1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10503, 10862, 97344, 108480, 32400], 'label': '162000.x.540.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '540.bb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '200.48'}
-
id: 62909984
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1.a1', '180.z1.a1', '180.bi1.a1'], 'contains': ['1080.ba1.a1', '1620.g1.a1', '2700.ba1.a1', '2700.bc1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 10862, 129744, 108480, 131760], 'label': '162000.x.540.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.z1.a1', 'old_label': '540.bc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909985
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1.a1', '180.ba1.a1', '180.bj1.a1'], 'contains': ['1080.be1.a1', '1620.h1.a1', '2700.bc1.a1', '2700.bd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 10862, 129744, 108480, 66960], 'label': '162000.x.540.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.ba1.a1', 'old_label': '540.bd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62909986
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.g1.a1', '180.p1.a1', '180.bb1.a1', '180.bg2.a1', '270.f1.a1'], 'contains': ['1080.u1.a1', '1620.e2.a1', '2700.be1.a1', '2700.bg1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10503, 54480, 129744, 10862, 2160], 'label': '162000.x.540.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '540.be1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.be1.a1', 'subgroup_fusion': None, 'weyl_group': '600.163'}
-
id: 62909987
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.g1.a1', '180.o1.a1', '180.bc1.a1', '180.bg1.a1', '270.g1.a1'], 'contains': ['1080.v1.a1', '1620.e1.a1', '2700.be1.a1', '2700.bf1.a1', '2700.bh1.a1', '2700.bi1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10503, 54480, 32544, 10862, 2160], 'label': '162000.x.540.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '540.bf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '600.164'}
-
id: 62909988
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.d1.a1', '60.m1.a1', '60.n1.a1', '60.o1.a1', '90.f1.a1', '90.i1.a1', '150.e1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [2, 7200, 97344, 125640, 108000, 32400, 11100, 480], 'label': '162000.x.30.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62909989
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.g1.a1', '180.q1.a1', '180.bd1.a1', '180.bh1.a1', '270.c1.a1'], 'contains': ['1080.x1.a1', '1620.f1.a1', '2700.bg1.a1', '2700.bh1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10503, 54480, 97344, 10862, 32400], 'label': '162000.x.540.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '540.bg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '600.161'}
-
id: 62910629
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '13500.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8100.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1500.d1.a1', '2700.bk1.a1', '2700.bl1.a1', '2700.bn1.a1', '6750.b1.a1'], 'contains': ['27000.e1.a1', '40500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [1, 2, 7200], 'label': '162000.x.13500.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.b1.a1', 'old_label': '13500.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13500.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62909990
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.g1.a1', '180.r1.a1', '180.s1.a1', '180.be1.a1', '180.bi1.a1'], 'contains': ['1080.z1.a1', '1620.g1.a1', '2700.bf1.a1', '2700.bg1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 54480, 129744, 10862, 131760], 'label': '162000.x.540.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '540.bh1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62909991
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.g1.a1', '180.t1.a1', '180.u1.a1', '180.bf1.a1', '180.bj1.a1'], 'contains': ['1080.bd1.a1', '1620.h1.a1', '2700.bg1.a1', '2700.bi1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 54480, 129744, 10862, 66960], 'label': '162000.x.540.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '540.bi1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62909992
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.h1.a1', '180.v1.a1'], 'contains': ['1080.bf1.a1', '1620.h1.a1', '13500.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [75483, 25768, 138384, 10862, 66960], 'label': '162000.x.540.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.v1.a1', 'old_label': '540.bj1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '300.23'}
-
id: 62909993
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.j1.a1', '108.i1.a1', '270.b1.a1'], 'contains': ['1080.bg1.a1', '1620.i1.a1', '2700.bk1.a1', '2700.bl1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [1, 2, 7200, 32400, 97344], 'label': '162000.x.540.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.b1.a1', 'old_label': '540.bk1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62909994
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.k1.a1', '108.i1.a1', '270.e1.a1'], 'contains': ['1080.bj1.a1', '1620.j1.a1', '2700.bk1.a1', '2700.bn1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [1, 2, 7200, 64944, 2160], 'label': '162000.x.540.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1.a1', 'old_label': '540.bl1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '120.41'}
-
id: 62909995
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.l1.a1', '108.i1.a1', '270.e1.a1'], 'contains': ['1080.bj1.a1', '1620.k1.a1', '2700.bl1.a1', '2700.bn1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 7200, 97344, 2, 2160], 'label': '162000.x.540.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1.a1', 'old_label': '540.bm1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '600.166'}
-
id: 62909996
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '180.bl1.a1', '180.bm1.a1', '270.h1.a1'], 'contains': ['1080.bh1.a1', '1080.bl1.a1', '1080.bz1.a1', '1620.l1.a1', '2700.bm1.a1', '2700.bp1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [17642, 2160, 480, 11340, 144], 'label': '162000.x.540.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.h1.a1', 'old_label': '540.bn1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62909997
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '180.bl1.a1', '180.bq1.a1', '270.i1.a1'], 'contains': ['1080.bg1.a1', '1080.bp1.a1', '1080.ca1.a1', '1620.l1.a1', '2700.bm1.a1', '2700.bq1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [17642, 66960, 480, 11340, 32400], 'label': '162000.x.540.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.i1.a1', 'old_label': '540.bo1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62909998
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.k1.a1', '180.bm1.a1', '180.bq1.a1', '270.h1.a1'], 'contains': ['1080.bh1.a1', '1080.bo1.a1', '1080.bw1.a1', '1620.l1.a1', '2700.bo1.a1', '2700.br1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [17882, 66960, 7200, 11100, 32400], 'label': '162000.x.540.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.h1.a1', 'old_label': '540.bp1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62909999
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.a1.a1'], 'contains': ['72.d1.a1', '72.f1.a1', '72.i1.a1', '108.a1.a1', '108.c1.a1', '180.a1.a1', '180.d1.a1', '180.e1.a1', '180.f1.a1', '180.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10862, 66960, 7200, 54480, 119340, 32400, 97344], 'label': '162000.x.36.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910000
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '180.bn1.a1', '180.br1.a1', '270.h1.a1'], 'contains': ['1080.bl1.a1', '1080.bo1.a1', '1080.cg1.a1', '1620.m1.a1', '2700.bp1.a1', '2700.bq1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [17642, 480, 97344, 11340, 32400], 'label': '162000.x.540.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1.a1', 'old_label': '540.bq1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '600.174'}
-
id: 62910001
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.k1.a1', '180.br1.a1', '270.i1.a1'], 'contains': ['1080.bp1.a1', '1080.cf1.a1', '1620.m1.a1', '2700.br1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [17882, 7200, 97344, 11100, 32400], 'label': '162000.x.540.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '540.br1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.br1.a1', 'subgroup_fusion': None, 'weyl_group': '600.170'}
-
id: 62910002
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.m1.a1', '180.bs1.a1', '270.i1.a1'], 'contains': ['1080.ca1.a1', '1080.cf1.a1', '1620.n1.a1', '2700.bs1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 135, 'diagramx': None, 'generators': [119340, 480, 66960, 125640, 32400], 'label': '162000.x.540.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1.a1', 'old_label': '540.bs1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '600.170'}
-
id: 62910003
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '540.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.m1.a1', '180.bs1.a1', '180.bt1.a1', '270.h1.a1'], 'contains': ['1080.bw1.a1', '1080.bz1.a1', '1080.cg1.a1', '1620.n1.a1', '2700.bs1.a1', '2700.bt1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [119340, 480, 97344, 125640, 32400], 'label': '162000.x.540.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.h1.a1', 'old_label': '540.bt1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '600.174'}
-
id: 62910004
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '200.a1.a1', '300.e1.a1'], 'contains': ['1200.a1.a1', '1800.c1.a1', '1800.j1.a1', '3000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': None, 'generators': [10862, 61200, 58080, 25768, 136224], 'label': '162000.x.600.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '600.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.a1.a1', 'subgroup_fusion': None, 'weyl_group': '540.37'}
-
id: 62910005
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '200.a1.a1'], 'contains': ['1200.b1.a1', '1800.c1.a1', '1800.k1.a1', '3000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': None, 'generators': [10862, 61200, 58080, 25288, 136224], 'label': '162000.x.600.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.a1.a1', 'old_label': '600.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.b1.a1', 'subgroup_fusion': None, 'weyl_group': '270.6'}
-
id: 62910006
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '120.d1.a1', '120.e1.a1', '300.a1.a1', '300.d1.a1', '300.f1.a1'], 'contains': ['1200.c1.a1', '1800.a1.a1', '1800.l1.a1', '1800.m1.a1', '1800.y1.a1', '1800.z1.a1', '3000.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [10862, 7200, 108000, 480, 32400], 'label': '162000.x.600.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '600.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.c1.a1', 'subgroup_fusion': None, 'weyl_group': '80.34'}
-
id: 62910007
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '120.e1.a1', '120.f1.a1', '300.b1.a1'], 'contains': ['1200.d1.a1', '1800.b1.a1', '1800.n1.a1', '1800.o1.a1', '1800.ba1.a1', '1800.bb1.a1', '3000.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 7200, 108000, 480, 97344], 'label': '162000.x.600.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.a1', 'old_label': '600.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.d1.a1', 'subgroup_fusion': None, 'weyl_group': '40.5'}
-
id: 62910008
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '120.f1.a1', '200.a1.a1', '300.g1.a1'], 'contains': ['1200.e1.a1', '1800.c1.a1', '1800.d1.a1', '1800.p1.a1', '1800.q1.a1', '1800.bc1.a1', '3000.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': None, 'generators': [10862, 61200, 108000, 58080, 136224], 'label': '162000.x.600.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '600.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.e1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910009
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '120.e1.a1', '120.f1.a1', '120.g1.a1', '300.c1.a1', '300.h1.a1', '300.h2.a1'], 'contains': ['1200.f1.a1', '1800.e1.a1', '1800.f1.a1', '1800.r1.a1', '1800.s1.a1', '1800.t1.a1', '1800.bd1.a1', '1800.be1.a1', '3000.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 7200, 108000, 480, 66960], 'label': '162000.x.600.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '600.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.f1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910010
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.d1.a1'], 'contains': ['72.e1.a1', '72.g1.a1', '72.j1.a1', '108.a1.a1', '108.b1.a1', '180.b1.a1', '180.h1.a1', '180.i1.a1', '180.j1.a1', '180.k1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2, 2160, 7200, 480, 11340, 32400, 97344], 'label': '162000.x.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910011
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '120.d1.a1', '120.f1.a1', '120.g1.a1', '300.i1.a1'], 'contains': ['1200.g1.a1', '1800.g1.a1', '1800.h1.a1', '1800.i1.a1', '1800.u1.a1', '1800.v1.a1', '1800.w1.a1', '1800.x1.a1', '1800.bf1.a1', '1800.bg1.a1', '3000.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 7200, 108000, 54480, 41184], 'label': '162000.x.600.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '600.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.g1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910012
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.h1.a1', '120.k1.a1', '300.a1.a1', '300.l1.a1', '300.n1.a1'], 'contains': ['1200.c1.a1', '1800.bh1.a1', '1800.bl1.a1', '1800.bm1.a1', '1800.bp1.a1', '3000.d1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [2, 32400, 480, 7200, 108000], 'label': '162000.x.600.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1.a1', 'old_label': '600.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.h1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 62910013
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.h1.a1', '120.i1.a1', '300.b1.a1', '300.j1.a1', '300.k1.a1'], 'contains': ['1200.d1.a1', '1800.bi1.a1', '1800.bn1.a1', '1800.bq1.a1', '3000.d1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [2, 97344, 480, 7200, 108000], 'label': '162000.x.600.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '600.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.i1.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
-
id: 62910014
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.h1.a1', '120.j1.a1', '300.c1.a1'], 'contains': ['1200.f1.a1', '1800.bj1.a1', '1800.bk1.a1', '1800.bo1.a1', '1800.br1.a1', '3000.d1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [2, 32544, 480, 7200, 108000], 'label': '162000.x.600.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '600.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.j1.a1', 'subgroup_fusion': None, 'weyl_group': '72.21'}
-
id: 62910015
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.i1.a1', '120.j1.a1', '120.k1.a1', '300.d1.a1', '300.m1.a1', '300.n1.a1'], 'contains': ['1200.c1.a1', '1800.bs1.a1', '1800.bt1.a1', '1800.bu1.a1', '3000.d1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 480, 108000, 7200, 2160], 'label': '162000.x.600.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '600.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.k1.a1', 'subgroup_fusion': None, 'weyl_group': '720.774'}
-
id: 62910016
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.l1.a1', '120.m1.a1', '120.n1.a1', '300.d1.a1', '300.l1.a1', '300.o1.a1'], 'contains': ['1200.c1.a1', '1800.bv1.a1', '1800.bw1.a1', '1800.bx1.a1', '3000.e1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [11100, 2160, 480, 7200, 108000], 'label': '162000.x.600.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '600.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.l1.a1', 'subgroup_fusion': None, 'weyl_group': '144.115'}
-
id: 62910017
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.n1.a1', '120.o1.a1', '300.a1.a1', '300.n1.a1', '300.o1.a1'], 'contains': ['1200.c1.a1', '1800.by1.a1', '1800.cc1.a1', '1800.cd1.a1', '1800.cg1.a1', '3000.e1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [11100, 480, 108000, 7200, 32400], 'label': '162000.x.600.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1.a1', 'old_label': '600.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.m1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62910018
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.l1.a1', '120.o1.a1', '300.b1.a1'], 'contains': ['1200.d1.a1', '1800.bz1.a1', '1800.ce1.a1', '1800.ch1.a1', '3000.e1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [11100, 480, 108000, 7200, 97344], 'label': '162000.x.600.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '600.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.n1.a1', 'subgroup_fusion': None, 'weyl_group': '360.130'}
-
id: 62910019
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '600.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.m1.a1', '120.o1.a1', '300.c1.a1'], 'contains': ['1200.f1.a1', '1800.ca1.a1', '1800.cb1.a1', '1800.cf1.a1', '1800.ci1.a1', '3000.e1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [11100, 480, 108000, 7200, 32544], 'label': '162000.x.600.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '600.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.o1.a1', 'subgroup_fusion': None, 'weyl_group': '360.129'}
-
id: 62910020
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.b1.a1', '216.c1.a1', '216.d1.a1', '324.a1.a1', '324.b1.a1'], 'contains': ['1296.a1.a1', '3240.a1.a1', '3240.b1.a1', '3240.c1.a1', '3240.d1.a1', '3240.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [10862, 66960, 32400, 97344], 'label': '162000.x.648.a1.a1', 'mobius_quo': 0, 'mobius_sub': 324, 'normal_closure': '648.a1.a1', 'normal_contained_in': ['24.a1.a1'], 'normal_contains': ['1296.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '648.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6000.bm'}
-
id: 62910021
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.b1.a1', '18.c1.a1', '18.d1.a1'], 'contains': ['72.e1.a1', '72.h1.a1', '72.k1.a1', '108.b1.a1', '108.c1.a1', '180.c1.a1', '180.l1.a1', '180.m1.a1', '180.n1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 2160, 108480, 108000, 119340, 32400, 97344], 'label': '162000.x.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910022
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '216.f1.a1', '216.g1.a1', '324.a1.a1', '324.c1.a1', '324.d1.a1'], 'contains': ['1296.a1.a1', '3240.f1.a1', '3240.g1.a1', '3240.h1.a1', '3240.i1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [2, 32400, 2160, 97344], 'label': '162000.x.648.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '648.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1.a1', 'subgroup_fusion': None, 'weyl_group': '80.34'}
-
id: 62910023
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.h1.a1', '216.i1.a1', '216.j1.a1', '324.a1.a1', '324.d1.a1', '324.e1.a1'], 'contains': ['1296.a1.a1', '3240.j1.a1', '3240.k1.a1', '3240.l1.a1', '3240.m1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [11100, 97344, 32400, 66960], 'label': '162000.x.648.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '648.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1.a1', 'subgroup_fusion': None, 'weyl_group': '400.129'}
-
id: 62910024
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '675.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.b1.a1', '75.a1.a1'], 'contains': ['1350.e1.a1', '1350.f1.a1', '1350.g1.a1', '2025.a1.a1', '3375.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [108001, 2160, 108482, 119340, 125640, 7200], 'label': '162000.x.675.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '675.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '675.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910025
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.c1.a1', '360.a1.a1'], 'contains': ['2160.a1.a1', '2160.s1.a1', '2160.t1.a1', '3600.a1.a1', '3600.b1.a1', '3600.g1.a1', '3600.h1.a1', '3600.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [115680, 101664, 2160, 61200], 'label': '162000.x.720.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '720.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910026
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.d1.a1', '360.b1.a1'], 'contains': ['2160.b1.a1', '2160.v1.a1', '2160.w1.a1', '3600.a1.a1', '3600.c1.a1', '3600.d1.a1', '3600.f1.a1', '3600.g1.a1', '3600.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54480, 34704, 2160, 61200], 'label': '162000.x.720.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '720.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910027
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.d1.a1', '360.c1.a1'], 'contains': ['2160.c1.a1', '2160.u1.a1', '2160.w1.a1', '3600.a1.a1', '3600.d1.a1', '3600.e1.a1', '3600.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [115680, 144, 66960, 61200], 'label': '162000.x.720.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '720.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910028
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.e1.a1', '360.d1.a1'], 'contains': ['2160.d1.a1', '2160.x1.a1', '2160.y1.a1', '3600.a1.a1', '3600.b1.a1', '3600.e1.a1', '3600.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54480, 129744, 32400, 61200], 'label': '162000.x.720.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '720.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910029
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.f1.a1', '360.e1.a1'], 'contains': ['2160.e1.a1', '2160.z1.a1', '2160.bc1.a1', '3600.b1.a1', '3600.c1.a1', '3600.e1.a1', '3600.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [115680, 6624, 131760, 61200], 'label': '162000.x.720.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '720.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910030
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.f1.a1', '360.f1.a1'], 'contains': ['2160.g1.a1', '2160.z1.a1', '2160.bb1.a1', '3600.b1.a1', '3600.d1.a1', '3600.e1.a1', '3600.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [115680, 97344, 66960, 61200], 'label': '162000.x.720.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '720.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910031
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.f1.a1', '360.g1.a1'], 'contains': ['2160.f1.a1', '2160.ba1.a1', '2160.bb1.a1', '2160.bc1.a1', '3600.b1.a1', '3600.d1.a1', '3600.f1.a1', '3600.g1.a1', '3600.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [115680, 73584, 34560, 61200], 'label': '162000.x.720.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '720.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910032
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.d1.a1'], 'contains': ['72.a1.a1', '108.d1.a1', '108.g1.a1', '180.o1.a1', '180.p1.a1', '180.q1.a1', '180.r1.a1', '180.s1.a1', '180.t1.a1', '180.u1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [10503, 99360, 10862, 54480, 61200, 32400, 97344], 'label': '162000.x.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '36.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1500.148'}
-
id: 62910033
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.g1.a1', '360.h1.a1'], 'contains': ['2160.i1.a1', '2160.bd1.a1', '2160.be1.a1', '3600.e1.a1', '3600.f1.a1', '3600.h1.a1', '3600.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [115680, 32544, 66960, 61200], 'label': '162000.x.720.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '720.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910034
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.a1.a1', '240.b1.a1', '240.g1.a1', '360.i1.a1'], 'contains': ['2160.h1.a1', '2160.bd1.a1', '3600.e1.a1', '3600.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [115680, 129744, 66960, 61200], 'label': '162000.x.720.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '720.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.1'}
-
id: 62910035
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '240.a1.a1', '360.j1.a1'], 'contains': ['2160.h1.a1', '2160.bf1.a1', '18000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [25768, 4464, 66960, 58080], 'label': '162000.x.720.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '720.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.j1.a1', 'subgroup_fusion': None, 'weyl_group': '900.90'}
-
id: 62910036
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '240.b1.a1', '360.k1.a1'], 'contains': ['2160.h1.a1', '18000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25288, 4464, 66960, 58080], 'label': '162000.x.720.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '720.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.k1.a1', 'subgroup_fusion': None, 'weyl_group': '450.22'}
-
id: 62910037
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.c1.a1', '360.l1.a1', '360.bk1.a1', '360.bv1.a1'], 'contains': ['2160.a1.a1', '2160.j1.a1', '2160.s1.a1', '3600.l1.a1', '3600.n1.a1', '3600.v1.a1', '3600.x1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 144, 131760, 61200], 'label': '162000.x.720.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '720.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910038
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.c1.a1', '360.m1.a1'], 'contains': ['2160.a1.a1', '2160.k1.a1', '2160.t1.a1', '3600.m1.a1', '3600.o1.a1', '3600.u1.a1', '3600.v1.a1', '3600.w1.a1', '3600.x1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [480, 97344, 2160, 61200], 'label': '162000.x.720.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '720.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910039
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.d1.a1', '360.n1.a1'], 'contains': ['2160.b1.a1', '2160.c1.a1', '2160.m1.a1', '2160.w1.a1', '3600.m1.a1', '3600.p1.a1', '3600.q1.a1', '3600.t1.a1', '3600.v1.a1', '3600.x1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [480, 32544, 2160, 61200], 'label': '162000.x.720.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '720.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910040
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.d1.a1', '360.o1.a1', '360.bl1.a1', '360.bw1.a1'], 'contains': ['2160.b1.a1', '2160.l1.a1', '2160.u1.a1', '3600.l1.a1', '3600.p1.a1', '3600.r1.a1', '3600.u1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 144, 66960, 61200], 'label': '162000.x.720.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '720.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910041
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.d1.a1', '360.p1.a1', '360.bm1.a1', '360.bx1.a1'], 'contains': ['2160.c1.a1', '2160.l1.a1', '2160.v1.a1', '3600.l1.a1', '3600.q1.a1', '3600.s1.a1', '3600.w1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 144, 99360, 61200], 'label': '162000.x.720.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '720.p1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.p1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910113
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bk1.a1', '180.bo1.a1', '300.j1.a1', '450.d1.a1'], 'contains': ['1800.bq1.a1', '4500.j1.a1', '8100.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [1, 2, 108480, 64944, 108000], 'label': '162000.x.900.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.d1.a1', 'old_label': '900.bl1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
-
id: 62910042
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.e1.a1', '360.q1.a1', '360.bn1.a1', '360.by1.a1'], 'contains': ['2160.d1.a1', '2160.n1.a1', '2160.y1.a1', '3600.l1.a1', '3600.m1.a1', '3600.o1.a1', '3600.t1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 97344, 32400, 61200], 'label': '162000.x.720.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '720.q1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910043
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': ['40500.c1.a1', '40500.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.a1.a1', '16.a1.a1', '108.l1.a1', '500.b1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [32400, 66960, 64860, 108000, 480, 32544, 29128, 68040, 7200], 'label': '162000.x.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '162000.x'}
-
id: 62910044
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1'], 'contains': ['72.b1.a1', '108.d1.a1', '108.h1.a1', '180.v1.a1', '900.v1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [75483, 32544, 10862, 25768, 58080, 66960, 32400], 'label': '162000.x.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1.a1', 'old_label': '36.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1500.115'}
-
id: 62910045
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.e1.a1', '360.r1.a1', '360.bh1.a1', '360.cg1.a1'], 'contains': ['2160.d1.a1', '2160.o1.a1', '2160.x1.a1', '3600.m1.a1', '3600.n1.a1', '3600.r1.a1', '3600.s1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 66960, 32400, 61200], 'label': '162000.x.720.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '720.r1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910046
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.f1.a1', '360.s1.a1'], 'contains': ['2160.e1.a1', '2160.f1.a1', '2160.p1.a1', '2160.bb1.a1', '3600.n1.a1', '3600.o1.a1', '3600.p1.a1', '3600.t1.a1', '3600.v1.a1', '3600.w1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [480, 97344, 34560, 61200], 'label': '162000.x.720.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '720.s1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910047
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.f1.a1', '360.t1.a1'], 'contains': ['2160.e1.a1', '2160.g1.a1', '2160.q1.a1', '2160.ba1.a1', '3600.o1.a1', '3600.p1.a1', '3600.s1.a1', '3600.x1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 97344, 99360, 61200], 'label': '162000.x.720.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '720.t1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910048
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.f1.a1', '360.u1.a1'], 'contains': ['2160.f1.a1', '2160.g1.a1', '2160.p1.a1', '2160.bc1.a1', '3600.n1.a1', '3600.o1.a1', '3600.q1.a1', '3600.t1.a1', '3600.u1.a1', '3600.x1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [480, 97344, 131760, 61200], 'label': '162000.x.720.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '720.u1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910049
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.f1.a1', '360.v1.a1'], 'contains': ['2160.f1.a1', '2160.q1.a1', '2160.z1.a1', '3600.o1.a1', '3600.q1.a1', '3600.r1.a1', '3600.v1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 97344, 66960, 61200], 'label': '162000.x.720.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '720.v1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910050
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.g1.a1', '360.w1.a1'], 'contains': ['2160.i1.a1', '2160.r1.a1', '2160.bd1.a1', '3600.r1.a1', '3600.t1.a1', '3600.w1.a1', '3600.x1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 32544, 66960, 61200], 'label': '162000.x.720.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '720.w1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910051
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.g1.a1', '360.x1.a1'], 'contains': ['2160.h1.a1', '2160.i1.a1', '2160.r1.a1', '2160.be1.a1', '3600.s1.a1', '3600.t1.a1', '3600.u1.a1', '3600.v1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 129744, 99360, 61200], 'label': '162000.x.720.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '720.x1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910052
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '240.c1.a1', '360.y1.a1', '360.bo1.a1', '360.bz1.a1'], 'contains': ['2160.j1.a1', '2160.k1.a1', '2160.t1.a1', '3600.y1.a1', '3600.ba1.a1', '3600.bf1.a1', '3600.bg1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 97344, 2160, 7200], 'label': '162000.x.720.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '720.y1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910053
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '240.c1.a1', '360.z1.a1', '360.bs1.a1', '360.cd1.a1'], 'contains': ['2160.k1.a1', '2160.s1.a1', '3600.z1.a1', '3600.bb1.a1', '3600.bf1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 41184, 32400, 7200], 'label': '162000.x.720.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '720.z1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910054
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '240.d1.a1', '360.ba1.a1', '360.bp1.a1', '360.ca1.a1'], 'contains': ['2160.l1.a1', '2160.m1.a1', '2160.w1.a1', '3600.y1.a1', '3600.bc1.a1', '3600.bd1.a1', '3600.bf1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 144, 66960, 7200], 'label': '162000.x.720.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '720.ba1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910055
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.a1.a1'], 'contains': ['72.d1.a1', '108.d1.a1', '108.e1.a1', '108.f1.a1', '180.w1.a1', '180.x1.a1', '180.y1.a1', '180.z1.a1', '180.ba1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [10503, 99360, 7200, 10862, 108480, 32400, 97344], 'label': '162000.x.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1000.170'}
-
id: 62910056
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '240.d1.a1', '360.bb1.a1', '360.bt1.a1', '360.ce1.a1'], 'contains': ['2160.m1.a1', '2160.u1.a1', '2160.v1.a1', '3600.z1.a1', '3600.bc1.a1', '3600.be1.a1', '3600.bg1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 69264, 32400, 7200], 'label': '162000.x.720.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '720.bb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910057
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '240.e1.a1', '360.bc1.a1', '360.bi1.a1', '360.bq1.a1', '360.bu1.a1', '360.cb1.a1', '360.cf1.a1', '360.ch1.a1'], 'contains': ['2160.n1.a1', '2160.o1.a1', '2160.y1.a1', '3600.y1.a1', '3600.z1.a1', '3600.ba1.a1', '3600.bd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 97344, 32400, 7200], 'label': '162000.x.720.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '720.bc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 62910058
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '240.e1.a1', '360.bd1.a1', '360.bj1.a1', '360.br1.a1', '360.cc1.a1', '360.ci1.a1'], 'contains': ['2160.n1.a1', '2160.x1.a1', '3600.y1.a1', '3600.bb1.a1', '3600.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [480, 144, 2160, 7200], 'label': '162000.x.720.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '720.bd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
-
id: 62910059
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '240.f1.a1', '360.be1.a1'], 'contains': ['2160.p1.a1', '2160.q1.a1', '2160.bb1.a1', '2160.bc1.a1', '3600.ba1.a1', '3600.bb1.a1', '3600.bc1.a1', '3600.bd1.a1', '3600.bf1.a1', '3600.bg1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [480, 97344, 66960, 7200], 'label': '162000.x.720.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '720.be1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.be1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910060
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '240.f1.a1', '360.bf1.a1'], 'contains': ['2160.p1.a1', '2160.z1.a1', '2160.ba1.a1', '3600.ba1.a1', '3600.bc1.a1', '3600.be1.a1', '3600.bf1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7680, 97344, 34560, 7200], 'label': '162000.x.720.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '720.bf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910061
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '720.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '240.g1.a1', '360.bg1.a1'], 'contains': ['2160.r1.a1', '2160.bd1.a1', '2160.be1.a1', '3600.bd1.a1', '3600.be1.a1', '3600.bf1.a1', '3600.bg1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7680, 32544, 66960, 7200], 'label': '162000.x.720.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '720.bg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910062
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '750.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.a1.a1', '150.c1.a1', '375.a1.a1'], 'contains': ['1500.a1.a1', '1500.c1.a1', '2250.a1.a1', '2250.b1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': None, 'generators': [10503, 108000, 54480, 11100, 7200, 10862], 'label': '162000.x.750.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '750.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '750.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
-
id: 62910063
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '750.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.b1.a1', '150.d1.a1', '375.a1.a1'], 'contains': ['1500.a1.a1', '1500.d1.a1', '2250.c1.a1', '6750.b1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': None, 'generators': [1, 108000, 7200, 11100, 2, 108480], 'label': '162000.x.750.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '750.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '750.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.158'}
-
id: 62910064
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '750.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.e1.a1', '250.a1.a1', '375.a1.a1'], 'contains': ['1500.a1.a1', '1500.e1.a1', '1500.f1.a1', '2250.d1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': None, 'generators': [2, 108000, 7200, 11100, 125640, 480], 'label': '162000.x.750.c1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '750.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '750.c1.a1', 'subgroup_fusion': None, 'weyl_group': '648.704'}
-
id: 62910065
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '810.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.a1.a1', '270.a1.a1', '270.c1.a1', '405.a1.a1'], 'contains': ['1620.a1.a1', '1620.f1.a1', '4050.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 135, 'diagramx': None, 'generators': [64263, 10862, 97344, 11100, 32400], 'label': '162000.x.810.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1.a1', 'old_label': '810.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.a1.a1', 'subgroup_fusion': None, 'weyl_group': '200.43'}
-
id: 62910066
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.a1.a1'], 'contains': ['72.d1.a1', '108.e1.a1', '108.g1.a1', '180.bb1.a1', '180.bc1.a1', '180.bd1.a1', '180.be1.a1', '180.bf1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10503, 99360, 10862, 54480, 7200, 32400, 97344], 'label': '162000.x.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910067
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '810.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.c1.a1', '162.b1.a1', '270.b1.a1', '405.a1.a1'], 'contains': ['1620.a1.a1', '1620.i1.a1', '4050.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [1, 2, 97344, 10860, 32400], 'label': '162000.x.810.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '810.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.b1.a1', 'subgroup_fusion': None, 'weyl_group': '200.43'}
-
id: 62910068
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '810.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.a1.a1', '270.d1.a1', '270.f1.a1', '270.g1.a1'], 'contains': ['1620.c1.a1', '1620.e1.a1', '1620.e2.a1', '4050.a1.a1', '4050.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [64263, 10862, 32544, 11100, 2160], 'label': '162000.x.810.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.d1.a1', 'old_label': '810.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.c1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62910069
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '810.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.h1.a1', '162.b1.a1', '270.e1.a1'], 'contains': ['1620.b1.a1', '1620.j1.a1', '1620.k1.a1', '4050.b1.a1', '4050.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [1, 2, 97344, 10860, 2160], 'label': '162000.x.810.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.d1.a1', 'old_label': '810.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.d1.a1', 'subgroup_fusion': None, 'weyl_group': '200.41'}
-
id: 62910070
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '810.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.c1.a1', '270.h1.a1', '270.i1.a1', '405.a1.a1'], 'contains': ['1620.a1.a1', '1620.d1.a1', '1620.l1.a1', '1620.m1.a1', '1620.n1.a1', '4050.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [108242, 125640, 97344, 119100, 32400], 'label': '162000.x.810.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '810.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.e1.a1', 'subgroup_fusion': None, 'weyl_group': '200.43'}
-
id: 62910071
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.g1.a1', '300.a1.a1'], 'contains': ['1800.m1.a1', '1800.bh1.a1', '1800.by1.a1', '2700.a1.a1', '2700.h1.a1', '4500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10862, 7200, 54480, 119340, 32400], 'label': '162000.x.900.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.a1.a1', 'old_label': '900.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910072
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.d1.a1', '300.b1.a1'], 'contains': ['1800.n1.a1', '1800.bi1.a1', '1800.bz1.a1', '2700.b1.a1', '2700.i1.a1', '4500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10862, 7200, 54480, 119340, 97344], 'label': '162000.x.900.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.b1.a1', 'old_label': '900.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.b1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910073
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.e1.a1', '300.c1.a1', '450.a1.a1'], 'contains': ['1800.r1.a1', '1800.bj1.a1', '1800.ca1.a1', '2700.c1.a1', '2700.j1.a1', '4500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10862, 7200, 54480, 119340, 129744], 'label': '162000.x.900.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.a1.a1', 'old_label': '900.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.c1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910074
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.f1.a1', '300.c1.a1', '450.b1.a1'], 'contains': ['1800.s1.a1', '1800.bk1.a1', '1800.cb1.a1', '2700.c1.a1', '2700.k1.a1', '4500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10862, 7200, 54480, 119340, 32544], 'label': '162000.x.900.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '900.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.d1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910075
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.b1.a1', '180.k1.a1', '300.a1.a1', '450.f1.a1'], 'contains': ['1800.y1.a1', '1800.bl1.a1', '1800.cc1.a1', '2700.a1.a1', '2700.d1.a1', '4500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [2, 7200, 480, 11340, 144], 'label': '162000.x.900.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.f1.a1', 'old_label': '900.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.e1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62910076
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.b1.a1', '180.j1.a1', '300.a1.a1', '450.i1.a1'], 'contains': ['1800.z1.a1', '1800.bm1.a1', '1800.cd1.a1', '2700.a1.a1', '2700.e1.a1', '4500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [2, 7200, 480, 11340, 32400], 'label': '162000.x.900.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.i1.a1', 'old_label': '900.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.f1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62910077
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.b1.a1'], 'contains': ['72.e1.a1', '108.f1.a1', '108.g1.a1', '180.bg1.a1', '180.bg2.a1', '180.bh1.a1', '180.bi1.a1', '180.bj1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10503, 99360, 10862, 54480, 108000, 32400, 97344], 'label': '162000.x.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910078
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.b1.a1', '180.h1.a1', '300.b1.a1'], 'contains': ['1800.ba1.a1', '1800.bn1.a1', '1800.ce1.a1', '2700.b1.a1', '2700.f1.a1', '4500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [2, 7200, 480, 11340, 97344], 'label': '162000.x.900.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.g1.a1', 'old_label': '900.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.g1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910079
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.b1.a1', '180.i1.a1', '300.c1.a1'], 'contains': ['1800.bd1.a1', '1800.bo1.a1', '1800.cf1.a1', '2700.c1.a1', '2700.g1.a1', '4500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [2, 7200, 480, 11340, 32544], 'label': '162000.x.900.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.h1.a1', 'old_label': '900.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.h1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910080
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.c1.a1', '180.n1.a1', '300.a1.a1', '450.f1.a1'], 'contains': ['1800.y1.a1', '1800.bp1.a1', '1800.cg1.a1', '2700.d1.a1', '2700.e1.a1', '2700.h1.a1', '4500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [2, 108480, 108000, 119340, 32400], 'label': '162000.x.900.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.e1.a1', 'old_label': '900.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.i1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62910081
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.c1.a1', '180.l1.a1', '300.b1.a1', '450.d1.a1'], 'contains': ['1800.bb1.a1', '1800.bq1.a1', '1800.ch1.a1', '2700.f1.a1', '2700.i1.a1', '4500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [2, 108480, 108000, 119340, 97344], 'label': '162000.x.900.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.a1', 'old_label': '900.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.j1.a1', 'subgroup_fusion': None, 'weyl_group': '360.130'}
-
id: 62910082
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.c1.a1', '180.m1.a1', '300.c1.a1', '450.c1.a1'], 'contains': ['1800.be1.a1', '1800.br1.a1', '1800.ci1.a1', '2700.g1.a1', '2700.j1.a1', '2700.k1.a1', '4500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 108480, 108000, 119340, 32544], 'label': '162000.x.900.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '900.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.k1.a1', 'subgroup_fusion': None, 'weyl_group': '360.129'}
-
id: 62910083
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.d1.a1', '180.e1.a1', '180.f1.a1', '180.g1.a1', '300.d1.a1', '450.e1.a1'], 'contains': ['1800.l1.a1', '1800.bs1.a1', '1800.bv1.a1', '2700.l1.a1', '2700.n1.a1', '4500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10862, 7200, 54480, 119340, 2160], 'label': '162000.x.900.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.e1.a1', 'old_label': '900.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.l1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910084
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.h1.a1', '180.i1.a1', '180.j1.a1', '180.k1.a1', '300.d1.a1', '450.f1.a1'], 'contains': ['1800.y1.a1', '1800.bt1.a1', '1800.bw1.a1', '2700.l1.a1', '2700.m1.a1', '4500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [2, 7200, 480, 11340, 2160], 'label': '162000.x.900.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.f1.a1', 'old_label': '900.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.m1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62910085
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.l1.a1', '180.m1.a1', '180.n1.a1', '300.d1.a1', '450.g1.a1', '450.h1.a1', '450.i1.a1'], 'contains': ['1800.z1.a1', '1800.bu1.a1', '1800.bx1.a1', '2700.m1.a1', '2700.n1.a1', '4500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [2, 108480, 108000, 119340, 2160], 'label': '162000.x.900.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '900.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.n1.a1', 'subgroup_fusion': None, 'weyl_group': '720.774'}
-
id: 62910086
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.o1.a1', '180.p1.a1', '300.f1.a1'], 'contains': ['1800.a1.a1', '2700.o1.a1', '2700.be1.a1', '4500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 10862, 54480, 61200, 2160], 'label': '162000.x.900.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.f1.a1', 'old_label': '900.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.o1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910087
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.o1.a1', '180.r1.a1', '300.e1.a1', '300.g1.a1'], 'contains': ['1800.c1.a1', '2700.p1.a1', '2700.bf1.a1', '4500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 10862, 54480, 61200, 36864], 'label': '162000.x.900.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '900.p1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.p1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910088
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.d1.a1'], 'contains': ['72.g1.a1', '72.k1.a1', '108.j1.a1', '180.bl1.a1', '180.bn1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [17642, 97344, 66960, 480, 119340, 32400, 108000], 'label': '162000.x.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62910089
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.o1.a1', '180.s1.a1', '300.g1.a1'], 'contains': ['1800.d1.a1', '2700.q1.a1', '2700.bf1.a1', '4500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 10862, 54480, 61200, 39024], 'label': '162000.x.900.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '900.q1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.q1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910090
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.p1.a1', '180.q1.a1', '180.r1.a1', '180.s1.a1', '180.t1.a1', '180.u1.a1', '300.h2.a1'], 'contains': ['1800.e1.a1', '2700.s1.a1', '2700.bg1.a1', '4500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 10862, 54480, 61200, 129744], 'label': '162000.x.900.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.h2.a1', 'old_label': '900.r1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.r1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910091
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.o1.a1', '180.q1.a1', '300.h1.a1'], 'contains': ['1800.f1.a1', '2700.r1.a1', '2700.bh1.a1', '4500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 10862, 54480, 61200, 32544], 'label': '162000.x.900.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.h1.a1', 'old_label': '900.s1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.s1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910092
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.o1.a1', '180.u1.a1', '300.i1.a1'], 'contains': ['1800.g1.a1', '2700.t1.a1', '2700.bi1.a1', '4500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 10862, 54480, 61200, 34704], 'label': '162000.x.900.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '900.t1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.t1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910093
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.o1.a1', '180.t1.a1', '300.i1.a1'], 'contains': ['1800.h1.a1', '2700.u1.a1', '2700.bi1.a1', '4500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 10862, 54480, 61200, 41184], 'label': '162000.x.900.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '900.u1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.u1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910094
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '300.e1.a1'], 'contains': ['1800.j1.a1', '2700.p1.a1', '2700.bj1.a1', '4500.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [75483, 10862, 25768, 58080, 136224], 'label': '162000.x.900.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.v1.a1', 'old_label': '900.v1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.v1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910095
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.w1.a1', '180.x1.a1', '300.f1.a1', '450.e1.a1'], 'contains': ['1800.l1.a1', '2700.o1.a1', '2700.v1.a1', '2700.z1.a1', '4500.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10503, 7200, 10862, 108480, 2160], 'label': '162000.x.900.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.e1.a1', 'old_label': '900.w1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.w1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910096
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.w1.a1', '180.z1.a1', '300.g1.a1'], 'contains': ['1800.p1.a1', '2700.p1.a1', '2700.q1.a1', '2700.w1.a1', '2700.ba1.a1', '4500.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 7200, 10862, 108480, 39024], 'label': '162000.x.900.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.x1.a1', 'old_label': '900.x1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.x1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910097
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.w1.a1', '180.y1.a1', '300.h1.a1', '450.a1.a1'], 'contains': ['1800.r1.a1', '2700.r1.a1', '2700.x1.a1', '2700.bb1.a1', '4500.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10503, 7200, 10862, 108480, 32544], 'label': '162000.x.900.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.a1.a1', 'old_label': '900.y1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.y1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910098
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.x1.a1', '180.y1.a1', '180.z1.a1', '180.ba1.a1', '300.h2.a1', '450.b1.a1'], 'contains': ['1800.s1.a1', '2700.s1.a1', '2700.x2.a1', '2700.bc1.a1', '4500.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10503, 7200, 10862, 108480, 129744], 'label': '162000.x.900.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '900.z1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.z1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910099
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.c1.a1'], 'contains': ['72.h1.a1', '180.bk1.a1', '180.bo1.a1', '180.bp1.a1', '324.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 97344, 2, 108480, 32400, 2160, 108000], 'label': '162000.x.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '36.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.646'}
-
id: 62910100
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.w1.a1', '180.ba1.a1', '300.i1.a1'], 'contains': ['1800.u1.a1', '2700.t1.a1', '2700.u1.a1', '2700.y1.a1', '2700.bd1.a1', '4500.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 7200, 10862, 108480, 41184], 'label': '162000.x.900.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.ba1.a1', 'old_label': '900.ba1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910101
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bb1.a1', '180.bc1.a1', '300.f1.a1', '450.e1.a1'], 'contains': ['1800.l1.a1', '2700.v1.a1', '2700.be1.a1', '4500.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10503, 10862, 54480, 7200, 2160], 'label': '162000.x.900.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '900.bb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910102
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bc1.a1', '180.be1.a1', '300.g1.a1'], 'contains': ['1800.q1.a1', '2700.w1.a1', '2700.bf1.a1', '4500.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 10862, 54480, 7200, 39024], 'label': '162000.x.900.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '900.bc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910103
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bb1.a1', '180.bd1.a1', '180.be1.a1', '180.bf1.a1', '300.h2.a1', '450.a1.a1'], 'contains': ['1800.r1.a1', '2700.x2.a1', '2700.bg1.a1', '4500.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10503, 10862, 54480, 7200, 129744], 'label': '162000.x.900.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '900.bd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910104
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bc1.a1', '180.bd1.a1', '300.h1.a1', '450.b1.a1'], 'contains': ['1800.s1.a1', '2700.x1.a1', '2700.bh1.a1', '4500.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10503, 10862, 54480, 7200, 32544], 'label': '162000.x.900.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '900.be1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.be1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910105
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bc1.a1', '180.bf1.a1', '300.i1.a1'], 'contains': ['1800.w1.a1', '2700.y1.a1', '2700.bi1.a1', '4500.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 10862, 54480, 7200, 41184], 'label': '162000.x.900.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '900.bf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910106
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bg1.a1', '180.bg2.a1', '300.f1.a1', '450.g1.a1'], 'contains': ['1800.z1.a1', '2700.z1.a1', '2700.be1.a1', '4500.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10503, 10862, 54480, 108000, 2160], 'label': '162000.x.900.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '900.bg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910107
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bg1.a1', '180.bi1.a1', '300.g1.a1'], 'contains': ['1800.bc1.a1', '2700.ba1.a1', '2700.bf1.a1', '4500.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 10862, 54480, 108000, 39024], 'label': '162000.x.900.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '900.bh1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910108
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bg1.a1', '180.bh1.a1', '300.h1.a1', '450.c1.a1'], 'contains': ['1800.be1.a1', '2700.bb1.a1', '2700.bh1.a1', '4500.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10503, 10862, 54480, 108000, 32544], 'label': '162000.x.900.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '900.bi1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910109
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bi2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bg2.a1', '180.bh1.a1', '180.bi1.a1', '180.bj1.a1', '300.h2.a1', '450.c1.a1'], 'contains': ['1800.be1.a1', '2700.bc1.a1', '2700.bg1.a1', '4500.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10503, 10862, 54480, 108000, 129744], 'label': '162000.x.900.bi2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '900.bi2.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bi2.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910110
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.d1.a1'], 'contains': ['72.g1.a1', '72.h1.a1', '72.j1.a1', '108.j1.a1', '108.k1.a1', '180.bm1.a1', '180.bq1.a1', '180.br1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [17642, 97344, 66960, 480, 11340, 32400, 7200], 'label': '162000.x.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.679'}
-
id: 62910111
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bg1.a1', '180.bj1.a1', '300.i1.a1'], 'contains': ['1800.bg1.a1', '2700.bd1.a1', '2700.bi1.a1', '4500.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 10862, 54480, 108000, 41184], 'label': '162000.x.900.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '900.bj1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910112
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bl1.a1', '300.l1.a1', '450.i1.a1'], 'contains': ['1800.bm1.a1', '1800.bx1.a1', '2700.bm1.a1', '4500.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': None, 'generators': [17642, 2160, 480, 119340, 108000], 'label': '162000.x.900.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '900.bk1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '144.115'}
-
id: 62910114
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bk1.a1', '180.bp1.a1', '300.k1.a1', '450.d1.a1'], 'contains': ['1800.bq1.a1', '4500.j1.a1', '8100.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [1, 108480, 108000, 2, 97344], 'label': '162000.x.900.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '900.bm1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '360.130'}
-
id: 62910115
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bm1.a1', '180.bq1.a1', '300.l1.a1', '450.f1.a1'], 'contains': ['1800.bl1.a1', '1800.bp1.a1', '1800.bw1.a1', '2700.bm1.a1', '2700.bo1.a1', '4500.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [17642, 2160, 480, 11340, 7200], 'label': '162000.x.900.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.f1.a1', 'old_label': '900.bn1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 62910116
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bl1.a1', '180.bn1.a1', '300.n1.a1', '450.f1.a1'], 'contains': ['1800.bl1.a1', '1800.bt1.a1', '1800.cg1.a1', '2700.bp1.a1', '2700.bq1.a1', '4500.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [17642, 480, 108000, 119340, 32400], 'label': '162000.x.900.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '900.bo1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62910117
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bm1.a1', '180.br1.a1', '300.n1.a1', '450.f1.a1'], 'contains': ['1800.bp1.a1', '1800.bt1.a1', '1800.cc1.a1', '2700.bp1.a1', '2700.br1.a1', '4500.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [17642, 480, 7200, 11340, 144], 'label': '162000.x.900.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1.a1', 'old_label': '900.bp1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62910118
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bo1.a1', '180.bp1.a1', '300.m1.a1', '450.h1.a1'], 'contains': ['1800.bu1.a1', '4500.j1.a1', '8100.l1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [1, 108480, 108000, 2, 2160], 'label': '162000.x.900.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.h1.a1', 'old_label': '900.bq1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '360.131'}
-
id: 62910119
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bq1.a1', '180.br1.a1', '300.n1.a1', '450.i1.a1'], 'contains': ['1800.bm1.a1', '1800.bu1.a1', '1800.cd1.a1', '2700.bq1.a1', '2700.br1.a1', '4500.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [17642, 480, 7200, 11340, 32400], 'label': '162000.x.900.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '900.br1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.br1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62910120
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bs1.a1', '300.o1.a1', '450.i1.a1'], 'contains': ['1800.bx1.a1', '1800.cd1.a1', '2700.bs1.a1', '4500.l1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': None, 'generators': [6660, 480, 7200, 125640, 32400], 'label': '162000.x.900.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '900.bs1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '720.774'}
-
id: 62910121
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.d1.a1'], 'contains': ['72.j1.a1', '72.k1.a1', '108.m1.a1', '180.bs1.a1', '180.bt1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6660, 2160, 480, 7200, 125640, 32400, 144], 'label': '162000.x.36.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910122
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '900.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bs1.a1', '180.bt1.a1', '300.o1.a1', '450.f1.a1'], 'contains': ['1800.bw1.a1', '1800.cc1.a1', '1800.cg1.a1', '2700.bs1.a1', '2700.bt1.a1', '4500.l1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [6660, 480, 7200, 125640, 144], 'label': '162000.x.900.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.f1.a1', 'old_label': '900.bt1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62910123
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1000.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '200.a1.a1', '250.a1.a1', '500.a1.a1'], 'contains': ['2000.a1.a1', '3000.a1.a1', '3000.b1.a1', '3000.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 500, 'diagramx': None, 'generators': [10862, 58080, 83128, 108000, 61200], 'label': '162000.x.1000.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '500.a1.a1', 'old_label': '1000.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1000.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
-
id: 62910124
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '360.a1.a1', '360.l1.a1', '360.m1.a1'], 'contains': ['2160.a1.a1', '3240.a1.a1', '5400.a1.a1', '5400.b1.a1', '5400.g1.a1', '5400.h1.a1', '5400.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 105984, 2160, 61680], 'label': '162000.x.1080.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.c1.a1', 'old_label': '1080.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.a1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62910125
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '360.b1.a1', '360.n1.a1', '360.o1.a1', '540.o1.a1'], 'contains': ['2160.b1.a1', '3240.b1.a1', '5400.a1.a1', '5400.c1.a1', '5400.d1.a1', '5400.e1.a1', '5400.g1.a1', '5400.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 105984, 66960, 61680], 'label': '162000.x.1080.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.f1.a1', 'old_label': '1080.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.b1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
-
id: 62910126
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '360.c1.a1', '360.n1.a1', '360.p1.a1', '540.p1.a1'], 'contains': ['2160.c1.a1', '3240.b1.a1', '5400.a1.a1', '5400.d1.a1', '5400.f1.a1', '5400.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 32544, 2160, 61680], 'label': '162000.x.1080.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.f2.a1', 'old_label': '1080.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.c1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910127
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '360.d1.a1', '360.q1.a1', '360.r1.a1', '540.q1.a1'], 'contains': ['2160.d1.a1', '3240.c1.a1', '5400.a1.a1', '5400.b1.a1', '5400.e1.a1', '5400.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 32544, 32400, 61680], 'label': '162000.x.1080.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.g1.a1', 'old_label': '1080.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.d1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910128
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '360.e1.a1', '360.s1.a1', '360.t1.a1', '540.r1.a1'], 'contains': ['2160.e1.a1', '3240.d1.a1', '5400.b1.a1', '5400.c1.a1', '5400.f1.a1', '5400.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 97344, 99360, 61680], 'label': '162000.x.1080.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '1080.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.e1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910129
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '360.g1.a1', '360.s1.a1', '360.u1.a1', '360.v1.a1'], 'contains': ['2160.f1.a1', '3240.d1.a1', '5400.b1.a1', '5400.d1.a1', '5400.e1.a1', '5400.g1.a1', '5400.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 69264, 66960, 61680], 'label': '162000.x.1080.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.f1.a1', 'old_label': '1080.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.f1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62910130
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '360.f1.a1', '360.t1.a1', '360.u1.a1', '540.s1.a1'], 'contains': ['2160.g1.a1', '3240.d1.a1', '5400.b1.a1', '5400.d1.a1', '5400.f1.a1', '5400.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 6624, 131760, 61680], 'label': '162000.x.1080.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '1080.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.g1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910131
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '360.i1.a1', '360.j1.a1', '360.k1.a1', '360.x1.a1', '540.t1.a1'], 'contains': ['2160.h1.a1', '3240.e1.a1', '5400.f1.a1', '5400.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [10862, 32544, 99360, 61680], 'label': '162000.x.1080.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '1080.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.h1.a1', 'subgroup_fusion': None, 'weyl_group': '300.23'}
-
id: 62910132
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1'], 'contains': ['80.a1.a1', '120.a1.a1', '120.b1.a1', '120.g1.a1', '1000.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [10862, 32544, 108000, 61200, 83128, 66960, 58080], 'label': '162000.x.40.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2700.o'}
-
id: 62910133
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '360.h1.a1', '360.w1.a1', '360.x1.a1', '540.u1.a1'], 'contains': ['2160.i1.a1', '3240.e1.a1', '5400.e1.a1', '5400.f1.a1', '5400.h1.a1', '5400.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 32544, 66960, 61680], 'label': '162000.x.1080.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '1080.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.i1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910134
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '360.l1.a1', '360.y1.a1', '540.d1.a1'], 'contains': ['2160.j1.a1', '3240.a1.a1', '5400.j1.a1', '5400.l1.a1', '5400.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 144, 131760, 480], 'label': '162000.x.1080.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '1080.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.j1.a1', 'subgroup_fusion': None, 'weyl_group': '200.41'}
-
id: 62910135
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '360.m1.a1', '360.y1.a1', '360.z1.a1', '540.g1.a1'], 'contains': ['2160.k1.a1', '3240.a1.a1', '5400.k1.a1', '5400.m1.a1', '5400.q1.a1', '5400.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 97344, 2160, 480], 'label': '162000.x.1080.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '1080.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.k1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
-
id: 62910136
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '360.o1.a1', '360.p1.a1', '360.ba1.a1', '540.e1.a1', '540.v1.a1', '540.v2.a1'], 'contains': ['2160.l1.a1', '3240.b1.a1', '5400.j1.a1', '5400.n1.a1', '5400.o1.a1', '5400.q1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 144, 66960, 480], 'label': '162000.x.1080.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '1080.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.l1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62910137
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '360.n1.a1', '360.ba1.a1', '360.bb1.a1', '540.h1.a1'], 'contains': ['2160.m1.a1', '3240.b1.a1', '5400.k1.a1', '5400.n1.a1', '5400.p1.a1', '5400.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 32544, 2160, 480], 'label': '162000.x.1080.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.c1.a1', 'old_label': '1080.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.m1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
-
id: 62910138
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '360.q1.a1', '360.bc1.a1', '360.bd1.a1', '540.b1.a1', '540.f1.a1', '540.i1.a1'], 'contains': ['2160.n1.a1', '3240.c1.a1', '5400.j1.a1', '5400.k1.a1', '5400.m1.a1', '5400.p1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 97344, 32400, 480], 'label': '162000.x.1080.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1.a1', 'old_label': '1080.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.n1.a1', 'subgroup_fusion': None, 'weyl_group': '200.49'}
-
id: 62910139
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '360.r1.a1', '360.bc1.a1', '540.a1.a1', '540.j1.a1', '540.w1.a1'], 'contains': ['2160.o1.a1', '3240.c1.a1', '5400.k1.a1', '5400.l1.a1', '5400.o1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [10862, 66960, 32400, 480], 'label': '162000.x.1080.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '1080.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.o1.a1', 'subgroup_fusion': None, 'weyl_group': '200.43'}
-
id: 62910140
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '360.s1.a1', '360.u1.a1', '360.be1.a1', '360.bf1.a1'], 'contains': ['2160.p1.a1', '3240.d1.a1', '5400.l1.a1', '5400.m1.a1', '5400.n1.a1', '5400.p1.a1', '5400.q1.a1', '5400.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 97344, 34560, 480], 'label': '162000.x.1080.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.f1.a1', 'old_label': '1080.p1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.p1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62910141
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '360.t1.a1', '360.v1.a1', '360.be1.a1', '540.x1.a1'], 'contains': ['2160.q1.a1', '3240.d1.a1', '5400.m1.a1', '5400.n1.a1', '5400.o1.a1', '5400.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 97344, 66960, 480], 'label': '162000.x.1080.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '1080.q1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.q1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910142
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '360.w1.a1', '360.x1.a1', '360.bg1.a1', '540.y1.a1'], 'contains': ['2160.r1.a1', '3240.e1.a1', '5400.o1.a1', '5400.p1.a1', '5400.q1.a1', '5400.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 32544, 66960, 480], 'label': '162000.x.1080.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '1080.r1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.r1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910143
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '45.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '15.a1.a1'], 'contains': ['90.b1.a1', '90.c1.a1', '90.f1.a1', '405.a1.a1', '1125.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': '45T1152', 'count': 45, 'diagramx': None, 'generators': [7201, 108480, 97344, 2, 108000, 32400, 125640, 119340], 'label': '162000.x.45.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '45.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62910144
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.a1.a1', '360.l1.a1', '360.z1.a1', '540.k1.a1'], 'contains': ['2160.s1.a1', '3240.a1.a1', '5400.s1.a1', '5400.u1.a1', '5400.bd1.a1', '5400.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 41184, 32400, 4080], 'label': '162000.x.1080.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '1080.s1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.s1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
-
id: 62910145
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.a1.a1', '360.m1.a1', '360.y1.a1'], 'contains': ['2160.t1.a1', '3240.a1.a1', '5400.t1.a1', '5400.v1.a1', '5400.bb1.a1', '5400.bc1.a1', '5400.bd1.a1', '5400.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 97344, 2160, 4080], 'label': '162000.x.1080.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.c1.a1', 'old_label': '1080.t1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.t1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62910146
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.c1.a1', '360.o1.a1', '360.bb1.a1', '540.l1.a1', '540.z1.a1', '540.be1.a1'], 'contains': ['2160.u1.a1', '3240.b1.a1', '5400.s1.a1', '5400.w1.a1', '5400.y1.a1', '5400.bc1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 136224, 32400, 4080], 'label': '162000.x.1080.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '1080.u1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.u1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62910147
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.b1.a1', '360.p1.a1', '360.bb1.a1', '540.m1.a1', '540.ba1.a1', '540.bf1.a1'], 'contains': ['2160.v1.a1', '3240.b1.a1', '5400.s1.a1', '5400.x1.a1', '5400.z1.a1', '5400.bb1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 69264, 32400, 4080], 'label': '162000.x.1080.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '1080.v1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.v1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62910148
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.b1.a1', '360.c1.a1', '360.n1.a1', '360.ba1.a1'], 'contains': ['2160.w1.a1', '3240.b1.a1', '5400.t1.a1', '5400.w1.a1', '5400.x1.a1', '5400.ba1.a1', '5400.bd1.a1', '5400.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 144, 66960, 4080], 'label': '162000.x.1080.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.d1.a1', 'old_label': '1080.w1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.w1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62910149
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.d1.a1', '360.r1.a1', '360.bd1.a1', '540.c1.a1', '540.bb1.a1', '540.bg1.a1'], 'contains': ['2160.x1.a1', '3240.c1.a1', '5400.t1.a1', '5400.u1.a1', '5400.y1.a1', '5400.z1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 144, 2160, 4080], 'label': '162000.x.1080.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '1080.x1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.x1.a1', 'subgroup_fusion': None, 'weyl_group': '200.48'}
-
id: 62910150
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.d1.a1', '360.q1.a1', '360.bc1.a1', '540.n1.a1'], 'contains': ['2160.y1.a1', '3240.c1.a1', '5400.s1.a1', '5400.t1.a1', '5400.v1.a1', '5400.ba1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 97344, 32400, 4080], 'label': '162000.x.1080.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '1080.y1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.y1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
-
id: 62910151
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.e1.a1', '360.f1.a1', '360.v1.a1', '360.bf1.a1', '540.bh1.a1'], 'contains': ['2160.z1.a1', '3240.d1.a1', '5400.v1.a1', '5400.x1.a1', '5400.y1.a1', '5400.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 97344, 131760, 4080], 'label': '162000.x.1080.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '1080.z1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.z1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910152
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.g1.a1', '360.t1.a1', '360.bf1.a1', '540.bc1.a1'], 'contains': ['2160.ba1.a1', '3240.d1.a1', '5400.v1.a1', '5400.w1.a1', '5400.z1.a1', '5400.bd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 97344, 34560, 4080], 'label': '162000.x.1080.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '1080.ba1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910153
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.f1.a1', '360.g1.a1', '360.s1.a1', '360.be1.a1'], 'contains': ['2160.bb1.a1', '3240.d1.a1', '5400.u1.a1', '5400.v1.a1', '5400.w1.a1', '5400.ba1.a1', '5400.bb1.a1', '5400.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 97344, 66960, 4080], 'label': '162000.x.1080.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.f1.a1', 'old_label': '1080.bb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62910154
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '12.c1.a1', '12.d1.a1', '20.a1.a1', '100.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [66960, 32544, 108000, 32400, 25768, 58080, 75483, 10862, 61200], 'label': '162000.x.4.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '4.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '13500.e'}
-
id: 62910155
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': ['3375.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.d1.a1', '24.e1.a1'], 'contains': ['144.a1.a1', '144.d1.a1', '144.e1.a1', '240.c1.a1', '240.d1.a1', '240.e1.a1', '240.f1.a1', '240.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [480, 32400, 108000, 97344, 7200, 66960], 'label': '162000.x.48.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.a1.a1', '24.a1.a1'], 'normal_contains': ['1296.a1.a1', '6000.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': '48.30', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.30'}
-
id: 62910156
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.e1.a1', '360.g1.a1', '360.u1.a1', '360.be1.a1'], 'contains': ['2160.bc1.a1', '3240.d1.a1', '5400.u1.a1', '5400.v1.a1', '5400.x1.a1', '5400.ba1.a1', '5400.bc1.a1', '5400.bd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [10862, 97344, 99360, 4080], 'label': '162000.x.1080.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.f1.a1', 'old_label': '1080.bc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '50.4'}
-
id: 62910157
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.h1.a1', '360.i1.a1', '360.w1.a1', '360.bg1.a1', '540.bi1.a1'], 'contains': ['2160.bd1.a1', '3240.e1.a1', '5400.y1.a1', '5400.ba1.a1', '5400.bb1.a1', '5400.bd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 129744, 66960, 4080], 'label': '162000.x.1080.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '1080.bd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910158
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.h1.a1', '360.x1.a1', '360.bg1.a1', '540.bd1.a1'], 'contains': ['2160.be1.a1', '3240.e1.a1', '5400.z1.a1', '5400.ba1.a1', '5400.bc1.a1', '5400.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 32544, 66960, 4080], 'label': '162000.x.1080.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '1080.be1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.be1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910159
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1.a1', '360.j1.a1', '540.bj1.a1'], 'contains': ['2160.bf1.a1', '3240.e1.a1', '27000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10862, 32544, 66960, 83128], 'label': '162000.x.1080.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.v1.a1', 'old_label': '1080.bf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '300.23'}
-
id: 62910160
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bg1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '360.bh1.a1', '360.bi1.a1', '540.a1.a1', '540.bk1.a1', '540.bo1.a1'], 'contains': ['2160.o1.a1', '3240.f1.a1', '5400.bg1.a1', '5400.bh1.a1', '5400.bi1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 135, 'diagramx': None, 'generators': [2, 97344, 32400, 7200], 'label': '162000.x.1080.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1.a1', 'old_label': '1080.bg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 62910161
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.f1.a1', '360.bi1.a1', '360.bj1.a1', '540.b1.a1', '540.bn1.a1', '540.bp1.a1'], 'contains': ['2160.n1.a1', '3240.f1.a1', '5400.bj1.a1', '5400.bk1.a1', '5400.bl1.a1', '5400.bm1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 32400, 480, 97344], 'label': '162000.x.1080.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '1080.bh1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 62910162
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.g1.a1', '360.bh1.a1', '360.bj1.a1', '540.c1.a1'], 'contains': ['2160.x1.a1', '3240.f1.a1', '5400.bn1.a1', '5400.bo1.a1', '5400.bp1.a1', '5400.bq1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [54482, 32400, 54480, 97344], 'label': '162000.x.1080.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1080.bi1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
-
id: 62910163
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '360.bk1.a1', '360.bo1.a1', '540.d1.a1', '540.bl1.a1', '540.bm1.a1'], 'contains': ['2160.j1.a1', '3240.g1.a1', '5400.bh1.a1', '5400.br1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2, 97344, 2160, 7200], 'label': '162000.x.1080.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1.a1', 'old_label': '1080.bj1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910164
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '360.bl1.a1', '360.bm1.a1', '360.bp1.a1', '540.e1.a1'], 'contains': ['2160.l1.a1', '3240.h1.a1', '5400.bi1.a1', '5400.br1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2, 32544, 2160, 7200], 'label': '162000.x.1080.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '1080.bk1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910165
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '360.bn1.a1', '360.bq1.a1', '360.br1.a1', '540.f1.a1', '540.bn1.a1', '540.bq1.a1'], 'contains': ['2160.n1.a1', '3240.i1.a1', '5400.bg1.a1', '5400.br1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2, 32400, 2160, 7200], 'label': '162000.x.1080.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1.a1', 'old_label': '1080.bl1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
-
id: 62910166
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.b1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '240.a1.a1', '1200.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25768, 66960, 32400, 58080, 61200, 32544], 'label': '162000.x.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2700.o'}
-
id: 62910167
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.f1.a1', '360.bo1.a1', '360.bs1.a1', '540.g1.a1'], 'contains': ['2160.k1.a1', '3240.g1.a1', '5400.bl1.a1', '5400.bs1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2, 480, 2160, 97344], 'label': '162000.x.1080.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '1080.bm1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910168
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.f1.a1', '360.bp1.a1', '360.bt1.a1', '540.h1.a1'], 'contains': ['2160.m1.a1', '3240.h1.a1', '5400.bm1.a1', '5400.bs1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2, 480, 2160, 32544], 'label': '162000.x.1080.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '1080.bn1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910169
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.f1.a1', '360.br1.a1', '360.bu1.a1', '540.i1.a1', '540.bp1.a1', '540.bq1.a1'], 'contains': ['2160.n1.a1', '3240.i1.a1', '5400.bj1.a1', '5400.bs1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2, 480, 2160, 144], 'label': '162000.x.1080.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '1080.bo1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62910170
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.f1.a1', '360.bq1.a1', '360.bu1.a1', '540.j1.a1', '540.bo1.a1', '540.br1.a1'], 'contains': ['2160.o1.a1', '3240.i1.a1', '5400.bk1.a1', '5400.bs1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2, 480, 2160, 32400], 'label': '162000.x.1080.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '1080.bp1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910171
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.g1.a1', '360.bk1.a1', '360.bs1.a1', '540.k1.a1'], 'contains': ['2160.s1.a1', '3240.g1.a1', '5400.bo1.a1', '5400.bt1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [54482, 54480, 2160, 97344], 'label': '162000.x.1080.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '1080.bq1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910172
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.g1.a1', '360.bl1.a1', '360.bt1.a1', '540.l1.a1'], 'contains': ['2160.u1.a1', '3240.h1.a1', '5400.bp1.a1', '5400.bt1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [54482, 54480, 2160, 129744], 'label': '162000.x.1080.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '1080.br1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.br1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910173
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.g1.a1', '360.bm1.a1', '360.bt1.a1', '540.m1.a1'], 'contains': ['2160.v1.a1', '3240.h1.a1', '5400.bq1.a1', '5400.bt1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [54482, 54480, 2160, 32544], 'label': '162000.x.1080.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '1080.bs1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910174
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.g1.a1', '360.bn1.a1', '360.bu1.a1', '540.n1.a1'], 'contains': ['2160.y1.a1', '3240.i1.a1', '5400.bn1.a1', '5400.bt1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [54482, 54480, 2160, 32400], 'label': '162000.x.1080.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '1080.bt1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910175
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.h1.a1', '360.bv1.a1', '360.bz1.a1', '540.d1.a1'], 'contains': ['2160.j1.a1', '3240.j1.a1', '5400.bu1.a1', '5400.by1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [11100, 2160, 97344, 7200], 'label': '162000.x.1080.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1.a1', 'old_label': '1080.bu1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '40.5'}
-
id: 62910176
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.h1.a1', '360.bw1.a1', '360.bx1.a1', '360.ca1.a1', '540.e1.a1'], 'contains': ['2160.l1.a1', '3240.k1.a1', '5400.bu1.a1', '5400.bz1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [11100, 2160, 32544, 7200], 'label': '162000.x.1080.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.d1.a1', 'old_label': '1080.bv1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910177
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.c1.a1'], 'contains': ['144.a1.a1', '144.c1.a1', '240.b1.a1', '1200.b1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25288, 66960, 32400, 58080, 61200, 32544], 'label': '162000.x.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1350.51'}
-
id: 62910178
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.h1.a1', '360.by1.a1', '360.cb1.a1', '360.cc1.a1', '540.f1.a1', '540.bp1.a1', '540.bt1.a1'], 'contains': ['2160.n1.a1', '3240.l1.a1', '5400.bu1.a1', '5400.bx1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [11100, 66960, 32400, 7200], 'label': '162000.x.1080.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.h1.a1', 'old_label': '1080.bw1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
-
id: 62910179
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.i1.a1', '360.bz1.a1', '360.cd1.a1', '540.g1.a1'], 'contains': ['2160.k1.a1', '3240.j1.a1', '5400.bv1.a1', '5400.cc1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [11340, 480, 97344, 2160], 'label': '162000.x.1080.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.h1.a1', 'old_label': '1080.bx1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910180
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.i1.a1', '360.ca1.a1', '360.ce1.a1', '540.h1.a1'], 'contains': ['2160.m1.a1', '3240.k1.a1', '5400.bv1.a1', '5400.cd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [11340, 480, 32544, 2160], 'label': '162000.x.1080.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.i1.a1', 'old_label': '1080.by1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.by1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910181
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.i1.a1', '360.cc1.a1', '360.cf1.a1', '540.i1.a1', '540.bn1.a1', '540.bt1.a1'], 'contains': ['2160.n1.a1', '3240.l1.a1', '5400.bv1.a1', '5400.ca1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [11340, 480, 144, 2160], 'label': '162000.x.1080.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1.a1', 'old_label': '1080.bz1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62910182
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.i1.a1', '360.cb1.a1', '360.cf1.a1', '540.j1.a1', '540.bo1.a1', '540.bs1.a1'], 'contains': ['2160.o1.a1', '3240.l1.a1', '5400.bv1.a1', '5400.cb1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [11340, 480, 32400, 66960], 'label': '162000.x.1080.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '1080.ca1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910183
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.j1.a1', '360.bv1.a1', '360.cd1.a1', '540.k1.a1'], 'contains': ['2160.s1.a1', '3240.j1.a1', '5400.bw1.a1', '5400.cf1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [119340, 54480, 97344, 2160], 'label': '162000.x.1080.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.d1.a1', 'old_label': '1080.cb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910184
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.j1.a1', '360.bw1.a1', '360.ce1.a1', '540.l1.a1'], 'contains': ['2160.u1.a1', '3240.k1.a1', '5400.bw1.a1', '5400.cg1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [119340, 54480, 129744, 2160], 'label': '162000.x.1080.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.d1.a1', 'old_label': '1080.cc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910185
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.j1.a1', '360.bx1.a1', '360.ce1.a1', '540.m1.a1'], 'contains': ['2160.v1.a1', '3240.k1.a1', '5400.bw1.a1', '5400.ch1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [119340, 54480, 32544, 2160], 'label': '162000.x.1080.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1.a1', 'old_label': '1080.cd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910186
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.j1.a1', '360.by1.a1', '360.cf1.a1', '540.n1.a1'], 'contains': ['2160.y1.a1', '3240.l1.a1', '5400.bw1.a1', '5400.ce1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [119340, 54480, 32400, 66960], 'label': '162000.x.1080.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.g1.a1', 'old_label': '1080.ce1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910187
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.h1.a1', '360.cg1.a1', '360.ch1.a1', '540.a1.a1', '540.br1.a1', '540.bs1.a1'], 'contains': ['2160.o1.a1', '3240.m1.a1', '5400.bx1.a1', '5400.by1.a1', '5400.bz1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [11100, 97344, 32400, 7200], 'label': '162000.x.1080.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '1080.cf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '200.43'}
-
id: 62910188
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '108.e1.a1', '162.a1.a1', '270.a1.a1', '270.d1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [75001, 34560, 7200, 10862, 11100, 32400, 64944], 'label': '162000.x.54.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '54.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2000.905'}
-
id: 62910189
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.i1.a1', '360.ch1.a1', '360.ci1.a1', '540.b1.a1', '540.bq1.a1', '540.bt1.a1'], 'contains': ['2160.n1.a1', '3240.m1.a1', '5400.ca1.a1', '5400.cb1.a1', '5400.cc1.a1', '5400.cd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [11340, 97344, 32400, 480], 'label': '162000.x.1080.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '1080.cg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '600.174'}
-
id: 62910190
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1080.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.j1.a1', '360.cg1.a1', '360.ci1.a1', '540.c1.a1'], 'contains': ['2160.x1.a1', '3240.m1.a1', '5400.ce1.a1', '5400.cf1.a1', '5400.cg1.a1', '5400.ch1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119340, 97344, 32400, 54480], 'label': '162000.x.1080.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '1080.ch1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '600.161'}
-
id: 62910191
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1125.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1', '225.a1.a1', '375.a1.a1'], 'contains': ['2250.b1.a1', '2250.c1.a1', '2250.d1.a1', '10125.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1125, 'diagramx': None, 'generators': [7201, 108000, 108480, 125640, 2, 119340], 'label': '162000.x.1125.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1125.a1.a1', 'old_label': '1125.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1125.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
-
id: 62910192
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1200.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '400.a1.a1', '600.a1.a1'], 'contains': ['3600.c1.a1', '3600.j1.a1', '6000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': None, 'generators': [25768, 136224, 58080, 61200], 'label': '162000.x.1200.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '1200.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.8'}
-
id: 62910193
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1200.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '400.a1.a1', '600.b1.a1'], 'contains': ['3600.c1.a1', '3600.k1.a1', '6000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': None, 'generators': [25288, 136224, 58080, 61200], 'label': '162000.x.1200.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.a1.a1', 'old_label': '1200.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.b1.a1', 'subgroup_fusion': None, 'weyl_group': '54.10'}
-
id: 62910194
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1200.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.c1.a1', '240.d1.a1', '240.e1.a1', '600.c1.a1', '600.h1.a1', '600.k1.a1', '600.l1.a1', '600.m1.a1'], 'contains': ['3600.a1.a1', '3600.l1.a1', '3600.m1.a1', '3600.y1.a1', '3600.z1.a1', '6000.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [480, 108000, 32400, 7200], 'label': '162000.x.1200.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '1200.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
-
id: 62910195
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1200.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.c1.a1', '240.e1.a1', '240.f1.a1', '600.d1.a1', '600.i1.a1', '600.n1.a1'], 'contains': ['3600.b1.a1', '3600.n1.a1', '3600.o1.a1', '3600.ba1.a1', '3600.bb1.a1', '6000.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 108000, 97344, 7200], 'label': '162000.x.1200.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '1200.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910196
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1200.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d1.a1', '240.f1.a1', '400.a1.a1', '600.e1.a1'], 'contains': ['3600.c1.a1', '3600.d1.a1', '3600.p1.a1', '3600.q1.a1', '3600.bc1.a1', '6000.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [58080, 108000, 136224, 7200], 'label': '162000.x.1200.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '1200.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.1'}
-
id: 62910197
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1200.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d1.a1', '240.e1.a1', '240.f1.a1', '240.g1.a1', '600.f1.a1', '600.j1.a1', '600.o1.a1'], 'contains': ['3600.e1.a1', '3600.f1.a1', '3600.r1.a1', '3600.s1.a1', '3600.t1.a1', '3600.bd1.a1', '3600.be1.a1', '6000.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 108000, 66960, 7200], 'label': '162000.x.1200.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '1200.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910198
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1200.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.c1.a1', '240.d1.a1', '240.f1.a1', '240.g1.a1', '600.g1.a1'], 'contains': ['3600.g1.a1', '3600.h1.a1', '3600.i1.a1', '3600.u1.a1', '3600.v1.a1', '3600.w1.a1', '3600.x1.a1', '3600.bf1.a1', '3600.bg1.a1', '6000.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54480, 108000, 41184, 7200], 'label': '162000.x.1200.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '1200.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910199
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '108.i1.a1', '162.b1.a1', '270.b1.a1', '270.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 2160, 2, 7200, 10860, 32400, 97344], 'label': '162000.x.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '54.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910200
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1296.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': ['125.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '432.b1.a1', '432.c1.a1', '432.d1.a1', '648.a1.a1', '648.b1.a1', '648.c1.a1'], 'contains': ['6480.a1.a1', '6480.b1.a1', '6480.c1.a1', '6480.d1.a1', '6480.e1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [97344, 32400, 66960], 'label': '162000.x.1296.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': ['48.a1.a1', '648.a1.a1'], 'normal_contains': ['162000.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1296.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': '48.30', 'quotient_action_kernel': '27.5', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '1296.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.30'}
-
id: 62910201
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1350.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.a1.a1', '270.d1.a1', '450.a1.a1', '450.b1.a1'], 'contains': ['2700.c1.a1', '2700.x1.a1', '2700.x2.a1', '4050.a1.a1', '6750.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [75001, 7200, 10862, 11100, 32544], 'label': '162000.x.1350.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.a1.a1', 'old_label': '1350.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910202
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1350.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.b1.a1', '270.b1.a1', '270.e1.a1'], 'contains': ['2700.b1.a1', '2700.bk1.a1', '2700.bl1.a1', '4050.b1.a1', '6750.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [1, 2, 7200, 10860, 97344], 'label': '162000.x.1350.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.b1.a1', 'old_label': '1350.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.b1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910203
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1350.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.c1.a1', '270.f1.a1', '450.a1.a1', '450.c1.a1'], 'contains': ['2700.j1.a1', '2700.bb1.a1', '2700.bg1.a1', '4050.a1.a1', '6750.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [64263, 10862, 54480, 119340, 129744], 'label': '162000.x.1350.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.a1.a1', 'old_label': '1350.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.c1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910204
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1350.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.c1.a1', '270.g1.a1', '450.b1.a1', '450.c1.a1'], 'contains': ['2700.k1.a1', '2700.bc1.a1', '2700.bh1.a1', '4050.a1.a1', '6750.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [64263, 10862, 54480, 119340, 32544], 'label': '162000.x.1350.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '1350.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.d1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910205
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1350.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.d1.a1', '450.e1.a1', '675.a1.a1'], 'contains': ['2700.l1.a1', '2700.v1.a1', '4050.c1.a1', '6750.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [75001, 7200, 10862, 11100, 2160], 'label': '162000.x.1350.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '1350.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.e1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910206
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1350.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.d1.a1', '270.e1.a1', '675.a1.a1'], 'contains': ['2700.l1.a1', '2700.bn1.a1', '4050.d1.a1', '6750.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [1, 2, 7200, 10860, 2160], 'label': '162000.x.1350.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '1350.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.f1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910207
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1350.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.h1.a1', '450.f1.a1', '675.a1.a1'], 'contains': ['2700.d1.a1', '2700.l1.a1', '2700.bo1.a1', '2700.bp1.a1', '2700.bt1.a1', '4050.e1.a1', '6750.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [10862, 125640, 480, 119340, 144], 'label': '162000.x.1350.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '1350.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.g1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910208
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1350.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.f1.a1', '270.g1.a1', '450.e1.a1', '450.g1.a1'], 'contains': ['2700.n1.a1', '2700.z1.a1', '2700.be1.a1', '4050.c1.a1', '6750.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [64263, 10862, 54480, 119340, 2160], 'label': '162000.x.1350.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.e1.a1', 'old_label': '1350.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.h1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910209
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1350.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.h1.a1', '270.i1.a1', '450.f1.a1', '450.i1.a1'], 'contains': ['2700.a1.a1', '2700.e1.a1', '2700.m1.a1', '2700.bm1.a1', '2700.bq1.a1', '2700.br1.a1', '2700.bs1.a1', '4050.e1.a1', '6750.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [10862, 125640, 480, 119340, 32400], 'label': '162000.x.1350.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.i1.a1', 'old_label': '1350.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.i1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910210
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.b1.a1'], 'contains': ['108.c1.a1', '108.f1.a1', '108.g1.a1', '162.a1.a1', '270.c1.a1', '270.f1.a1', '270.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [64263, 99360, 10862, 54480, 119340, 32400, 97344], 'label': '162000.x.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910211
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1500.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.a1.a1', '300.b1.a1', '300.c1.a1', '300.d1.a1', '750.a1.a1', '750.b1.a1', '750.c1.a1'], 'contains': ['3000.c1.a1', '3000.d1.a1', '3000.e1.a1', '4500.a1.a1', '4500.b1.a1', '4500.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': None, 'generators': [2, 108000, 11100, 7200, 480], 'label': '162000.x.1500.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '1500.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1500.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
-
id: 62910212
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1500.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.e1.a1', '300.e1.a1', '500.a1.a1'], 'contains': ['3000.a1.a1', '4500.d1.a1', '4500.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 500, 'diagramx': None, 'generators': [75483, 58080, 10862, 25768, 61200], 'label': '162000.x.1500.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '500.a1.a1', 'old_label': '1500.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1500.b1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
-
id: 62910213
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1500.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.f1.a1', '300.g1.a1', '300.h1.a1', '300.h2.a1', '300.i1.a1', '500.a1.a1', '750.a1.a1'], 'contains': ['3000.c1.a1', '4500.d1.a1', '4500.f1.a1', '4500.g1.a1', '4500.h1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 750, 'diagramx': None, 'generators': [10503, 54480, 7200, 108000, 10862], 'label': '162000.x.1500.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '750.a1.a1', 'old_label': '1500.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1500.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910214
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1500.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.j1.a1', '300.k1.a1', '300.m1.a1', '750.b1.a1'], 'contains': ['3000.d1.a1', '4500.j1.a1', '13500.i1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [1, 108000, 2, 108480, 7200], 'label': '162000.x.1500.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.a1', 'old_label': '1500.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1500.d1.a1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
-
id: 62910215
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1500.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.l1.a1', '300.n1.a1', '750.c1.a1'], 'contains': ['3000.d1.a1', '3000.e1.a1', '4500.i1.a1', '4500.k1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [17402, 108000, 11100, 480, 7200], 'label': '162000.x.1500.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '1500.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1500.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.158'}
-
id: 62910216
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1500.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.o1.a1', '500.b1.a1', '750.c1.a1'], 'contains': ['3000.e1.a1', '4500.l1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': None, 'generators': [11100, 108000, 125640, 480, 7200], 'label': '162000.x.1500.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '1500.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1500.f1.a1', 'subgroup_fusion': None, 'weyl_group': '648.704'}
-
id: 62910217
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1.a1', '540.a1.a1', '540.b1.a1', '540.c1.a1', '810.a1.a1', '810.b1.a1', '810.e1.a1'], 'contains': ['3240.c1.a1', '3240.f1.a1', '3240.m1.a1', '8100.a1.a1', '8100.b1.a1', '8100.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 135, 'diagramx': None, 'generators': [242, 97344, 32400, 11100], 'label': '162000.x.1620.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1.a1', 'old_label': '1620.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.a1.a1', 'subgroup_fusion': None, 'weyl_group': '200.43'}
-
id: 62910218
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1.a1', '540.d1.a1', '540.g1.a1', '540.k1.a1', '810.d1.a1'], 'contains': ['3240.a1.a1', '3240.g1.a1', '3240.j1.a1', '8100.b1.a1', '8100.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [242, 97344, 2160, 11100], 'label': '162000.x.1620.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1.a1', 'old_label': '1620.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.b1.a1', 'subgroup_fusion': None, 'weyl_group': '200.41'}
-
id: 62910219
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1.a1', '540.e1.a1', '540.h1.a1', '540.l1.a1', '540.m1.a1', '810.c1.a1'], 'contains': ['3240.b1.a1', '3240.h1.a1', '3240.k1.a1', '8100.c1.a1', '8100.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [10862, 32544, 2160, 11100], 'label': '162000.x.1620.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.d1.a1', 'old_label': '1620.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.c1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62910220
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1.a1', '540.f1.a1', '540.i1.a1', '540.j1.a1', '540.n1.a1', '810.e1.a1'], 'contains': ['3240.c1.a1', '3240.i1.a1', '3240.l1.a1', '8100.a1.a1', '8100.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [242, 2160, 32400, 11100], 'label': '162000.x.1620.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.h1.a1', 'old_label': '1620.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.d1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
-
id: 62910221
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '27.a1.a1'], 'contains': ['108.l1.a1', '162.c1.a1', '216.d1.a1', '6750.d1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [2, 2160, 3300, 14040, 83128, 32400, 8784], 'label': '162000.x.54.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6000.bm'}
-
id: 62910222
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.b1.a1', '540.o1.a1', '540.v1.a1', '540.z1.a1', '540.bf1.a1', '810.c1.a1'], 'contains': ['3240.b1.a1', '8100.e1.a1', '8100.f1.a1', '8100.g1.a1', '8100.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10503, 32544, 2160, 10862], 'label': '162000.x.1620.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.d1.a1', 'old_label': '1620.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.e1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62910223
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.e2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.b1.a1', '540.p1.a1', '540.v2.a1', '540.ba1.a1', '540.be1.a1', '810.c1.a1'], 'contains': ['3240.b1.a1', '8100.e1.a1', '8100.g2.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10503, 129744, 2160, 10862], 'label': '162000.x.1620.e2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1.a1', 'old_label': '1620.e2.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.e2.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62910224
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.b1.a1', '540.q1.a1', '540.w1.a1', '540.bb1.a1', '540.bg1.a1', '810.a1.a1'], 'contains': ['3240.c1.a1', '8100.g1.a1', '8100.g2.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [10503, 97344, 32400, 10862], 'label': '162000.x.1620.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1620.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.f1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910225
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.b1.a1', '540.r1.a1', '540.s1.a1', '540.x1.a1', '540.bc1.a1', '540.bh1.a1'], 'contains': ['3240.d1.a1', '8100.f1.a1', '8100.g2.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 129744, 131760, 10862], 'label': '162000.x.1620.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.z1.a1', 'old_label': '1620.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.g1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910226
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.b1.a1', '540.t1.a1', '540.u1.a1', '540.y1.a1', '540.bd1.a1', '540.bi1.a1', '540.bj1.a1'], 'contains': ['3240.e1.a1', '8100.g2.a1', '8100.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [10503, 129744, 66960, 10862], 'label': '162000.x.1620.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.ba1.a1', 'old_label': '1620.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.h1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910227
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bk1.a1', '324.c1.a1', '540.bk1.a1', '810.b1.a1'], 'contains': ['3240.f1.a1', '8100.i1.a1', '8100.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [1, 2, 97344, 32400], 'label': '162000.x.1620.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.b1.a1', 'old_label': '1620.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.i1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910228
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bo1.a1', '324.c1.a1', '540.bl1.a1', '810.d1.a1'], 'contains': ['3240.g1.a1', '8100.i1.a1', '8100.l1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [1, 2, 2160, 64944], 'label': '162000.x.1620.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.d1.a1', 'old_label': '1620.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.j1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910229
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.bp1.a1', '324.c1.a1', '540.bm1.a1', '810.d1.a1'], 'contains': ['3240.g1.a1', '8100.j1.a1', '8100.l1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1, 97344, 2160, 2], 'label': '162000.x.1620.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.b1.a1', 'old_label': '1620.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.k1.a1', 'subgroup_fusion': None, 'weyl_group': '200.41'}
-
id: 62910230
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.d1.a1', '540.bn1.a1', '540.bo1.a1', '540.bp1.a1', '810.e1.a1'], 'contains': ['3240.f1.a1', '3240.i1.a1', '3240.l1.a1', '8100.k1.a1', '8100.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [17882, 66960, 32400, 11100], 'label': '162000.x.1620.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.e1.a1', 'old_label': '1620.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.l1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910231
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.d1.a1', '540.bq1.a1', '540.br1.a1', '810.e1.a1'], 'contains': ['3240.i1.a1', '3240.m1.a1', '8100.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [17882, 97344, 32400, 11100], 'label': '162000.x.1620.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1620.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.m1.a1', 'subgroup_fusion': None, 'weyl_group': '200.43'}
-
id: 62910232
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '108.b1.a1', '108.j1.a1', '108.k1.a1', '108.m1.a1', '162.c1.a1', '270.h1.a1', '270.i1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [108482, 2160, 125640, 480, 119340, 32400, 97344], 'label': '162000.x.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '54.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910233
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1620.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.e1.a1', '540.bs1.a1', '540.bt1.a1', '810.e1.a1'], 'contains': ['3240.l1.a1', '3240.m1.a1', '8100.n1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': None, 'generators': [119100, 97344, 32400, 125640], 'label': '162000.x.1620.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '1620.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.n1.a1', 'subgroup_fusion': None, 'weyl_group': '200.43'}
-
id: 62910234
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '360.b1.a1', '360.c1.a1', '360.d1.a1', '600.c1.a1', '900.o1.a1'], 'contains': ['3600.a1.a1', '5400.a1.a1', '5400.s1.a1', '5400.t1.a1', '9000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 61200, 32400, 4080], 'label': '162000.x.1800.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.f1.a1', 'old_label': '1800.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910235
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '360.d1.a1', '360.e1.a1', '360.f1.a1', '360.g1.a1', '600.d1.a1'], 'contains': ['3600.b1.a1', '5400.b1.a1', '5400.u1.a1', '5400.v1.a1', '9000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 61200, 97344, 115680], 'label': '162000.x.1800.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.d1.a1', 'old_label': '1800.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.b1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910236
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.b1.a1', '360.e1.a1', '600.a1.a1', '600.b1.a1', '600.e1.a1', '900.p1.a1'], 'contains': ['3600.c1.a1', '5400.c1.a1', '5400.x1.a1', '9000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': None, 'generators': [10862, 61200, 36864, 115680], 'label': '162000.x.1800.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '1800.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.c1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910237
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.b1.a1', '360.c1.a1', '360.f1.a1', '360.g1.a1', '600.e1.a1', '900.q1.a1'], 'contains': ['3600.d1.a1', '5400.d1.a1', '5400.w1.a1', '5400.x1.a1', '9000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 61200, 136224, 115680], 'label': '162000.x.1800.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '1800.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910238
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.c1.a1', '360.d1.a1', '360.e1.a1', '360.f1.a1', '360.h1.a1', '360.i1.a1', '600.f1.a1', '900.r1.a1'], 'contains': ['3600.e1.a1', '5400.f1.a1', '5400.y1.a1', '5400.ba1.a1', '9000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 61200, 66960, 115680], 'label': '162000.x.1800.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.h2.a1', 'old_label': '1800.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.e1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910239
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.b1.a1', '360.d1.a1', '360.g1.a1', '360.h1.a1', '600.f1.a1', '900.s1.a1'], 'contains': ['3600.f1.a1', '5400.e1.a1', '5400.z1.a1', '5400.ba1.a1', '9000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 61200, 32544, 54480], 'label': '162000.x.1800.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.h1.a1', 'old_label': '1800.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.f1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910240
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '360.b1.a1', '360.g1.a1', '360.i1.a1', '600.g1.a1', '900.t1.a1'], 'contains': ['3600.g1.a1', '5400.g1.a1', '5400.bb1.a1', '5400.bd1.a1', '9000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 61200, 73584, 115680], 'label': '162000.x.1800.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '1800.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.g1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910241
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '360.b1.a1', '360.f1.a1', '360.h1.a1', '600.g1.a1', '900.u1.a1'], 'contains': ['3600.h1.a1', '5400.h1.a1', '5400.bb1.a1', '5400.be1.a1', '9000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 61200, 41184, 54480], 'label': '162000.x.1800.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '1800.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.h1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910242
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '360.c1.a1', '360.e1.a1', '360.g1.a1', '360.h1.a1', '600.g1.a1'], 'contains': ['3600.i1.a1', '5400.i1.a1', '5400.bc1.a1', '5400.bd1.a1', '5400.be1.a1', '9000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 61200, 131904, 115680], 'label': '162000.x.1800.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.g1.a1', 'old_label': '1800.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.i1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910243
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '30.a1.a1', '30.b1.a1', '30.e1.a1'], 'contains': ['120.e1.a1', '120.h1.a1', '120.o1.a1', '180.a1.a1', '180.b1.a1', '180.c1.a1', '300.a1.a1', '300.b1.a1', '300.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [2, 97344, 7200, 480, 11100, 32400, 108000], 'label': '162000.x.60.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62910244
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '600.a1.a1', '900.v1.a1'], 'contains': ['3600.j1.a1', '5400.c1.a1', '5400.bf1.a1', '9000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 58080, 136224, 25768], 'label': '162000.x.1800.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.e1.a1', 'old_label': '1800.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.j1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910245
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '600.b1.a1'], 'contains': ['3600.k1.a1', '5400.c1.a1', '9000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 58080, 136224, 25288], 'label': '162000.x.1800.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.b1.a1', 'old_label': '1800.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.k1.a1', 'subgroup_fusion': None, 'weyl_group': '30.2'}
-
id: 62910246
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.l1.a1', '360.o1.a1', '360.p1.a1', '360.q1.a1', '600.c1.a1', '900.l1.a1', '900.w1.a1', '900.bb1.a1'], 'contains': ['3600.l1.a1', '5400.a1.a1', '5400.j1.a1', '5400.s1.a1', '9000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 61200, 144, 480], 'label': '162000.x.1800.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '1800.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.l1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910247
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.m1.a1', '360.n1.a1', '360.q1.a1', '360.r1.a1', '600.c1.a1', '900.a1.a1'], 'contains': ['3600.m1.a1', '5400.a1.a1', '5400.k1.a1', '5400.t1.a1', '9000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 61200, 32400, 480], 'label': '162000.x.1800.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.a1.a1', 'old_label': '1800.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.m1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910248
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.l1.a1', '360.r1.a1', '360.s1.a1', '360.u1.a1', '600.d1.a1', '900.b1.a1'], 'contains': ['3600.n1.a1', '5400.b1.a1', '5400.l1.a1', '5400.u1.a1', '9000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 61200, 34560, 480], 'label': '162000.x.1800.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '1800.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.n1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910249
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.m1.a1', '360.q1.a1', '360.s1.a1', '360.t1.a1', '360.u1.a1', '360.v1.a1', '600.d1.a1'], 'contains': ['3600.o1.a1', '5400.b1.a1', '5400.m1.a1', '5400.v1.a1', '9000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 61200, 97344, 480], 'label': '162000.x.1800.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.d1.a1', 'old_label': '1800.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.o1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910250
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.n1.a1', '360.o1.a1', '360.s1.a1', '360.t1.a1', '600.e1.a1', '900.x1.a1'], 'contains': ['3600.p1.a1', '5400.c1.a1', '5400.d1.a1', '5400.n1.a1', '5400.w1.a1', '9000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 61200, 39024, 480], 'label': '162000.x.1800.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '1800.p1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.p1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910251
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.n1.a1', '360.p1.a1', '360.u1.a1', '360.v1.a1', '600.e1.a1', '900.bc1.a1'], 'contains': ['3600.q1.a1', '5400.d1.a1', '5400.n1.a1', '5400.x1.a1', '9000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 61200, 136224, 480], 'label': '162000.x.1800.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '1800.q1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.q1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910252
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.o1.a1', '360.r1.a1', '360.v1.a1', '360.w1.a1', '600.f1.a1', '900.c1.a1', '900.y1.a1', '900.bd1.a1'], 'contains': ['3600.r1.a1', '5400.e1.a1', '5400.o1.a1', '5400.y1.a1', '9000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 61200, 66960, 480], 'label': '162000.x.1800.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '1800.r1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.r1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910253
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.p1.a1', '360.r1.a1', '360.t1.a1', '360.x1.a1', '600.f1.a1', '900.d1.a1', '900.z1.a1', '900.be1.a1'], 'contains': ['3600.s1.a1', '5400.f1.a1', '5400.o1.a1', '5400.z1.a1', '9000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 61200, 99360, 480], 'label': '162000.x.1800.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '1800.s1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.s1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910254
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '30.d1.a1'], 'contains': ['120.c1.a1', '120.i1.a1', '120.l1.a1', '180.d1.a1', '180.h1.a1', '180.l1.a1', '300.b1.a1', '300.d1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [2, 97344, 7200, 480, 11100, 2160, 108000], 'label': '162000.x.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '60.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.646'}
-
id: 62910255
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.n1.a1', '360.q1.a1', '360.s1.a1', '360.u1.a1', '360.w1.a1', '360.x1.a1', '600.f1.a1'], 'contains': ['3600.t1.a1', '5400.e1.a1', '5400.f1.a1', '5400.p1.a1', '5400.ba1.a1', '9000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 61200, 32544, 480], 'label': '162000.x.1800.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.f1.a1', 'old_label': '1800.t1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.t1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910256
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.m1.a1', '360.o1.a1', '360.u1.a1', '360.x1.a1', '600.g1.a1', '900.ba1.a1'], 'contains': ['3600.u1.a1', '5400.g1.a1', '5400.h1.a1', '5400.q1.a1', '5400.bc1.a1', '9000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 61200, 67104, 480], 'label': '162000.x.1800.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '1800.u1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.u1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910257
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.l1.a1', '360.m1.a1', '360.n1.a1', '360.s1.a1', '360.v1.a1', '360.x1.a1', '600.g1.a1'], 'contains': ['3600.v1.a1', '5400.g1.a1', '5400.i1.a1', '5400.r1.a1', '5400.be1.a1', '9000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 61200, 41184, 480], 'label': '162000.x.1800.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.g1.a1', 'old_label': '1800.v1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.v1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910258
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.m1.a1', '360.p1.a1', '360.s1.a1', '360.w1.a1', '600.g1.a1', '900.bf1.a1'], 'contains': ['3600.w1.a1', '5400.i1.a1', '5400.q1.a1', '5400.bb1.a1', '9000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 61200, 73584, 480], 'label': '162000.x.1800.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '1800.w1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.w1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910259
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.l1.a1', '360.m1.a1', '360.n1.a1', '360.t1.a1', '360.u1.a1', '360.w1.a1', '600.g1.a1'], 'contains': ['3600.x1.a1', '5400.h1.a1', '5400.i1.a1', '5400.r1.a1', '5400.bd1.a1', '9000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 61200, 138384, 480], 'label': '162000.x.1800.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.g1.a1', 'old_label': '1800.x1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.x1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910260
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.y1.a1', '360.ba1.a1', '360.bc1.a1', '360.bd1.a1', '600.c1.a1', '900.e1.a1', '900.i1.a1', '900.m1.a1'], 'contains': ['3600.y1.a1', '5400.j1.a1', '5400.k1.a1', '5400.t1.a1', '9000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 7200, 144, 480], 'label': '162000.x.1800.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.e1.a1', 'old_label': '1800.y1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.y1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
-
id: 62910261
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.z1.a1', '360.bb1.a1', '360.bc1.a1', '600.c1.a1', '900.f1.a1', '900.n1.a1', '900.bg1.a1'], 'contains': ['3600.z1.a1', '5400.k1.a1', '5400.s1.a1', '9000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [10862, 7200, 32400, 480], 'label': '162000.x.1800.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '1800.z1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.z1.a1', 'subgroup_fusion': None, 'weyl_group': '80.34'}
-
id: 62910262
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.y1.a1', '360.bc1.a1', '360.be1.a1', '360.bf1.a1', '600.d1.a1', '900.g1.a1'], 'contains': ['3600.ba1.a1', '5400.l1.a1', '5400.m1.a1', '5400.v1.a1', '9000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 7200, 97344, 480], 'label': '162000.x.1800.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '1800.ba1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910263
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.z1.a1', '360.bd1.a1', '360.be1.a1', '600.d1.a1', '900.j1.a1'], 'contains': ['3600.bb1.a1', '5400.m1.a1', '5400.u1.a1', '9000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 7200, 2304, 480], 'label': '162000.x.1800.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.a1', 'old_label': '1800.bb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '40.5'}
-
id: 62910264
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.ba1.a1', '360.bb1.a1', '360.be1.a1', '360.bf1.a1', '600.e1.a1', '900.bh1.a1'], 'contains': ['3600.bc1.a1', '5400.n1.a1', '5400.w1.a1', '5400.x1.a1', '9000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 7200, 136224, 7680], 'label': '162000.x.1800.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '1800.bc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910265
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.f1.a1', '18.d1.a1', '30.e1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [32400, 2160, 11100, 108000, 480, 97344, 2, 125640, 7200], 'label': '162000.x.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '162000.x'}
-
id: 62910266
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '30.c1.a1'], 'contains': ['120.d1.a1', '120.j1.a1', '120.m1.a1', '180.e1.a1', '180.f1.a1', '180.i1.a1', '180.m1.a1', '300.c1.a1', '300.d1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 32544, 7200, 480, 11100, 2160, 108000], 'label': '162000.x.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '60.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.632'}
-
id: 62910267
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.ba1.a1', '360.bc1.a1', '360.be1.a1', '360.bg1.a1', '600.f1.a1', '900.h1.a1'], 'contains': ['3600.bd1.a1', '5400.o1.a1', '5400.p1.a1', '5400.ba1.a1', '9000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 7200, 66960, 480], 'label': '162000.x.1800.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.c1.a1', 'old_label': '1800.bd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910268
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bb1.a1', '360.bd1.a1', '360.bf1.a1', '360.bg1.a1', '600.f1.a1', '900.k1.a1', '900.bi1.a1', '900.bi2.a1'], 'contains': ['3600.be1.a1', '5400.p1.a1', '5400.y1.a1', '5400.z1.a1', '9000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 7200, 4464, 480], 'label': '162000.x.1800.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '1800.be1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.be1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910269
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.y1.a1', '360.z1.a1', '360.ba1.a1', '360.be1.a1', '360.bf1.a1', '360.bg1.a1', '600.g1.a1'], 'contains': ['3600.bf1.a1', '5400.q1.a1', '5400.r1.a1', '5400.bd1.a1', '5400.be1.a1', '9000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 7200, 41184, 480], 'label': '162000.x.1800.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.g1.a1', 'old_label': '1800.bf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910270
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.y1.a1', '360.bb1.a1', '360.be1.a1', '360.bg1.a1', '600.g1.a1', '900.bj1.a1'], 'contains': ['3600.bg1.a1', '5400.r1.a1', '5400.bb1.a1', '5400.bc1.a1', '9000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 7200, 69264, 4080], 'label': '162000.x.1800.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '1800.bg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910271
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bh1.a1', '360.bn1.a1', '600.h1.a1', '900.a1.a1'], 'contains': ['3600.m1.a1', '5400.bg1.a1', '5400.bn1.a1', '9000.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [54482, 32400, 54480, 7200], 'label': '162000.x.1800.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.a1.a1', 'old_label': '1800.bh1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910272
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bh1.a1', '360.bk1.a1', '600.i1.a1', '900.b1.a1'], 'contains': ['3600.n1.a1', '5400.bh1.a1', '5400.bo1.a1', '9000.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [54482, 97344, 54480, 7200], 'label': '162000.x.1800.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.a1.a1', 'old_label': '1800.bi1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910273
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bh1.a1', '360.bl1.a1', '600.j1.a1', '900.c1.a1'], 'contains': ['3600.r1.a1', '5400.bi1.a1', '5400.bp1.a1', '9000.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [54482, 129744, 54480, 7200], 'label': '162000.x.1800.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1800.bj1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
-
id: 62910274
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bh1.a1', '360.bm1.a1', '600.j1.a1', '900.d1.a1'], 'contains': ['3600.s1.a1', '5400.bi1.a1', '5400.bq1.a1', '9000.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [54482, 32544, 54480, 7200], 'label': '162000.x.1800.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1800.bk1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
-
id: 62910275
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bi1.a1', '360.br1.a1', '600.h1.a1', '900.e1.a1', '900.bn1.a1', '900.bo1.a1'], 'contains': ['3600.y1.a1', '5400.bg1.a1', '5400.bj1.a1', '9000.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 144, 480, 7200], 'label': '162000.x.1800.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '1800.bl1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 62910276
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bi1.a1', '360.bq1.a1', '600.h1.a1', '900.f1.a1', '900.bk1.a1', '900.br1.a1'], 'contains': ['3600.z1.a1', '5400.bg1.a1', '5400.bk1.a1', '9000.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 32400, 480, 7200], 'label': '162000.x.1800.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '1800.bm1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 62910277
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '30.e1.a1'], 'contains': ['120.e1.a1', '120.k1.a1', '120.n1.a1', '180.g1.a1', '180.j1.a1', '180.k1.a1', '180.n1.a1', '300.a1.a1', '300.d1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [2, 2160, 7200, 480, 11100, 32400, 108000], 'label': '162000.x.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1.a1', 'old_label': '60.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.679'}
-
id: 62910278
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bi1.a1', '360.bo1.a1', '600.i1.a1', '900.g1.a1'], 'contains': ['3600.ba1.a1', '5400.bh1.a1', '5400.bl1.a1', '9000.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [2, 97344, 480, 7200], 'label': '162000.x.1800.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '1800.bn1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910279
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bi1.a1', '360.bp1.a1', '600.j1.a1', '900.h1.a1'], 'contains': ['3600.bd1.a1', '5400.bi1.a1', '5400.bm1.a1', '9000.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [2, 32544, 480, 7200], 'label': '162000.x.1800.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '1800.bo1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910280
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bj1.a1', '360.bu1.a1', '600.h1.a1', '900.i1.a1', '900.bn1.a1', '900.bp1.a1'], 'contains': ['3600.y1.a1', '5400.bj1.a1', '5400.bk1.a1', '5400.bn1.a1', '9000.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [2, 480, 108000, 32400], 'label': '162000.x.1800.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1.a1', 'old_label': '1800.bp1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 62910281
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bj1.a1', '360.bs1.a1', '600.i1.a1', '900.j1.a1', '900.bl1.a1', '900.bm1.a1'], 'contains': ['3600.bb1.a1', '5400.bl1.a1', '5400.bo1.a1', '9000.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [2, 480, 108000, 97344], 'label': '162000.x.1800.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '1800.bq1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
-
id: 62910282
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bj1.a1', '360.bt1.a1', '600.j1.a1', '900.k1.a1'], 'contains': ['3600.be1.a1', '5400.bm1.a1', '5400.bp1.a1', '5400.bq1.a1', '9000.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [2, 480, 108000, 32544], 'label': '162000.x.1800.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '1800.br1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.br1.a1', 'subgroup_fusion': None, 'weyl_group': '72.21'}
-
id: 62910283
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bk1.a1', '360.bl1.a1', '360.bm1.a1', '360.bn1.a1', '600.k1.a1', '900.l1.a1'], 'contains': ['3600.l1.a1', '5400.br1.a1', '5400.bt1.a1', '9000.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [54482, 54480, 2160, 7200], 'label': '162000.x.1800.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '1800.bs1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910284
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bo1.a1', '360.bp1.a1', '360.bq1.a1', '360.br1.a1', '600.k1.a1', '900.m1.a1', '900.bo1.a1', '900.bp1.a1'], 'contains': ['3600.y1.a1', '5400.br1.a1', '5400.bs1.a1', '9000.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2, 480, 2160, 7200], 'label': '162000.x.1800.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '1800.bt1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62910285
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bs1.a1', '360.bt1.a1', '360.bu1.a1', '600.k1.a1', '900.n1.a1', '900.bq1.a1', '900.br1.a1'], 'contains': ['3600.z1.a1', '5400.bs1.a1', '5400.bt1.a1', '9000.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 108000, 2160, 480], 'label': '162000.x.1800.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '1800.bu1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '720.774'}
-
id: 62910286
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bv1.a1', '360.bw1.a1', '360.bx1.a1', '360.by1.a1', '600.l1.a1', '900.l1.a1'], 'contains': ['3600.l1.a1', '5400.bu1.a1', '5400.bw1.a1', '9000.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [119340, 2160, 54480, 7200], 'label': '162000.x.1800.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.e1.a1', 'old_label': '1800.bv1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
-
id: 62910287
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bz1.a1', '360.ca1.a1', '360.cb1.a1', '360.cc1.a1', '600.l1.a1', '900.m1.a1', '900.bn1.a1', '900.bt1.a1'], 'contains': ['3600.y1.a1', '5400.bu1.a1', '5400.bv1.a1', '9000.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [11340, 2160, 480, 7200], 'label': '162000.x.1800.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.f1.a1', 'old_label': '1800.bw1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 62910288
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.a1.a1'], 'contains': ['120.a1.a1', '180.u1.a1', '180.v1.a1', '1500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [75483, 138384, 25768, 61200, 10862, 66960, 58080], 'label': '162000.x.60.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '60.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2700.o'}
-
id: 62910289
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.cd1.a1', '360.ce1.a1', '360.cf1.a1', '600.l1.a1', '900.n1.a1', '900.bk1.a1', '900.bs1.a1'], 'contains': ['3600.z1.a1', '5400.bv1.a1', '5400.bw1.a1', '9000.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [119340, 480, 108000, 2160], 'label': '162000.x.1800.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '1800.bx1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '144.115'}
-
id: 62910290
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.by1.a1', '360.cg1.a1', '600.m1.a1', '900.a1.a1'], 'contains': ['3600.m1.a1', '5400.bx1.a1', '5400.ce1.a1', '9000.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [119340, 54480, 32400, 7200], 'label': '162000.x.1800.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.g1.a1', 'old_label': '1800.by1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.by1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910291
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bv1.a1', '360.cg1.a1', '600.n1.a1', '900.b1.a1'], 'contains': ['3600.n1.a1', '5400.by1.a1', '5400.cf1.a1', '9000.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [119340, 54480, 97344, 7200], 'label': '162000.x.1800.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.d1.a1', 'old_label': '1800.bz1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910292
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bw1.a1', '360.cg1.a1', '600.o1.a1', '900.c1.a1'], 'contains': ['3600.r1.a1', '5400.bz1.a1', '5400.cg1.a1', '9000.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [119340, 54480, 129744, 7200], 'label': '162000.x.1800.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.d1.a1', 'old_label': '1800.ca1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910293
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bx1.a1', '360.cg1.a1', '600.o1.a1', '900.d1.a1'], 'contains': ['3600.s1.a1', '5400.bz1.a1', '5400.ch1.a1', '9000.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [119340, 54480, 32544, 7200], 'label': '162000.x.1800.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1.a1', 'old_label': '1800.cb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910294
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.cc1.a1', '360.ch1.a1', '600.m1.a1', '900.e1.a1', '900.bp1.a1', '900.bt1.a1'], 'contains': ['3600.y1.a1', '5400.bx1.a1', '5400.ca1.a1', '9000.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [11340, 480, 144, 7200], 'label': '162000.x.1800.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1.a1', 'old_label': '1800.cc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62910295
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.cb1.a1', '360.ch1.a1', '600.m1.a1', '900.f1.a1', '900.br1.a1', '900.bs1.a1'], 'contains': ['3600.z1.a1', '5400.bx1.a1', '5400.cb1.a1', '9000.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [11340, 480, 32400, 7200], 'label': '162000.x.1800.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '1800.cd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62910296
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.bz1.a1', '360.ch1.a1', '600.n1.a1', '900.g1.a1'], 'contains': ['3600.ba1.a1', '5400.by1.a1', '5400.cc1.a1', '9000.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [11340, 480, 97344, 7200], 'label': '162000.x.1800.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.h1.a1', 'old_label': '1800.ce1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910297
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.ca1.a1', '360.ch1.a1', '600.o1.a1', '900.h1.a1'], 'contains': ['3600.bd1.a1', '5400.bz1.a1', '5400.cd1.a1', '9000.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [11340, 480, 32544, 7200], 'label': '162000.x.1800.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.i1.a1', 'old_label': '1800.cf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910298
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.cf1.a1', '360.ci1.a1', '600.m1.a1', '900.i1.a1', '900.bo1.a1', '900.bt1.a1'], 'contains': ['3600.y1.a1', '5400.ca1.a1', '5400.cb1.a1', '5400.ce1.a1', '9000.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [119340, 108000, 32400, 480], 'label': '162000.x.1800.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1.a1', 'old_label': '1800.cg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
-
id: 62910299
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '30.c1.a1'], 'contains': ['120.d1.a1', '180.o1.a1', '180.w1.a1', '180.bc1.a1', '180.bg1.a1', '300.f1.a1', '300.g1.a1', '300.h1.a1', '300.i1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10503, 32544, 108000, 10862, 7200, 2160, 54480], 'label': '162000.x.60.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '60.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.a1', 'subgroup_fusion': None, 'weyl_group': '600.164'}
-
id: 62910300
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.cd1.a1', '360.ci1.a1', '600.n1.a1', '900.j1.a1'], 'contains': ['3600.bb1.a1', '5400.cc1.a1', '5400.cf1.a1', '9000.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [119340, 108000, 97344, 480], 'label': '162000.x.1800.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '1800.ch1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '360.130'}
-
id: 62910301
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '1800.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.ce1.a1', '360.ci1.a1', '600.o1.a1', '900.k1.a1'], 'contains': ['3600.be1.a1', '5400.cd1.a1', '5400.cg1.a1', '5400.ch1.a1', '9000.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [119340, 108000, 32544, 480], 'label': '162000.x.1800.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '1800.ci1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '360.129'}
-
id: 62910302
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2000.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a1.a1', '400.a1.a1', '500.b1.a1', '1000.a1.a1'], 'contains': ['6000.a1.a1', '6000.b1.a1', '6000.c1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': None, 'generators': [83128, 108000], 'label': '162000.x.2000.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '2000.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2000.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
-
id: 62910303
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2025.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1.a1', '225.a1.a1', '675.a1.a1'], 'contains': ['4050.c1.a1', '4050.d1.a1', '4050.e1.a1', '10125.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2025, 'diagramx': None, 'generators': [115201, 108482, 119340, 125640, 2160], 'label': '162000.x.2025.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2025.a1.a1', 'old_label': '2025.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2025.a1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910304
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '720.a1.a1', '720.l1.a1', '720.m1.a1', '1080.a1.a1'], 'contains': ['6480.a1.a1', '10800.a1.a1', '10800.b1.a1', '10800.g1.a1', '10800.h1.a1', '10800.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [61680, 2160, 105984], 'label': '162000.x.2160.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '2160.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910305
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '720.b1.a1', '720.n1.a1', '720.o1.a1', '1080.b1.a1'], 'contains': ['6480.b1.a1', '10800.a1.a1', '10800.c1.a1', '10800.d1.a1', '10800.e1.a1', '10800.g1.a1', '10800.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [61680, 66960, 105984], 'label': '162000.x.2160.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '2160.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910306
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '720.c1.a1', '720.n1.a1', '720.p1.a1', '1080.c1.a1'], 'contains': ['6480.b1.a1', '10800.a1.a1', '10800.d1.a1', '10800.f1.a1', '10800.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [61680, 2160, 32544], 'label': '162000.x.2160.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '2160.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910307
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '720.d1.a1', '720.q1.a1', '720.r1.a1', '1080.d1.a1'], 'contains': ['6480.c1.a1', '10800.a1.a1', '10800.b1.a1', '10800.e1.a1', '10800.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [61680, 32400, 32544], 'label': '162000.x.2160.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '2160.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910308
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '720.e1.a1', '720.s1.a1', '720.t1.a1', '1080.e1.a1'], 'contains': ['6480.d1.a1', '10800.b1.a1', '10800.c1.a1', '10800.f1.a1', '10800.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [61680, 99360, 97344], 'label': '162000.x.2160.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '2160.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910309
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '720.g1.a1', '720.s1.a1', '720.u1.a1', '720.v1.a1', '1080.f1.a1'], 'contains': ['6480.d1.a1', '10800.b1.a1', '10800.d1.a1', '10800.e1.a1', '10800.g1.a1', '10800.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [61680, 66960, 69264], 'label': '162000.x.2160.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '2160.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910310
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.f2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '30.c1.a1'], 'contains': ['120.d1.a1', '180.p1.a1', '180.x1.a1', '180.bb1.a1', '180.bg2.a1', '300.f1.a1', '300.h2.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10503, 129744, 108000, 10862, 7200, 2160, 54480], 'label': '162000.x.60.f2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '60.f2.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f2.a1', 'subgroup_fusion': None, 'weyl_group': '600.163'}
-
id: 62910311
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '720.f1.a1', '720.t1.a1', '720.u1.a1', '1080.g1.a1'], 'contains': ['6480.d1.a1', '10800.b1.a1', '10800.d1.a1', '10800.f1.a1', '10800.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [61680, 131760, 6624], 'label': '162000.x.2160.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '2160.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910312
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '720.i1.a1', '720.j1.a1', '720.k1.a1', '720.x1.a1', '1080.h1.a1'], 'contains': ['6480.e1.a1', '10800.f1.a1', '10800.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [61680, 99360, 32544], 'label': '162000.x.2160.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '2160.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.1'}
-
id: 62910313
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '720.h1.a1', '720.w1.a1', '720.x1.a1', '1080.i1.a1'], 'contains': ['6480.e1.a1', '10800.e1.a1', '10800.f1.a1', '10800.h1.a1', '10800.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [61680, 66960, 32544], 'label': '162000.x.2160.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '2160.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910314
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1.a1', '720.l1.a1', '720.y1.a1', '1080.j1.a1', '1080.bj1.a1', '1080.bu1.a1'], 'contains': ['6480.a1.a1', '10800.j1.a1', '10800.l1.a1', '10800.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 131760, 144], 'label': '162000.x.2160.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '2160.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910315
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1.a1', '720.m1.a1', '720.y1.a1', '720.z1.a1', '1080.k1.a1', '1080.bm1.a1', '1080.bx1.a1'], 'contains': ['6480.a1.a1', '10800.k1.a1', '10800.m1.a1', '10800.q1.a1', '10800.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 2160, 97344], 'label': '162000.x.2160.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '2160.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910316
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1.a1', '720.o1.a1', '720.p1.a1', '720.ba1.a1', '1080.l1.a1', '1080.bk1.a1', '1080.bv1.a1'], 'contains': ['6480.b1.a1', '10800.j1.a1', '10800.n1.a1', '10800.o1.a1', '10800.q1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 66960, 144], 'label': '162000.x.2160.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '2160.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910317
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1.a1', '720.n1.a1', '720.ba1.a1', '720.bb1.a1', '1080.m1.a1', '1080.bn1.a1', '1080.by1.a1'], 'contains': ['6480.b1.a1', '10800.k1.a1', '10800.n1.a1', '10800.p1.a1', '10800.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 2160, 32544], 'label': '162000.x.2160.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '2160.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910318
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1.a1', '720.q1.a1', '720.bc1.a1', '720.bd1.a1', '1080.n1.a1', '1080.bh1.a1', '1080.bl1.a1', '1080.bo1.a1', '1080.bw1.a1', '1080.bz1.a1', '1080.cg1.a1'], 'contains': ['6480.c1.a1', '10800.j1.a1', '10800.k1.a1', '10800.m1.a1', '10800.p1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 32400, 97344], 'label': '162000.x.2160.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '2160.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 62910319
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1.a1', '720.r1.a1', '720.bc1.a1', '1080.o1.a1', '1080.bg1.a1', '1080.bp1.a1', '1080.ca1.a1', '1080.cf1.a1'], 'contains': ['6480.c1.a1', '10800.k1.a1', '10800.l1.a1', '10800.o1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [480, 32400, 66960], 'label': '162000.x.2160.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '2160.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 62910320
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1.a1', '720.s1.a1', '720.u1.a1', '720.be1.a1', '720.bf1.a1', '1080.p1.a1'], 'contains': ['6480.d1.a1', '10800.l1.a1', '10800.m1.a1', '10800.n1.a1', '10800.p1.a1', '10800.q1.a1', '10800.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [480, 34560, 97344], 'label': '162000.x.2160.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '2160.p1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910321
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '30.a1.a1'], 'contains': ['120.e1.a1', '180.q1.a1', '180.y1.a1', '180.bd1.a1', '180.bh1.a1', '300.h1.a1', '300.h2.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10503, 97344, 108000, 10862, 7200, 32400, 54480], 'label': '162000.x.60.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.a1', 'subgroup_fusion': None, 'weyl_group': '600.161'}
-
id: 62910322
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1.a1', '720.t1.a1', '720.v1.a1', '720.be1.a1', '1080.q1.a1'], 'contains': ['6480.d1.a1', '10800.m1.a1', '10800.n1.a1', '10800.o1.a1', '10800.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 66960, 97344], 'label': '162000.x.2160.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '2160.q1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910323
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1.a1', '720.w1.a1', '720.x1.a1', '720.bg1.a1', '1080.r1.a1'], 'contains': ['6480.e1.a1', '10800.o1.a1', '10800.p1.a1', '10800.q1.a1', '10800.r1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 66960, 32544], 'label': '162000.x.2160.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '2160.r1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910324
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.a1.a1', '720.l1.a1', '720.z1.a1', '1080.s1.a1', '1080.bq1.a1', '1080.cb1.a1'], 'contains': ['6480.a1.a1', '10800.s1.a1', '10800.u1.a1', '10800.bd1.a1', '10800.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [4080, 32400, 41184], 'label': '162000.x.2160.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '2160.s1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910325
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.a1.a1', '720.m1.a1', '720.y1.a1', '1080.t1.a1'], 'contains': ['6480.a1.a1', '10800.t1.a1', '10800.v1.a1', '10800.bb1.a1', '10800.bc1.a1', '10800.bd1.a1', '10800.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [4080, 2160, 97344], 'label': '162000.x.2160.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '2160.t1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910326
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.c1.a1', '720.o1.a1', '720.bb1.a1', '1080.u1.a1', '1080.br1.a1', '1080.cc1.a1'], 'contains': ['6480.b1.a1', '10800.s1.a1', '10800.w1.a1', '10800.y1.a1', '10800.bc1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [4080, 32400, 136224], 'label': '162000.x.2160.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '2160.u1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910327
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.b1.a1', '720.p1.a1', '720.bb1.a1', '1080.v1.a1', '1080.bs1.a1', '1080.cd1.a1'], 'contains': ['6480.b1.a1', '10800.s1.a1', '10800.x1.a1', '10800.z1.a1', '10800.bb1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [4080, 32400, 69264], 'label': '162000.x.2160.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '2160.v1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.v1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910328
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.b1.a1', '720.c1.a1', '720.n1.a1', '720.ba1.a1', '1080.w1.a1'], 'contains': ['6480.b1.a1', '10800.t1.a1', '10800.w1.a1', '10800.x1.a1', '10800.ba1.a1', '10800.bd1.a1', '10800.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [4080, 66960, 144], 'label': '162000.x.2160.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '2160.w1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910329
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.d1.a1', '720.r1.a1', '720.bd1.a1', '1080.x1.a1', '1080.bi1.a1', '1080.ch1.a1'], 'contains': ['6480.c1.a1', '10800.t1.a1', '10800.u1.a1', '10800.y1.a1', '10800.z1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [4080, 2160, 144], 'label': '162000.x.2160.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '2160.x1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910330
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.d1.a1', '720.q1.a1', '720.bc1.a1', '1080.y1.a1', '1080.bt1.a1', '1080.ce1.a1'], 'contains': ['6480.c1.a1', '10800.s1.a1', '10800.t1.a1', '10800.v1.a1', '10800.ba1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [4080, 32400, 97344], 'label': '162000.x.2160.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '2160.y1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910331
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.e1.a1', '720.f1.a1', '720.v1.a1', '720.bf1.a1', '1080.z1.a1'], 'contains': ['6480.d1.a1', '10800.v1.a1', '10800.x1.a1', '10800.y1.a1', '10800.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [4080, 131760, 97344], 'label': '162000.x.2160.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '2160.z1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910332
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1'], 'contains': ['120.f1.a1', '180.r1.a1', '180.s1.a1', '180.z1.a1', '180.be1.a1', '180.bi1.a1', '300.g1.a1', '300.h2.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 129744, 108000, 10862, 7200, 131760, 54480], 'label': '162000.x.60.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '60.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62910333
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.g1.a1', '720.t1.a1', '720.bf1.a1', '1080.ba1.a1'], 'contains': ['6480.d1.a1', '10800.v1.a1', '10800.w1.a1', '10800.z1.a1', '10800.bd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [4080, 34560, 97344], 'label': '162000.x.2160.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '2160.ba1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910334
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.f1.a1', '720.g1.a1', '720.s1.a1', '720.be1.a1', '1080.bb1.a1'], 'contains': ['6480.d1.a1', '10800.u1.a1', '10800.v1.a1', '10800.w1.a1', '10800.ba1.a1', '10800.bb1.a1', '10800.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [4080, 66960, 97344], 'label': '162000.x.2160.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '2160.bb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910335
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.e1.a1', '720.g1.a1', '720.u1.a1', '720.be1.a1', '1080.bc1.a1'], 'contains': ['6480.d1.a1', '10800.u1.a1', '10800.v1.a1', '10800.x1.a1', '10800.ba1.a1', '10800.bc1.a1', '10800.bd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [4080, 99360, 97344], 'label': '162000.x.2160.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '2160.bc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910336
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.h1.a1', '720.i1.a1', '720.w1.a1', '720.bg1.a1', '1080.bd1.a1'], 'contains': ['6480.e1.a1', '10800.y1.a1', '10800.ba1.a1', '10800.bb1.a1', '10800.bd1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [4080, 66960, 129744], 'label': '162000.x.2160.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '2160.bd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910337
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.h1.a1', '720.x1.a1', '720.bg1.a1', '1080.be1.a1'], 'contains': ['6480.e1.a1', '10800.z1.a1', '10800.ba1.a1', '10800.bc1.a1', '10800.be1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [4080, 66960, 32544], 'label': '162000.x.2160.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '2160.be1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.be1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910338
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2160.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.d1.a1', '720.j1.a1', '1080.bf1.a1'], 'contains': ['6480.e1.a1', '54000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [83128, 66960, 4464], 'label': '162000.x.2160.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1.a1', 'old_label': '2160.bf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '300.23'}
-
id: 62910339
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2250.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13500.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.a1.a1', '450.b1.a1', '450.e1.a1', '750.a1.a1'], 'contains': ['4500.a1.a1', '4500.f1.a1', '4500.g1.a1', '6750.a1.a1', '6750.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2250, 'diagramx': None, 'generators': [64263, 54480, 119340, 7200, 10862], 'label': '162000.x.2250.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2250.a1.a1', 'old_label': '2250.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2250.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910340
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2250.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.c1.a1', '450.g1.a1', '750.a1.a1', '1125.a1.a1'], 'contains': ['4500.c1.a1', '4500.h1.a1', '6750.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': None, 'generators': [64263, 108000, 119340, 10862, 54480], 'label': '162000.x.2250.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '2250.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2250.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
-
id: 62910341
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2250.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.d1.a1', '450.h1.a1', '750.b1.a1', '1125.a1.a1'], 'contains': ['4500.c1.a1', '4500.j1.a1', '20250.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1125, 'diagramx': None, 'generators': [1, 108000, 119340, 2, 108480], 'label': '162000.x.2250.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1125.a1.a1', 'old_label': '2250.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2250.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
-
id: 62910342
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2250.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.f1.a1', '450.i1.a1', '750.c1.a1', '1125.a1.a1'], 'contains': ['4500.b1.a1', '4500.c1.a1', '4500.i1.a1', '4500.k1.a1', '4500.l1.a1', '6750.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1125, 'diagramx': None, 'generators': [21482, 7200, 6660, 125640, 4080], 'label': '162000.x.2250.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1125.a1.a1', 'old_label': '2250.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2250.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
-
id: 62910343
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '20.a1.a1'], 'contains': ['120.g1.a1', '180.t1.a1', '180.u1.a1', '180.ba1.a1', '180.bf1.a1', '180.bj1.a1', '300.h2.a1', '300.i1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10503, 129744, 108000, 10862, 7200, 66960, 54480], 'label': '162000.x.60.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '60.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.a1', 'subgroup_fusion': None, 'weyl_group': '300.35'}
-
id: 62910344
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.a1.a1', '540.f1.a1', '900.a1.a1', '900.e1.a1', '900.f1.a1', '1350.i1.a1'], 'contains': ['5400.k1.a1', '5400.bg1.a1', '5400.bx1.a1', '8100.a1.a1', '13500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [242, 7200, 32400, 11100], 'label': '162000.x.2700.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.i1.a1', 'old_label': '2700.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910345
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.a1.a1', '540.d1.a1', '900.b1.a1', '900.g1.a1', '1350.b1.a1'], 'contains': ['5400.l1.a1', '5400.bh1.a1', '5400.by1.a1', '8100.b1.a1', '13500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [242, 7200, 97344, 11100], 'label': '162000.x.2700.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.b1.a1', 'old_label': '2700.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910346
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.a1.a1', '540.e1.a1', '900.c1.a1', '900.d1.a1', '900.h1.a1', '1350.a1.a1'], 'contains': ['5400.o1.a1', '5400.bi1.a1', '5400.bz1.a1', '8100.c1.a1', '13500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [10862, 7200, 32544, 11100], 'label': '162000.x.2700.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.a1.a1', 'old_label': '2700.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910347
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.b1.a1', '540.i1.a1', '900.e1.a1', '900.i1.a1', '1350.g1.a1'], 'contains': ['5400.j1.a1', '5400.bj1.a1', '5400.ca1.a1', '8100.a1.a1', '13500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [2, 480, 144, 11340], 'label': '162000.x.2700.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.f1.a1', 'old_label': '2700.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.d1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910348
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.b1.a1', '540.j1.a1', '900.f1.a1', '900.i1.a1', '1350.i1.a1'], 'contains': ['5400.k1.a1', '5400.bk1.a1', '5400.cb1.a1', '8100.a1.a1', '13500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [2, 480, 32400, 11340], 'label': '162000.x.2700.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.i1.a1', 'old_label': '2700.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.e1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910349
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.b1.a1', '540.g1.a1', '900.g1.a1', '900.j1.a1'], 'contains': ['5400.m1.a1', '5400.bl1.a1', '5400.cc1.a1', '8100.b1.a1', '13500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [2, 480, 97344, 11340], 'label': '162000.x.2700.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.g1.a1', 'old_label': '2700.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.f1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910350
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.b1.a1', '540.h1.a1', '900.h1.a1', '900.k1.a1'], 'contains': ['5400.p1.a1', '5400.bm1.a1', '5400.cd1.a1', '8100.c1.a1', '13500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [2, 480, 32544, 11340], 'label': '162000.x.2700.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.h1.a1', 'old_label': '2700.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.g1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910351
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.c1.a1', '540.n1.a1', '900.a1.a1', '900.i1.a1'], 'contains': ['5400.t1.a1', '5400.bn1.a1', '5400.ce1.a1', '8100.a1.a1', '13500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10862, 54480, 32400, 119340], 'label': '162000.x.2700.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.a1.a1', 'old_label': '2700.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.h1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910352
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.c1.a1', '540.k1.a1', '900.b1.a1', '900.j1.a1'], 'contains': ['5400.u1.a1', '5400.bo1.a1', '5400.cf1.a1', '8100.b1.a1', '13500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10862, 54480, 97344, 119340], 'label': '162000.x.2700.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.b1.a1', 'old_label': '2700.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.i1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910353
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.c1.a1', '540.l1.a1', '900.c1.a1', '900.k1.a1', '1350.c1.a1'], 'contains': ['5400.y1.a1', '5400.bp1.a1', '5400.cg1.a1', '8100.c1.a1', '13500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10862, 54480, 129744, 119340], 'label': '162000.x.2700.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.a1.a1', 'old_label': '2700.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.j1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910354
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '30.b1.a1'], 'contains': ['120.h1.a1', '180.bk1.a1', '300.j1.a1', '300.k1.a1', '540.bk1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [1, 108000, 2, 108480, 32400, 97344, 7200], 'label': '162000.x.60.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '60.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1080.513'}
-
id: 62910355
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.c1.a1', '540.m1.a1', '900.d1.a1', '900.k1.a1', '1350.d1.a1'], 'contains': ['5400.z1.a1', '5400.bq1.a1', '5400.ch1.a1', '8100.c1.a1', '13500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10862, 54480, 32544, 119340], 'label': '162000.x.2700.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '2700.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.k1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910356
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.d1.a1', '540.e1.a1', '540.f1.a1', '900.l1.a1', '900.m1.a1', '1350.e1.a1', '1350.f1.a1', '1350.g1.a1'], 'contains': ['5400.j1.a1', '5400.br1.a1', '5400.bu1.a1', '8100.d1.a1', '13500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [242, 7200, 2160, 11100], 'label': '162000.x.2700.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.l1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910357
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.g1.a1', '540.h1.a1', '540.i1.a1', '540.j1.a1', '900.m1.a1', '900.n1.a1', '1350.i1.a1'], 'contains': ['5400.k1.a1', '5400.bs1.a1', '5400.bv1.a1', '8100.d1.a1', '13500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [2, 480, 2160, 11340], 'label': '162000.x.2700.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.f1.a1', 'old_label': '2700.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.m1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910358
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.k1.a1', '540.l1.a1', '540.m1.a1', '540.n1.a1', '900.l1.a1', '900.n1.a1', '1350.h1.a1'], 'contains': ['5400.s1.a1', '5400.bt1.a1', '5400.bw1.a1', '8100.d1.a1', '13500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10862, 54480, 2160, 119340], 'label': '162000.x.2700.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.e1.a1', 'old_label': '2700.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.n1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910359
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.o1.a1', '540.p1.a1', '900.o1.a1', '900.w1.a1'], 'contains': ['5400.a1.a1', '8100.e1.a1', '13500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 10862, 2160, 112080], 'label': '162000.x.2700.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.w1.a1', 'old_label': '2700.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.o1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910360
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.o1.a1', '540.r1.a1', '900.p1.a1', '900.v1.a1', '900.x1.a1'], 'contains': ['5400.c1.a1', '8100.f1.a1', '13500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 10862, 39024, 112080], 'label': '162000.x.2700.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.x1.a1', 'old_label': '2700.p1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.p1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910361
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.o1.a1', '540.s1.a1', '900.q1.a1', '900.x1.a1'], 'contains': ['5400.d1.a1', '8100.f1.a1', '13500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 10862, 36864, 112080], 'label': '162000.x.2700.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.x1.a1', 'old_label': '2700.q1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.q1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910362
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.o1.a1', '540.q1.a1', '900.s1.a1', '900.y1.a1'], 'contains': ['5400.e1.a1', '8100.g1.a1', '13500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 10862, 32544, 112080], 'label': '162000.x.2700.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.y1.a1', 'old_label': '2700.r1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.r1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910363
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.p1.a1', '540.q1.a1', '540.r1.a1', '540.s1.a1', '540.t1.a1', '540.u1.a1', '900.r1.a1', '900.z1.a1'], 'contains': ['5400.f1.a1', '8100.g2.a1', '13500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 10862, 129744, 112080], 'label': '162000.x.2700.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.z1.a1', 'old_label': '2700.s1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.s1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910364
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.o1.a1', '540.t1.a1', '900.t1.a1', '900.ba1.a1'], 'contains': ['5400.g1.a1', '8100.h1.a1', '13500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 10862, 41184, 112080], 'label': '162000.x.2700.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.ba1.a1', 'old_label': '2700.t1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.t1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910365
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '30.d1.a1'], 'contains': ['120.i1.a1', '180.bo1.a1', '300.j1.a1', '300.m1.a1', '540.bl1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [1, 108000, 2, 108480, 64944, 2160, 7200], 'label': '162000.x.60.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '60.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1080.512'}
-
id: 62910366
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.o1.a1', '540.u1.a1', '900.u1.a1', '900.ba1.a1'], 'contains': ['5400.h1.a1', '8100.h1.a1', '13500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 10862, 34704, 112080], 'label': '162000.x.2700.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.ba1.a1', 'old_label': '2700.u1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.u1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910367
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.v1.a1', '540.v2.a1', '900.w1.a1', '900.bb1.a1', '1350.e1.a1'], 'contains': ['5400.j1.a1', '8100.e1.a1', '13500.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10503, 10862, 2160, 7200], 'label': '162000.x.2700.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.e1.a1', 'old_label': '2700.v1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.v1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910368
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.v1.a1', '540.x1.a1', '900.x1.a1', '900.bc1.a1'], 'contains': ['5400.n1.a1', '8100.f1.a1', '13500.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 10862, 39024, 7200], 'label': '162000.x.2700.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.x1.a1', 'old_label': '2700.w1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.w1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910369
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.v1.a1', '540.w1.a1', '900.y1.a1', '900.be1.a1', '1350.a1.a1'], 'contains': ['5400.o1.a1', '8100.g1.a1', '13500.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10503, 10862, 32544, 7200], 'label': '162000.x.2700.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.a1.a1', 'old_label': '2700.x1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.x1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910370
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.x2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.v2.a1', '540.w1.a1', '540.x1.a1', '540.y1.a1', '900.z1.a1', '900.bd1.a1', '1350.a1.a1'], 'contains': ['5400.o1.a1', '8100.g2.a1', '13500.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10503, 10862, 129744, 7200], 'label': '162000.x.2700.x2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '2700.x2.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.x2.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910371
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.v1.a1', '540.y1.a1', '900.ba1.a1', '900.bf1.a1'], 'contains': ['5400.q1.a1', '8100.h1.a1', '13500.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 10862, 41184, 7200], 'label': '162000.x.2700.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.ba1.a1', 'old_label': '2700.y1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.y1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910372
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.z1.a1', '540.ba1.a1', '900.w1.a1', '900.bg1.a1', '1350.h1.a1'], 'contains': ['5400.s1.a1', '8100.e1.a1', '13500.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10503, 10862, 2160, 108480], 'label': '162000.x.2700.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.e1.a1', 'old_label': '2700.z1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.z1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910373
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.z1.a1', '540.bc1.a1', '900.x1.a1', '900.bh1.a1'], 'contains': ['5400.w1.a1', '8100.f1.a1', '13500.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 10862, 39024, 108480], 'label': '162000.x.2700.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.x1.a1', 'old_label': '2700.ba1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910374
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.z1.a1', '540.bb1.a1', '900.y1.a1', '900.bi1.a1', '1350.c1.a1'], 'contains': ['5400.y1.a1', '8100.g1.a1', '13500.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10503, 10862, 32544, 108480], 'label': '162000.x.2700.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.a1.a1', 'old_label': '2700.bb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910375
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.ba1.a1', '540.bb1.a1', '540.bc1.a1', '540.bd1.a1', '900.z1.a1', '900.bi2.a1', '1350.d1.a1'], 'contains': ['5400.z1.a1', '8100.g2.a1', '13500.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10503, 10862, 129744, 108480], 'label': '162000.x.2700.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '2700.bc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910376
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.b1.a1', '12.d1.a1', '18.a1.a1', '18.b1.a1', '30.a1.a1', '30.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [32400, 99360, 11100, 108000, 10862, 97344, 10503, 7200, 54480], 'label': '162000.x.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910377
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '30.d1.a1'], 'contains': ['120.i1.a1', '180.bp1.a1', '300.k1.a1', '300.m1.a1', '540.bm1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 97344, 108480, 7200, 2, 2160, 108000], 'label': '162000.x.60.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '60.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910378
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.z1.a1', '540.bd1.a1', '900.ba1.a1', '900.bj1.a1'], 'contains': ['5400.bc1.a1', '8100.h1.a1', '13500.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 10862, 41184, 108480], 'label': '162000.x.2700.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.ba1.a1', 'old_label': '2700.bd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910379
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.be1.a1', '540.bf1.a1', '900.o1.a1', '900.bb1.a1', '900.bg1.a1', '1350.h1.a1'], 'contains': ['5400.s1.a1', '8100.e1.a1', '13500.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10503, 54480, 2160, 10862], 'label': '162000.x.2700.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '2700.be1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.be1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910380
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.bf1.a1', '540.bh1.a1', '900.p1.a1', '900.q1.a1', '900.bc1.a1', '900.bh1.a1'], 'contains': ['5400.x1.a1', '8100.f1.a1', '13500.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 54480, 39024, 10862], 'label': '162000.x.2700.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '2700.bf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910381
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.be1.a1', '540.bg1.a1', '540.bh1.a1', '540.bi1.a1', '900.r1.a1', '900.bd1.a1', '900.bi2.a1', '1350.c1.a1'], 'contains': ['5400.y1.a1', '8100.g2.a1', '13500.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10503, 54480, 129744, 10862], 'label': '162000.x.2700.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '2700.bg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910382
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.bf1.a1', '540.bg1.a1', '900.s1.a1', '900.be1.a1', '900.bi1.a1', '1350.d1.a1'], 'contains': ['5400.z1.a1', '8100.g1.a1', '13500.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10503, 54480, 32544, 10862], 'label': '162000.x.2700.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '2700.bh1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910383
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.bf1.a1', '540.bi1.a1', '900.t1.a1', '900.u1.a1', '900.bf1.a1', '900.bj1.a1'], 'contains': ['5400.bb1.a1', '8100.h1.a1', '13500.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10503, 54480, 41184, 10862], 'label': '162000.x.2700.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '2700.bi1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910384
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.h1.a1', '900.v1.a1'], 'contains': ['5400.bf1.a1', '8100.f1.a1', '13500.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [75483, 25768, 136224, 10862], 'label': '162000.x.2700.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.v1.a1', 'old_label': '2700.bj1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910385
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.j1.a1', '540.bk1.a1', '540.bl1.a1', '1350.b1.a1'], 'contains': ['5400.bh1.a1', '8100.i1.a1', '13500.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [1, 2, 7200, 64944], 'label': '162000.x.2700.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.b1.a1', 'old_label': '2700.bk1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910386
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.k1.a1', '540.bk1.a1', '540.bm1.a1', '1350.b1.a1'], 'contains': ['5400.bh1.a1', '8100.j1.a1', '13500.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [1, 7200, 97344, 2], 'label': '162000.x.2700.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.b1.a1', 'old_label': '2700.bl1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910387
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.bn1.a1', '540.bo1.a1', '900.bk1.a1', '900.bn1.a1', '1350.i1.a1'], 'contains': ['5400.bg1.a1', '5400.bk1.a1', '5400.bv1.a1', '8100.k1.a1', '13500.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [17642, 2160, 480, 11340], 'label': '162000.x.2700.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.i1.a1', 'old_label': '2700.bm1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910388
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '30.e1.a1'], 'contains': ['120.h1.a1', '120.k1.a1', '120.n1.a1', '180.bl1.a1', '180.bm1.a1', '180.bq1.a1', '300.l1.a1', '300.n1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [17402, 108000, 66960, 480, 11100, 32400, 7200], 'label': '162000.x.60.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.e1.a1', 'old_label': '60.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1080.537'}
-
id: 62910389
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.m1.a1', '540.bl1.a1', '540.bm1.a1', '1350.f1.a1'], 'contains': ['5400.br1.a1', '8100.l1.a1', '13500.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [1, 7200, 2160, 2], 'label': '162000.x.2700.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1.a1', 'old_label': '2700.bn1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '60.7'}
-
id: 62910390
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.bp1.a1', '900.bn1.a1', '1350.g1.a1'], 'contains': ['5400.bj1.a1', '5400.bu1.a1', '8100.k1.a1', '13500.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [17882, 2160, 7200, 11100], 'label': '162000.x.2700.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.bo1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
-
id: 62910391
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.bn1.a1', '540.bq1.a1', '900.bo1.a1', '900.bp1.a1', '1350.g1.a1'], 'contains': ['5400.bj1.a1', '5400.br1.a1', '5400.ca1.a1', '8100.m1.a1', '13500.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [17642, 480, 144, 11340], 'label': '162000.x.2700.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.h1.a1', 'old_label': '2700.bp1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910392
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.bo1.a1', '540.bq1.a1', '900.bo1.a1', '900.br1.a1', '1350.i1.a1'], 'contains': ['5400.bg1.a1', '5400.bs1.a1', '5400.cb1.a1', '8100.m1.a1', '13500.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [17642, 480, 32400, 11340], 'label': '162000.x.2700.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.i1.a1', 'old_label': '2700.bq1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910393
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.bp1.a1', '540.br1.a1', '900.bp1.a1', '900.br1.a1', '1350.i1.a1'], 'contains': ['5400.bk1.a1', '5400.bs1.a1', '5400.bx1.a1', '8100.m1.a1', '13500.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [17882, 7200, 32400, 11100], 'label': '162000.x.2700.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.h1.a1', 'old_label': '2700.br1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.br1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910394
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.bs1.a1', '540.bt1.a1', '900.bs1.a1', '900.bt1.a1', '1350.i1.a1'], 'contains': ['5400.bv1.a1', '5400.bx1.a1', '5400.cb1.a1', '8100.n1.a1', '13500.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [119340, 480, 32400, 125640], 'label': '162000.x.2700.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.i1.a1', 'old_label': '2700.bs1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910395
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '2700.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.bt1.a1', '900.bt1.a1', '1350.g1.a1'], 'contains': ['5400.bu1.a1', '5400.ca1.a1', '8100.n1.a1', '13500.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [119340, 480, 144, 125640], 'label': '162000.x.2700.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.bt1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910396
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3000.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '600.a1.a1', '1000.a1.a1', '1500.b1.a1'], 'contains': ['6000.b1.a1', '9000.a1.a1', '9000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 500, 'diagramx': None, 'generators': [10862, 25768, 61200, 58080], 'label': '162000.x.3000.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '500.a1.a1', 'old_label': '3000.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3000.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
-
id: 62910397
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3000.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.a1', '600.b1.a1', '1000.a1.a1'], 'contains': ['6000.c1.a1', '9000.a1.a1', '9000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1000, 'diagramx': None, 'generators': [10862, 25288, 61200, 58080], 'label': '162000.x.3000.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1000.a1.a1', 'old_label': '3000.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3000.b1.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
-
id: 62910467
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4500.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4500.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.bb1.a1', '900.bc1.a1', '900.bd1.a1', '900.be1.a1', '900.bf1.a1', '1500.c1.a1', '2250.a1.a1'], 'contains': ['9000.d1.a1', '13500.e1.a1', '13500.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 750, 'diagramx': None, 'generators': [10503, 7200, 10862, 54480], 'label': '162000.x.4500.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '750.a1.a1', 'old_label': '4500.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910398
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3000.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.c1.a1', '600.d1.a1', '600.e1.a1', '600.f1.a1', '600.g1.a1', '1000.a1.a1', '1500.a1.a1', '1500.c1.a1'], 'contains': ['6000.a1.a1', '9000.a1.a1', '9000.d1.a1', '9000.e1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': None, 'generators': [10862, 480, 7200, 108000], 'label': '162000.x.3000.c1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '3000.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3000.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 62910399
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '30.e1.a1'], 'contains': ['120.k1.a1', '120.o1.a1', '180.bn1.a1', '180.br1.a1', '300.n1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [17402, 97344, 480, 7200, 11100, 32400, 108000], 'label': '162000.x.60.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910400
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3000.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.h1.a1', '600.i1.a1', '600.j1.a1', '600.k1.a1', '1500.a1.a1', '1500.d1.a1', '1500.e1.a1'], 'contains': ['6000.a1.a1', '9000.f1.a1', '9000.g1.a1', '9000.h1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [2, 7200, 480, 108000], 'label': '162000.x.3000.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '3000.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3000.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
-
id: 62910401
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3000.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.l1.a1', '600.m1.a1', '600.n1.a1', '600.o1.a1', '1500.a1.a1', '1500.e1.a1', '1500.f1.a1'], 'contains': ['6000.a1.a1', '9000.i1.a1', '9000.j1.a1', '9000.k1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [11100, 7200, 480, 108000], 'label': '162000.x.3000.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '3000.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3000.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
-
id: 62910402
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1.a1', '1080.a1.a1', '1080.j1.a1', '1080.k1.a1', '1080.s1.a1', '1080.t1.a1', '1620.b1.a1'], 'contains': ['6480.a1.a1', '16200.a1.a1', '16200.b1.a1', '16200.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 2160, 97344], 'label': '162000.x.3240.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.d1.a1', 'old_label': '3240.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '200.41'}
-
id: 62910403
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3240.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1.a1', '1080.b1.a1', '1080.c1.a1', '1080.l1.a1', '1080.m1.a1', '1080.u1.a1', '1080.v1.a1', '1080.w1.a1', '1620.c1.a1', '1620.e1.a1', '1620.e2.a1'], 'contains': ['6480.b1.a1', '16200.a1.a1', '16200.c1.a1', '16200.d1.a1', '16200.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [10862, 66960, 144], 'label': '162000.x.3240.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '3240.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
-
id: 62910404
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3240.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1.a1', '1080.d1.a1', '1080.n1.a1', '1080.o1.a1', '1080.x1.a1', '1080.y1.a1', '1620.a1.a1', '1620.d1.a1', '1620.f1.a1'], 'contains': ['6480.c1.a1', '16200.a1.a1', '16200.b1.a1', '16200.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [10862, 32400, 97344], 'label': '162000.x.3240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '3240.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '200.43'}
-
id: 62910405
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3240.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1.a1', '1080.e1.a1', '1080.f1.a1', '1080.g1.a1', '1080.p1.a1', '1080.q1.a1', '1080.z1.a1', '1080.ba1.a1', '1080.bb1.a1', '1080.bc1.a1', '1620.g1.a1'], 'contains': ['6480.d1.a1', '16200.b1.a1', '16200.c1.a1', '16200.d1.a1', '16200.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': None, 'generators': [10862, 66960, 97344], 'label': '162000.x.3240.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.h1.a1', 'old_label': '3240.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.d1.a1', 'subgroup_fusion': None, 'weyl_group': '100.12'}
-
id: 62910406
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3240.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1.a1', '1080.h1.a1', '1080.i1.a1', '1080.r1.a1', '1080.bd1.a1', '1080.be1.a1', '1080.bf1.a1', '1620.h1.a1'], 'contains': ['6480.e1.a1', '16200.d1.a1', '16200.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [10862, 66960, 32544], 'label': '162000.x.3240.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '3240.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.e1.a1', 'subgroup_fusion': None, 'weyl_group': '300.23'}
-
id: 62910407
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3240.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bg1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.b1.a1', '1080.bg1.a1', '1080.bh1.a1', '1080.bi1.a1', '1620.a1.a1', '1620.i1.a1', '1620.l1.a1'], 'contains': ['6480.c1.a1', '16200.f1.a1', '16200.g1.a1', '16200.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 135, 'diagramx': None, 'generators': [2, 32400, 97344], 'label': '162000.x.3240.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1.a1', 'old_label': '3240.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 62910408
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3240.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.b1.a1', '1080.bj1.a1', '1080.bm1.a1', '1080.bq1.a1', '1620.b1.a1', '1620.j1.a1', '1620.k1.a1'], 'contains': ['6480.a1.a1', '16200.g1.a1', '16200.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2, 2160, 97344], 'label': '162000.x.3240.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1.a1', 'old_label': '3240.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.g1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910409
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3240.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.b1.a1', '1080.bk1.a1', '1080.bn1.a1', '1080.br1.a1', '1080.bs1.a1', '1620.c1.a1'], 'contains': ['6480.b1.a1', '16200.h1.a1', '16200.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2, 2160, 32544], 'label': '162000.x.3240.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '3240.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.h1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910410
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '60.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '30.e1.a1'], 'contains': ['120.n1.a1', '120.o1.a1', '180.bs1.a1', '180.bt1.a1', '300.o1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [11100, 97344, 480, 7200, 125640, 32400, 108000], 'label': '162000.x.60.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910411
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3240.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.b1.a1', '1080.bl1.a1', '1080.bo1.a1', '1080.bp1.a1', '1080.bt1.a1', '1620.d1.a1', '1620.l1.a1', '1620.m1.a1'], 'contains': ['6480.c1.a1', '16200.f1.a1', '16200.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2, 2160, 32400], 'label': '162000.x.3240.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1.a1', 'old_label': '3240.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.i1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910412
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3240.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.c1.a1', '1080.bu1.a1', '1080.bx1.a1', '1080.cb1.a1', '1620.b1.a1'], 'contains': ['6480.a1.a1', '16200.j1.a1', '16200.l1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [11100, 97344, 2160], 'label': '162000.x.3240.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1.a1', 'old_label': '3240.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.j1.a1', 'subgroup_fusion': None, 'weyl_group': '40.5'}
-
id: 62910413
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3240.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.c1.a1', '1080.bv1.a1', '1080.by1.a1', '1080.cc1.a1', '1080.cd1.a1', '1620.c1.a1'], 'contains': ['6480.b1.a1', '16200.j1.a1', '16200.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [11100, 32544, 2160], 'label': '162000.x.3240.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.d1.a1', 'old_label': '3240.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.k1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910414
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3240.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.c1.a1', '1080.bw1.a1', '1080.bz1.a1', '1080.ca1.a1', '1080.ce1.a1', '1620.d1.a1', '1620.l1.a1', '1620.n1.a1'], 'contains': ['6480.c1.a1', '16200.j1.a1', '16200.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [11100, 32400, 66960], 'label': '162000.x.3240.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.h1.a1', 'old_label': '3240.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.l1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910415
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3240.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.c1.a1', '1080.cf1.a1', '1080.cg1.a1', '1080.ch1.a1', '1620.a1.a1', '1620.m1.a1', '1620.n1.a1'], 'contains': ['6480.c1.a1', '16200.k1.a1', '16200.l1.a1', '16200.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [11100, 32400, 97344], 'label': '162000.x.3240.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '3240.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.m1.a1', 'subgroup_fusion': None, 'weyl_group': '200.43'}
-
id: 62910416
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3375.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '125.a1.a1'], 'contains': ['6750.d1.a1', '10125.a1.a1', '13500.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3375, 'diagramx': None, 'generators': [115201, 125640, 108482, 28888, 119340], 'label': '162000.x.3375.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3375.a1.a1', 'old_label': '3375.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3375.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 62910417
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3375.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['135.a1.a1', '375.a1.a1', '675.a1.a1'], 'contains': ['6750.a1.a1', '6750.b1.a1', '6750.e1.a1', '10125.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3375, 'diagramx': None, 'generators': [108001, 7200, 125640, 108482, 119340], 'label': '162000.x.3375.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3375.b1.a1', 'old_label': '3375.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3375.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910418
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.a1.a1', '720.b1.a1', '720.c1.a1', '720.d1.a1', '1200.c1.a1', '1800.a1.a1'], 'contains': ['10800.a1.a1', '10800.s1.a1', '10800.t1.a1', '18000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [115680, 32400, 61200], 'label': '162000.x.3600.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '3600.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910419
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.a1.a1', '720.d1.a1', '720.e1.a1', '720.f1.a1', '720.g1.a1', '1200.d1.a1', '1800.b1.a1'], 'contains': ['10800.b1.a1', '10800.u1.a1', '10800.v1.a1', '18000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [115680, 97344, 61200], 'label': '162000.x.3600.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '3600.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910420
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.b1.a1', '720.e1.a1', '1200.a1.a1', '1200.b1.a1', '1200.e1.a1', '1800.c1.a1'], 'contains': ['10800.c1.a1', '10800.x1.a1', '18000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [115680, 36864, 61200], 'label': '162000.x.3600.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '3600.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.1'}
-
id: 62910421
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '36.d1.a1'], 'contains': ['144.a1.a1', '216.a1.a1', '216.c1.a1', '360.a1.a1', '360.b1.a1', '360.c1.a1', '360.d1.a1', '360.e1.a1', '360.f1.a1', '360.g1.a1', '360.h1.a1', '360.i1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [10862, 32400, 61200, 97344, 115680, 66960], 'label': '162000.x.72.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1500.115'}
-
id: 62910422
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.b1.a1', '720.c1.a1', '720.f1.a1', '720.g1.a1', '1200.e1.a1', '1800.d1.a1'], 'contains': ['10800.d1.a1', '10800.w1.a1', '10800.x1.a1', '18000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [115680, 136224, 61200], 'label': '162000.x.3600.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '3600.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910423
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.c1.a1', '720.d1.a1', '720.e1.a1', '720.f1.a1', '720.h1.a1', '720.i1.a1', '1200.f1.a1', '1800.e1.a1'], 'contains': ['10800.f1.a1', '10800.y1.a1', '10800.ba1.a1', '18000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [115680, 66960, 61200], 'label': '162000.x.3600.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '3600.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910424
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.b1.a1', '720.d1.a1', '720.g1.a1', '720.h1.a1', '1200.f1.a1', '1800.f1.a1'], 'contains': ['10800.e1.a1', '10800.z1.a1', '10800.ba1.a1', '18000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54480, 32544, 61200], 'label': '162000.x.3600.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '3600.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910425
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.a1.a1', '720.b1.a1', '720.g1.a1', '720.i1.a1', '1200.g1.a1', '1800.g1.a1'], 'contains': ['10800.g1.a1', '10800.bb1.a1', '10800.bd1.a1', '18000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [115680, 73584, 61200], 'label': '162000.x.3600.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '3600.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910426
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.a1.a1', '720.b1.a1', '720.f1.a1', '720.h1.a1', '1200.g1.a1', '1800.h1.a1'], 'contains': ['10800.h1.a1', '10800.bb1.a1', '10800.be1.a1', '18000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [54480, 41184, 61200], 'label': '162000.x.3600.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '3600.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910427
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.a1.a1', '720.c1.a1', '720.e1.a1', '720.g1.a1', '720.h1.a1', '1200.g1.a1', '1800.i1.a1'], 'contains': ['10800.i1.a1', '10800.bc1.a1', '10800.bd1.a1', '10800.be1.a1', '18000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [115680, 131904, 61200], 'label': '162000.x.3600.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '3600.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910428
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '1200.a1.a1', '1800.j1.a1'], 'contains': ['10800.c1.a1', '10800.bf1.a1', '18000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [25768, 136224, 58080], 'label': '162000.x.3600.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.e1.a1', 'old_label': '3600.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.1'}
-
id: 62910429
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '1200.b1.a1', '1800.k1.a1'], 'contains': ['10800.c1.a1', '18000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [25288, 58080, 136224], 'label': '162000.x.3600.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.b1.a1', 'old_label': '3600.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
-
id: 62910430
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.l1.a1', '720.o1.a1', '720.p1.a1', '720.q1.a1', '1200.c1.a1', '1800.l1.a1', '1800.bs1.a1', '1800.bv1.a1'], 'contains': ['10800.a1.a1', '10800.j1.a1', '10800.s1.a1', '18000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 144, 61200], 'label': '162000.x.3600.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '3600.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910431
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.m1.a1', '720.n1.a1', '720.q1.a1', '720.r1.a1', '1200.c1.a1', '1800.m1.a1', '1800.bh1.a1', '1800.by1.a1'], 'contains': ['10800.a1.a1', '10800.k1.a1', '10800.t1.a1', '18000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 32400, 61200], 'label': '162000.x.3600.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '3600.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910432
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.e1.a1'], 'contains': ['144.b1.a1', '216.a1.a1', '216.d1.a1', '360.j1.a1', '1800.j1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [10862, 32400, 58080, 97344, 25768, 99360], 'label': '162000.x.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '72.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4500.m'}
-
id: 62910433
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.l1.a1', '720.r1.a1', '720.s1.a1', '720.u1.a1', '1200.d1.a1', '1800.n1.a1', '1800.bi1.a1', '1800.bz1.a1'], 'contains': ['10800.b1.a1', '10800.l1.a1', '10800.u1.a1', '18000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 34560, 61200], 'label': '162000.x.3600.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '3600.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910434
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.m1.a1', '720.q1.a1', '720.s1.a1', '720.t1.a1', '720.u1.a1', '720.v1.a1', '1200.d1.a1', '1800.o1.a1'], 'contains': ['10800.b1.a1', '10800.m1.a1', '10800.v1.a1', '18000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [480, 97344, 61200], 'label': '162000.x.3600.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '3600.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910435
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.n1.a1', '720.o1.a1', '720.s1.a1', '720.t1.a1', '1200.e1.a1', '1800.p1.a1'], 'contains': ['10800.c1.a1', '10800.d1.a1', '10800.n1.a1', '10800.w1.a1', '18000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 39024, 61200], 'label': '162000.x.3600.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '3600.p1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910436
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.n1.a1', '720.p1.a1', '720.u1.a1', '720.v1.a1', '1200.e1.a1', '1800.q1.a1'], 'contains': ['10800.d1.a1', '10800.n1.a1', '10800.x1.a1', '18000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 136224, 61200], 'label': '162000.x.3600.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '3600.q1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910437
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.o1.a1', '720.r1.a1', '720.v1.a1', '720.w1.a1', '1200.f1.a1', '1800.r1.a1', '1800.bj1.a1', '1800.ca1.a1'], 'contains': ['10800.e1.a1', '10800.o1.a1', '10800.y1.a1', '18000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 66960, 61200], 'label': '162000.x.3600.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '3600.r1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910438
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.p1.a1', '720.r1.a1', '720.t1.a1', '720.x1.a1', '1200.f1.a1', '1800.s1.a1', '1800.bk1.a1', '1800.cb1.a1'], 'contains': ['10800.f1.a1', '10800.o1.a1', '10800.z1.a1', '18000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 99360, 61200], 'label': '162000.x.3600.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '3600.s1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910439
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.n1.a1', '720.q1.a1', '720.s1.a1', '720.u1.a1', '720.w1.a1', '720.x1.a1', '1200.f1.a1', '1800.t1.a1'], 'contains': ['10800.e1.a1', '10800.f1.a1', '10800.p1.a1', '10800.ba1.a1', '18000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [480, 32544, 61200], 'label': '162000.x.3600.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '3600.t1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910440
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.m1.a1', '720.o1.a1', '720.u1.a1', '720.x1.a1', '1200.g1.a1', '1800.u1.a1'], 'contains': ['10800.g1.a1', '10800.h1.a1', '10800.q1.a1', '10800.bc1.a1', '18000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 67104, 61200], 'label': '162000.x.3600.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '3600.u1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910441
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.l1.a1', '720.m1.a1', '720.n1.a1', '720.s1.a1', '720.v1.a1', '720.x1.a1', '1200.g1.a1', '1800.v1.a1'], 'contains': ['10800.g1.a1', '10800.i1.a1', '10800.r1.a1', '10800.be1.a1', '18000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [480, 41184, 61200], 'label': '162000.x.3600.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '3600.v1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910442
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.m1.a1', '720.p1.a1', '720.s1.a1', '720.w1.a1', '1200.g1.a1', '1800.w1.a1'], 'contains': ['10800.i1.a1', '10800.q1.a1', '10800.bb1.a1', '18000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 73584, 61200], 'label': '162000.x.3600.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '3600.w1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910443
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1'], 'contains': ['144.c1.a1', '216.a1.a1', '360.k1.a1', '1800.k1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [10862, 32400, 58080, 97344, 25288, 99360], 'label': '162000.x.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '72.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2250.g'}
-
id: 62910444
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.l1.a1', '720.m1.a1', '720.n1.a1', '720.t1.a1', '720.u1.a1', '720.w1.a1', '1200.g1.a1', '1800.x1.a1'], 'contains': ['10800.h1.a1', '10800.i1.a1', '10800.r1.a1', '10800.bd1.a1', '18000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [480, 138384, 61200], 'label': '162000.x.3600.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '3600.x1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910445
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.y1.a1', '720.ba1.a1', '720.bc1.a1', '720.bd1.a1', '1200.c1.a1', '1800.y1.a1', '1800.bl1.a1', '1800.bp1.a1', '1800.bt1.a1', '1800.bw1.a1', '1800.cc1.a1', '1800.cg1.a1'], 'contains': ['10800.j1.a1', '10800.k1.a1', '10800.t1.a1', '18000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 144, 7200], 'label': '162000.x.3600.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '3600.y1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 62910446
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.z1.a1', '720.bb1.a1', '720.bc1.a1', '1200.c1.a1', '1800.z1.a1', '1800.bm1.a1', '1800.bu1.a1', '1800.bx1.a1', '1800.cd1.a1'], 'contains': ['10800.k1.a1', '10800.s1.a1', '18000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [480, 32400, 7200], 'label': '162000.x.3600.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3600.z1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.z1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
-
id: 62910447
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.y1.a1', '720.bc1.a1', '720.be1.a1', '720.bf1.a1', '1200.d1.a1', '1800.ba1.a1', '1800.bn1.a1', '1800.ce1.a1'], 'contains': ['10800.l1.a1', '10800.m1.a1', '10800.v1.a1', '18000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 97344, 7200], 'label': '162000.x.3600.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '3600.ba1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910448
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.z1.a1', '720.bd1.a1', '720.be1.a1', '1200.d1.a1', '1800.bb1.a1', '1800.bq1.a1', '1800.ch1.a1'], 'contains': ['10800.m1.a1', '10800.u1.a1', '18000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 2304, 7200], 'label': '162000.x.3600.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '3600.bb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910449
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.ba1.a1', '720.bb1.a1', '720.be1.a1', '720.bf1.a1', '1200.e1.a1', '1800.bc1.a1'], 'contains': ['10800.n1.a1', '10800.w1.a1', '10800.x1.a1', '18000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7680, 136224, 7200], 'label': '162000.x.3600.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '3600.bc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910450
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.ba1.a1', '720.bc1.a1', '720.be1.a1', '720.bg1.a1', '1200.f1.a1', '1800.bd1.a1', '1800.bo1.a1', '1800.cf1.a1'], 'contains': ['10800.o1.a1', '10800.p1.a1', '10800.ba1.a1', '18000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 66960, 7200], 'label': '162000.x.3600.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '3600.bd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910451
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.bb1.a1', '720.bd1.a1', '720.bf1.a1', '720.bg1.a1', '1200.f1.a1', '1800.be1.a1', '1800.br1.a1', '1800.ci1.a1'], 'contains': ['10800.p1.a1', '10800.y1.a1', '10800.z1.a1', '18000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 4464, 7200], 'label': '162000.x.3600.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '3600.be1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.be1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910452
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.y1.a1', '720.z1.a1', '720.ba1.a1', '720.be1.a1', '720.bf1.a1', '720.bg1.a1', '1200.g1.a1', '1800.bf1.a1'], 'contains': ['10800.q1.a1', '10800.r1.a1', '10800.bd1.a1', '10800.be1.a1', '18000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [480, 41184, 7200], 'label': '162000.x.3600.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '3600.bf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910453
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '3600.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.y1.a1', '720.bb1.a1', '720.be1.a1', '720.bg1.a1', '1200.g1.a1', '1800.bg1.a1'], 'contains': ['10800.r1.a1', '10800.bb1.a1', '10800.bc1.a1', '18000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 69264, 7200], 'label': '162000.x.3600.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '3600.bg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910454
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.a1.a1', '36.f1.a1', '36.g1.a1'], 'contains': ['144.d1.a1', '216.a1.a1', '216.b1.a1', '216.c1.a1', '360.l1.a1', '360.m1.a1', '360.n1.a1', '360.o1.a1', '360.p1.a1', '360.q1.a1', '360.r1.a1', '360.s1.a1', '360.t1.a1', '360.u1.a1', '360.v1.a1', '360.w1.a1', '360.x1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10862, 32400, 61200, 97344, 480, 66960], 'label': '162000.x.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '72.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1000.170'}
-
id: 62910455
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4050.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['810.a1.a1', '810.c1.a1', '1350.a1.a1', '1350.c1.a1', '1350.d1.a1'], 'contains': ['8100.c1.a1', '8100.g1.a1', '8100.g2.a1', '20250.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [64263, 10862, 32544, 11100], 'label': '162000.x.4050.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.a1.a1', 'old_label': '4050.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4050.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910456
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4050.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40500.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.d1.a1', '810.b1.a1', '810.d1.a1', '1350.b1.a1'], 'contains': ['8100.b1.a1', '8100.i1.a1', '8100.j1.a1', '20250.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4050, 'diagramx': None, 'generators': [1, 2, 97344, 10860], 'label': '162000.x.4050.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4050.b1.a1', 'old_label': '4050.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4050.b1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910457
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4050.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['810.c1.a1', '1350.e1.a1', '1350.h1.a1', '2025.a1.a1'], 'contains': ['8100.d1.a1', '8100.e1.a1', '20250.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [64263, 10862, 2160, 11100], 'label': '162000.x.4050.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '4050.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4050.c1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910458
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4050.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.h1.a1', '810.d1.a1', '1350.f1.a1', '2025.a1.a1'], 'contains': ['8100.d1.a1', '8100.l1.a1', '20250.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2025, 'diagramx': None, 'generators': [1, 2, 2160, 10860], 'label': '162000.x.4050.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2025.a1.a1', 'old_label': '4050.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4050.d1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910459
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4050.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40500.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['810.e1.a1', '1350.g1.a1', '1350.i1.a1', '2025.a1.a1'], 'contains': ['8100.a1.a1', '8100.d1.a1', '8100.k1.a1', '8100.m1.a1', '8100.n1.a1', '20250.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2025, 'diagramx': None, 'generators': [17882, 125640, 32400, 7140], 'label': '162000.x.4050.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2025.a1.a1', 'old_label': '4050.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4050.e1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910460
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4500.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13500.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.a1.a1', '900.b1.a1', '900.c1.a1', '900.d1.a1', '900.l1.a1', '1500.a1.a1', '2250.a1.a1'], 'contains': ['9000.d1.a1', '9000.f1.a1', '9000.i1.a1', '13500.a1.a1', '13500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2250, 'diagramx': None, 'generators': [10862, 119340, 7200, 54480], 'label': '162000.x.4500.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2250.a1.a1', 'old_label': '4500.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910461
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4500.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.e1.a1', '900.f1.a1', '900.g1.a1', '900.h1.a1', '900.m1.a1', '1500.a1.a1', '2250.d1.a1'], 'contains': ['9000.e1.a1', '9000.g1.a1', '9000.j1.a1', '13500.a1.a1', '13500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2250, 'diagramx': None, 'generators': [2, 11340, 7200, 480], 'label': '162000.x.4500.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2250.d1.a1', 'old_label': '4500.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910462
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4500.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.i1.a1', '900.j1.a1', '900.k1.a1', '900.n1.a1', '1500.a1.a1', '2250.b1.a1', '2250.c1.a1', '2250.d1.a1'], 'contains': ['9000.e1.a1', '9000.h1.a1', '9000.k1.a1', '13500.b1.a1', '13500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': None, 'generators': [2, 119340, 108480, 108000], 'label': '162000.x.4500.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '4500.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
-
id: 62910463
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4500.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.o1.a1', '900.p1.a1', '900.q1.a1', '900.r1.a1', '900.s1.a1', '900.t1.a1', '900.u1.a1', '1500.b1.a1', '1500.c1.a1'], 'contains': ['9000.a1.a1', '13500.d1.a1', '13500.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1500, 'diagramx': None, 'generators': [10503, 61200, 10862, 54480], 'label': '162000.x.4500.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1500.c1.a1', 'old_label': '4500.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910464
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4500.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.v1.a1', '900.v1.a1', '1500.b1.a1'], 'contains': ['9000.b1.a1', '13500.d1.a1', '13500.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4500, 'diagramx': None, 'generators': [75483, 58080, 10862, 25768], 'label': '162000.x.4500.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4500.e1.a1', 'old_label': '4500.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910465
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.b1.a1', '36.c1.a1', '36.h1.a1'], 'contains': ['144.e1.a1', '216.b1.a1', '216.c1.a1', '360.y1.a1', '360.z1.a1', '360.ba1.a1', '360.bb1.a1', '360.bc1.a1', '360.bd1.a1', '360.be1.a1', '360.bf1.a1', '360.bg1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [10862, 32400, 7200, 97344, 480, 66960], 'label': '162000.x.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2000.905'}
-
id: 62910466
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4500.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4500.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.w1.a1', '900.x1.a1', '900.y1.a1', '900.z1.a1', '900.ba1.a1', '1500.c1.a1', '2250.a1.a1'], 'contains': ['9000.d1.a1', '13500.d1.a1', '13500.e1.a1', '13500.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2250, 'diagramx': None, 'generators': [10503, 108480, 7200, 10862], 'label': '162000.x.4500.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2250.a1.a1', 'old_label': '4500.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910468
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4500.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.bg1.a1', '900.bh1.a1', '900.bi1.a1', '900.bi2.a1', '900.bj1.a1', '1500.c1.a1', '2250.b1.a1'], 'contains': ['9000.e1.a1', '13500.f1.a1', '13500.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 750, 'diagramx': None, 'generators': [10503, 108000, 10862, 54480], 'label': '162000.x.4500.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '750.a1.a1', 'old_label': '4500.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910469
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4500.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.bk1.a1', '900.bo1.a1', '1500.e1.a1', '2250.d1.a1'], 'contains': ['9000.g1.a1', '9000.k1.a1', '13500.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': None, 'generators': [17642, 119340, 480, 108000], 'label': '162000.x.4500.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '4500.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.i1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
-
id: 62910470
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4500.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.bl1.a1', '900.bm1.a1', '900.bq1.a1', '1500.d1.a1', '2250.c1.a1'], 'contains': ['9000.h1.a1', '40500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [1, 2, 108480, 108000], 'label': '162000.x.4500.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.d1.a1', 'old_label': '4500.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.j1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
-
id: 62910471
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4500.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.bn1.a1', '900.bp1.a1', '900.br1.a1', '1500.e1.a1', '2250.d1.a1'], 'contains': ['9000.g1.a1', '9000.h1.a1', '9000.j1.a1', '13500.j1.a1', '13500.k1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [17642, 11340, 480, 7200], 'label': '162000.x.4500.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.f1.a1', 'old_label': '4500.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.k1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 62910472
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '4500.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.bs1.a1', '900.bt1.a1', '1500.f1.a1', '2250.d1.a1'], 'contains': ['9000.j1.a1', '9000.k1.a1', '13500.m1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1125, 'diagramx': None, 'generators': [6660, 125640, 480, 7200], 'label': '162000.x.4500.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1125.a1.a1', 'old_label': '4500.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.l1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
-
id: 62910473
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.a1.a1', '1080.b1.a1', '1080.c1.a1', '1080.d1.a1', '1800.a1.a1', '1800.l1.a1', '1800.m1.a1', '2700.o1.a1'], 'contains': ['10800.a1.a1', '16200.a1.a1', '27000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 32400, 61680], 'label': '162000.x.5400.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.f1.a1', 'old_label': '5400.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910474
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.a1.a1', '1080.d1.a1', '1080.e1.a1', '1080.f1.a1', '1080.g1.a1', '1800.b1.a1', '1800.n1.a1', '1800.o1.a1'], 'contains': ['10800.b1.a1', '16200.b1.a1', '27000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 97344, 61680], 'label': '162000.x.5400.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.d1.a1', 'old_label': '5400.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.b1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910475
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.b1.a1', '1080.e1.a1', '1800.c1.a1', '1800.j1.a1', '1800.k1.a1', '1800.p1.a1', '2700.p1.a1'], 'contains': ['10800.c1.a1', '16200.c1.a1', '27000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': None, 'generators': [10862, 134064, 61680], 'label': '162000.x.5400.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '5400.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910476
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.a1.a1'], 'contains': ['144.d1.a1', '216.e1.a1', '216.g1.a1', '360.bh1.a1', '360.bk1.a1', '360.bl1.a1', '360.bm1.a1', '360.bn1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [54482, 2160, 97344, 32400, 7200, 54480], 'label': '162000.x.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910477
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.b1.a1', '1080.c1.a1', '1080.f1.a1', '1080.g1.a1', '1800.d1.a1', '1800.p1.a1', '1800.q1.a1', '2700.q1.a1'], 'contains': ['10800.d1.a1', '16200.c1.a1', '27000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 136224, 61680], 'label': '162000.x.5400.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '5400.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910478
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.b1.a1', '1080.d1.a1', '1080.f1.a1', '1080.i1.a1', '1800.f1.a1', '1800.r1.a1', '1800.t1.a1', '2700.r1.a1'], 'contains': ['10800.e1.a1', '16200.d1.a1', '27000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 66960, 61680], 'label': '162000.x.5400.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.h1.a1', 'old_label': '5400.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.e1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910479
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.c1.a1', '1080.d1.a1', '1080.e1.a1', '1080.g1.a1', '1080.h1.a1', '1080.i1.a1', '1800.e1.a1', '1800.s1.a1', '1800.t1.a1', '2700.s1.a1'], 'contains': ['10800.f1.a1', '16200.d1.a1', '27000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 32544, 61680], 'label': '162000.x.5400.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.h2.a1', 'old_label': '5400.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.f1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910480
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.a1.a1', '1080.b1.a1', '1080.f1.a1', '1080.h1.a1', '1800.g1.a1', '1800.u1.a1', '1800.v1.a1', '2700.t1.a1'], 'contains': ['10800.g1.a1', '16200.e1.a1', '27000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 69264, 61680], 'label': '162000.x.5400.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '5400.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.g1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910481
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.a1.a1', '1080.b1.a1', '1080.g1.a1', '1080.i1.a1', '1800.h1.a1', '1800.u1.a1', '1800.x1.a1', '2700.u1.a1'], 'contains': ['10800.h1.a1', '16200.e1.a1', '27000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 67104, 61680], 'label': '162000.x.5400.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '5400.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.h1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910482
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.a1.a1', '1080.c1.a1', '1080.e1.a1', '1080.f1.a1', '1080.i1.a1', '1800.i1.a1', '1800.v1.a1', '1800.w1.a1', '1800.x1.a1'], 'contains': ['10800.i1.a1', '16200.e1.a1', '27000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 41184, 61680], 'label': '162000.x.5400.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.g1.a1', 'old_label': '5400.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.i1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910483
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.j1.a1', '1080.l1.a1', '1080.n1.a1', '1800.l1.a1', '1800.y1.a1', '2700.d1.a1', '2700.l1.a1', '2700.v1.a1'], 'contains': ['10800.j1.a1', '16200.a1.a1', '27000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [10862, 144, 480], 'label': '162000.x.5400.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '5400.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.j1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910484
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.k1.a1', '1080.m1.a1', '1080.n1.a1', '1080.o1.a1', '1800.m1.a1', '1800.y1.a1', '1800.z1.a1', '2700.a1.a1', '2700.e1.a1', '2700.m1.a1'], 'contains': ['10800.k1.a1', '16200.a1.a1', '27000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 32400, 480], 'label': '162000.x.5400.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.e1.a1', 'old_label': '5400.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.k1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910485
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.j1.a1', '1080.o1.a1', '1080.p1.a1', '1800.n1.a1', '1800.ba1.a1', '2700.b1.a1'], 'contains': ['10800.l1.a1', '16200.b1.a1', '27000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 34560, 480], 'label': '162000.x.5400.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.a1', 'old_label': '5400.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.l1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910486
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.k1.a1', '1080.n1.a1', '1080.p1.a1', '1080.q1.a1', '1800.o1.a1', '1800.ba1.a1', '1800.bb1.a1', '2700.f1.a1'], 'contains': ['10800.m1.a1', '16200.b1.a1', '27000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 97344, 480], 'label': '162000.x.5400.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '5400.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.m1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910487
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '18.c1.a1', '30.b1.a1', '30.d1.a1', '54.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [32400, 2160, 11100, 108000, 108480, 97344, 1, 2, 7200], 'label': '162000.x.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
id: 62910488
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.b1.a1', '36.i1.a1', '36.k1.a1'], 'contains': ['144.e1.a1', '216.e1.a1', '216.f1.a1', '360.bi1.a1', '360.bo1.a1', '360.bp1.a1', '360.bq1.a1', '360.br1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2, 2160, 97344, 32400, 7200, 480], 'label': '162000.x.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
-
id: 62910489
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.l1.a1', '1080.m1.a1', '1080.p1.a1', '1080.q1.a1', '1800.p1.a1', '1800.q1.a1', '1800.bc1.a1', '2700.w1.a1'], 'contains': ['10800.n1.a1', '16200.c1.a1', '27000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 136224, 480], 'label': '162000.x.5400.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '5400.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.n1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910490
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.l1.a1', '1080.o1.a1', '1080.q1.a1', '1080.r1.a1', '1800.r1.a1', '1800.s1.a1', '1800.bd1.a1', '2700.c1.a1', '2700.x1.a1', '2700.x2.a1'], 'contains': ['10800.o1.a1', '16200.d1.a1', '27000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 66960, 480], 'label': '162000.x.5400.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '5400.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.o1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910491
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.m1.a1', '1080.n1.a1', '1080.p1.a1', '1080.r1.a1', '1800.t1.a1', '1800.bd1.a1', '1800.be1.a1', '2700.g1.a1'], 'contains': ['10800.p1.a1', '16200.d1.a1', '27000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 32544, 480], 'label': '162000.x.5400.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.c1.a1', 'old_label': '5400.p1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.p1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910492
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.k1.a1', '1080.l1.a1', '1080.p1.a1', '1080.r1.a1', '1800.u1.a1', '1800.w1.a1', '1800.bf1.a1', '2700.y1.a1'], 'contains': ['10800.q1.a1', '16200.e1.a1', '27000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 73584, 480], 'label': '162000.x.5400.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '5400.q1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.q1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910493
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.j1.a1', '1080.k1.a1', '1080.m1.a1', '1080.p1.a1', '1080.q1.a1', '1080.r1.a1', '1800.v1.a1', '1800.x1.a1', '1800.bf1.a1', '1800.bg1.a1'], 'contains': ['10800.r1.a1', '16200.e1.a1', '27000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 41184, 480], 'label': '162000.x.5400.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.g1.a1', 'old_label': '5400.r1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.r1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910494
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.s1.a1', '1080.u1.a1', '1080.v1.a1', '1080.y1.a1', '1800.a1.a1', '1800.l1.a1', '1800.z1.a1', '2700.n1.a1', '2700.z1.a1', '2700.be1.a1'], 'contains': ['10800.s1.a1', '16200.a1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 32400, 4080], 'label': '162000.x.5400.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '5400.s1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.s1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910495
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.t1.a1', '1080.w1.a1', '1080.x1.a1', '1080.y1.a1', '1800.a1.a1', '1800.m1.a1', '1800.y1.a1', '2700.h1.a1'], 'contains': ['10800.t1.a1', '16200.a1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 144, 4080], 'label': '162000.x.5400.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.a1.a1', 'old_label': '5400.t1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.t1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910496
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.s1.a1', '1080.x1.a1', '1080.bb1.a1', '1080.bc1.a1', '1800.b1.a1', '1800.n1.a1', '1800.bb1.a1', '2700.i1.a1'], 'contains': ['10800.u1.a1', '16200.b1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 2304, 4080], 'label': '162000.x.5400.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '5400.u1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.u1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910497
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.t1.a1', '1080.y1.a1', '1080.z1.a1', '1080.ba1.a1', '1080.bb1.a1', '1080.bc1.a1', '1800.b1.a1', '1800.o1.a1', '1800.ba1.a1'], 'contains': ['10800.v1.a1', '16200.b1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 97344, 4080], 'label': '162000.x.5400.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.d1.a1', 'old_label': '5400.v1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.v1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910498
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.u1.a1', '1080.w1.a1', '1080.ba1.a1', '1080.bb1.a1', '1800.d1.a1', '1800.p1.a1', '1800.bc1.a1', '2700.ba1.a1'], 'contains': ['10800.w1.a1', '16200.c1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 136224, 4080], 'label': '162000.x.5400.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '5400.w1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.w1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910499
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.c1.a1', '36.j1.a1', '36.k1.a1'], 'contains': ['144.e1.a1', '216.f1.a1', '216.g1.a1', '360.bj1.a1', '360.bs1.a1', '360.bt1.a1', '360.bu1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 2160, 32400, 480, 97344, 108000], 'label': '162000.x.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '720.774'}
-
id: 62910500
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.v1.a1', '1080.w1.a1', '1080.z1.a1', '1080.bc1.a1', '1800.c1.a1', '1800.d1.a1', '1800.q1.a1', '1800.bc1.a1', '2700.bf1.a1'], 'contains': ['10800.x1.a1', '16200.c1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 36864, 4080], 'label': '162000.x.5400.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.g1.a1', 'old_label': '5400.x1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.x1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910501
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.u1.a1', '1080.x1.a1', '1080.z1.a1', '1080.bd1.a1', '1800.e1.a1', '1800.r1.a1', '1800.be1.a1', '2700.j1.a1', '2700.bb1.a1', '2700.bg1.a1'], 'contains': ['10800.y1.a1', '16200.d1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 6624, 4080], 'label': '162000.x.5400.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '5400.y1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.y1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910502
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.v1.a1', '1080.x1.a1', '1080.ba1.a1', '1080.be1.a1', '1800.f1.a1', '1800.s1.a1', '1800.be1.a1', '2700.k1.a1', '2700.bc1.a1', '2700.bh1.a1'], 'contains': ['10800.z1.a1', '16200.d1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 4464, 4080], 'label': '162000.x.5400.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '5400.z1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.z1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910503
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.w1.a1', '1080.y1.a1', '1080.bb1.a1', '1080.bc1.a1', '1080.bd1.a1', '1080.be1.a1', '1800.e1.a1', '1800.f1.a1', '1800.t1.a1', '1800.bd1.a1'], 'contains': ['10800.ba1.a1', '16200.d1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 66960, 4080], 'label': '162000.x.5400.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.f1.a1', 'old_label': '5400.ba1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910504
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.t1.a1', '1080.v1.a1', '1080.bb1.a1', '1080.bd1.a1', '1800.g1.a1', '1800.h1.a1', '1800.w1.a1', '1800.bg1.a1', '2700.bi1.a1'], 'contains': ['10800.bb1.a1', '16200.e1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 69264, 4080], 'label': '162000.x.5400.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '5400.bb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910505
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.t1.a1', '1080.u1.a1', '1080.bc1.a1', '1080.be1.a1', '1800.i1.a1', '1800.u1.a1', '1800.bg1.a1', '2700.bd1.a1'], 'contains': ['10800.bc1.a1', '16200.e1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 103824, 4080], 'label': '162000.x.5400.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '5400.bc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910506
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.s1.a1', '1080.t1.a1', '1080.w1.a1', '1080.ba1.a1', '1080.bc1.a1', '1080.bd1.a1', '1800.g1.a1', '1800.i1.a1', '1800.x1.a1', '1800.bf1.a1'], 'contains': ['10800.bd1.a1', '16200.e1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 131904, 4080], 'label': '162000.x.5400.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.g1.a1', 'old_label': '5400.bd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910507
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.s1.a1', '1080.t1.a1', '1080.w1.a1', '1080.z1.a1', '1080.bb1.a1', '1080.be1.a1', '1800.h1.a1', '1800.i1.a1', '1800.v1.a1', '1800.bf1.a1'], 'contains': ['10800.be1.a1', '16200.e1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [10862, 41184, 4080], 'label': '162000.x.5400.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.g1.a1', 'old_label': '5400.be1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.be1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910508
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1.a1', '1800.j1.a1', '2700.bj1.a1'], 'contains': ['10800.bf1.a1', '16200.c1.a1', '27000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10862, 136224, 83128], 'label': '162000.x.5400.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.v1.a1', 'old_label': '5400.bf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910509
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bg1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bg1.a1', '1080.bl1.a1', '1800.bh1.a1', '1800.bl1.a1', '1800.bm1.a1', '2700.a1.a1', '2700.bm1.a1', '2700.bq1.a1'], 'contains': ['10800.k1.a1', '16200.f1.a1', '27000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [2, 32400, 7200], 'label': '162000.x.5400.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.i1.a1', 'old_label': '5400.bg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910510
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.a1.a1'], 'contains': ['144.d1.a1', '216.h1.a1', '216.j1.a1', '360.bv1.a1', '360.bw1.a1', '360.bx1.a1', '360.by1.a1', '360.cg1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [119340, 32400, 66960, 54480, 7200, 97344], 'label': '162000.x.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '600.161'}
-
id: 62910511
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bg1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bg1.a1', '1080.bj1.a1', '1800.bi1.a1', '1800.bn1.a1', '2700.b1.a1', '2700.bk1.a1', '2700.bl1.a1'], 'contains': ['10800.l1.a1', '16200.g1.a1', '27000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [2, 97344, 7200], 'label': '162000.x.5400.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.b1.a1', 'old_label': '5400.bh1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910512
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bg1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bg1.a1', '1080.bk1.a1', '1800.bj1.a1', '1800.bk1.a1', '1800.bo1.a1', '2700.c1.a1'], 'contains': ['10800.o1.a1', '16200.h1.a1', '27000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [2, 32544, 7200], 'label': '162000.x.5400.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '5400.bi1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910513
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.ca1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bh1.a1', '1080.bo1.a1', '1800.bl1.a1', '1800.bp1.a1', '2700.d1.a1', '2700.bo1.a1', '2700.bp1.a1'], 'contains': ['10800.j1.a1', '16200.f1.a1', '27000.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 480, 144], 'label': '162000.x.5400.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '5400.bj1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910514
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bh1.a1', '1080.bp1.a1', '1800.bm1.a1', '1800.bp1.a1', '2700.e1.a1', '2700.bm1.a1', '2700.br1.a1'], 'contains': ['10800.k1.a1', '16200.f1.a1', '27000.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 480, 32400], 'label': '162000.x.5400.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '5400.bk1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910515
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bh1.a1', '1080.bm1.a1', '1800.bn1.a1', '1800.bq1.a1', '2700.f1.a1'], 'contains': ['10800.m1.a1', '16200.g1.a1', '27000.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [2, 480, 97344], 'label': '162000.x.5400.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '5400.bl1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910516
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bh1.a1', '1080.bn1.a1', '1800.bo1.a1', '1800.br1.a1', '2700.g1.a1'], 'contains': ['10800.p1.a1', '16200.h1.a1', '27000.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [2, 480, 32544], 'label': '162000.x.5400.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '5400.bm1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910517
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bi1.a1', '1080.bt1.a1', '1800.bh1.a1', '1800.bp1.a1', '2700.h1.a1'], 'contains': ['10800.t1.a1', '16200.f1.a1', '27000.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [54482, 54480, 32400], 'label': '162000.x.5400.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.a1.a1', 'old_label': '5400.bn1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910518
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bi1.a1', '1080.bq1.a1', '1800.bi1.a1', '1800.bq1.a1', '2700.i1.a1'], 'contains': ['10800.u1.a1', '16200.g1.a1', '27000.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [54482, 54480, 97344], 'label': '162000.x.5400.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.a1.a1', 'old_label': '5400.bo1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910519
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bi1.a1', '1080.br1.a1', '1800.bj1.a1', '1800.br1.a1', '2700.j1.a1'], 'contains': ['10800.y1.a1', '16200.h1.a1', '27000.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [54482, 54480, 129744], 'label': '162000.x.5400.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '5400.bp1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
-
id: 62910520
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bi1.a1', '1080.bs1.a1', '1800.bk1.a1', '1800.br1.a1', '2700.k1.a1'], 'contains': ['10800.z1.a1', '16200.h1.a1', '27000.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [54482, 54480, 32544], 'label': '162000.x.5400.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '5400.bq1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
-
id: 62910521
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.b1.a1', '36.k1.a1', '36.l1.a1'], 'contains': ['144.e1.a1', '216.h1.a1', '216.i1.a1', '360.bz1.a1', '360.ca1.a1', '360.cb1.a1', '360.cc1.a1', '360.ch1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [11340, 32400, 66960, 480, 7200, 97344], 'label': '162000.x.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '600.174'}
-
id: 62910522
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.cf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bj1.a1', '1080.bk1.a1', '1080.bl1.a1', '1800.bs1.a1', '1800.bt1.a1', '2700.l1.a1', '2700.bn1.a1', '2700.bp1.a1'], 'contains': ['10800.j1.a1', '16200.i1.a1', '27000.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [2, 2160, 7200], 'label': '162000.x.5400.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '5400.br1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.br1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
-
id: 62910523
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bm1.a1', '1080.bn1.a1', '1080.bo1.a1', '1080.bp1.a1', '1800.bt1.a1', '1800.bu1.a1', '2700.m1.a1', '2700.bq1.a1', '2700.br1.a1'], 'contains': ['10800.k1.a1', '16200.i1.a1', '27000.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2, 2160, 480], 'label': '162000.x.5400.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '5400.bs1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910524
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bq1.a1', '1080.br1.a1', '1080.bs1.a1', '1080.bt1.a1', '1800.bs1.a1', '1800.bu1.a1', '2700.n1.a1'], 'contains': ['10800.s1.a1', '16200.i1.a1', '27000.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [54482, 2160, 54480], 'label': '162000.x.5400.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '5400.bt1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910525
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.bu1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bu1.a1', '1080.bv1.a1', '1080.bw1.a1', '1800.bv1.a1', '1800.bw1.a1', '2700.l1.a1', '2700.bo1.a1', '2700.bt1.a1'], 'contains': ['10800.j1.a1', '16200.j1.a1', '27000.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [11100, 2160, 7200], 'label': '162000.x.5400.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '5400.bu1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910526
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bx1.a1', '1080.by1.a1', '1080.bz1.a1', '1080.ca1.a1', '1800.bw1.a1', '1800.bx1.a1', '2700.m1.a1', '2700.bm1.a1', '2700.bs1.a1'], 'contains': ['10800.k1.a1', '16200.j1.a1', '27000.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [11340, 480, 2160], 'label': '162000.x.5400.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.f1.a1', 'old_label': '5400.bv1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910527
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.cb1.a1', '1080.cc1.a1', '1080.cd1.a1', '1080.ce1.a1', '1800.bv1.a1', '1800.bx1.a1', '2700.n1.a1'], 'contains': ['10800.s1.a1', '16200.j1.a1', '27000.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [119340, 54480, 2160], 'label': '162000.x.5400.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.e1.a1', 'old_label': '5400.bw1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
-
id: 62910528
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bw1.a1', '1080.cf1.a1', '1800.by1.a1', '1800.cc1.a1', '1800.cd1.a1', '2700.a1.a1', '2700.br1.a1', '2700.bs1.a1'], 'contains': ['10800.k1.a1', '16200.k1.a1', '27000.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [11100, 32400, 7200], 'label': '162000.x.5400.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.h1.a1', 'old_label': '5400.bx1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910529
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bu1.a1', '1080.cf1.a1', '1800.bz1.a1', '1800.ce1.a1', '2700.b1.a1'], 'contains': ['10800.l1.a1', '16200.l1.a1', '27000.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [11100, 97344, 7200], 'label': '162000.x.5400.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1.a1', 'old_label': '5400.by1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.by1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 62910530
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bv1.a1', '1080.cf1.a1', '1800.ca1.a1', '1800.cb1.a1', '1800.cf1.a1', '2700.c1.a1'], 'contains': ['10800.o1.a1', '16200.m1.a1', '27000.h1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [11100, 32544, 7200], 'label': '162000.x.5400.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.d1.a1', 'old_label': '5400.bz1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910531
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.ca1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bz1.a1', '1080.cg1.a1', '1800.cc1.a1', '1800.cg1.a1', '2700.d1.a1', '2700.bp1.a1', '2700.bt1.a1'], 'contains': ['10800.j1.a1', '16200.k1.a1', '27000.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [11340, 144, 480], 'label': '162000.x.5400.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.f1.a1', 'old_label': '5400.ca1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910532
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.c1.a1', '36.i1.a1', '36.l1.a1'], 'contains': ['144.e1.a1', '216.i1.a1', '216.j1.a1', '360.cd1.a1', '360.ce1.a1', '360.cf1.a1', '360.ci1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [119340, 32400, 480, 108000, 66960, 97344], 'label': '162000.x.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62910533
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.ca1.a1', '1080.cg1.a1', '1800.cd1.a1', '1800.cg1.a1', '2700.e1.a1', '2700.bq1.a1', '2700.bs1.a1'], 'contains': ['10800.k1.a1', '16200.k1.a1', '27000.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [11340, 32400, 480], 'label': '162000.x.5400.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '5400.cb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910534
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bx1.a1', '1080.cg1.a1', '1800.ce1.a1', '1800.ch1.a1', '2700.f1.a1'], 'contains': ['10800.m1.a1', '16200.l1.a1', '27000.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [11340, 97344, 480], 'label': '162000.x.5400.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.h1.a1', 'old_label': '5400.cc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910535
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.by1.a1', '1080.cg1.a1', '1800.cf1.a1', '1800.ci1.a1', '2700.g1.a1'], 'contains': ['10800.p1.a1', '16200.m1.a1', '27000.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [11340, 32544, 480], 'label': '162000.x.5400.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.i1.a1', 'old_label': '5400.cd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910536
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.ce1.a1', '1080.ch1.a1', '1800.by1.a1', '1800.cg1.a1', '2700.h1.a1'], 'contains': ['10800.t1.a1', '16200.k1.a1', '27000.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [119340, 32400, 54480], 'label': '162000.x.5400.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.g1.a1', 'old_label': '5400.ce1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910537
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.cb1.a1', '1080.ch1.a1', '1800.bz1.a1', '1800.ch1.a1', '2700.i1.a1'], 'contains': ['10800.u1.a1', '16200.l1.a1', '27000.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': None, 'generators': [119340, 97344, 54480], 'label': '162000.x.5400.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.d1.a1', 'old_label': '5400.cf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 62910538
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.cc1.a1', '1080.ch1.a1', '1800.ca1.a1', '1800.ci1.a1', '2700.j1.a1'], 'contains': ['10800.y1.a1', '16200.m1.a1', '27000.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [119340, 129744, 54480], 'label': '162000.x.5400.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.d1.a1', 'old_label': '5400.cg1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910539
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '5400.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.cd1.a1', '1080.ch1.a1', '1800.cb1.a1', '1800.ci1.a1', '2700.k1.a1'], 'contains': ['10800.z1.a1', '16200.m1.a1', '27000.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [119340, 32544, 54480], 'label': '162000.x.5400.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1.a1', 'old_label': '5400.ch1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
-
id: 62910540
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6000.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': ['27.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1200.c1.a1', '1200.d1.a1', '1200.e1.a1', '1200.f1.a1', '1200.g1.a1', '2000.a1.a1', '3000.c1.a1', '3000.d1.a1', '3000.e1.a1'], 'contains': ['18000.a1.a1', '18000.d1.a1', '18000.e1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [480, 7200, 108000], 'label': '162000.x.6000.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '6000.a1.a1', 'normal_contained_in': ['48.a1.a1'], 'normal_contains': ['162000.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6000.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': '24.12', 'quotient_action_kernel': '250.14', 'quotient_action_kernel_order': 250, 'quotient_fusion': None, 'short_label': '6000.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 62910541
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6000.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '1200.a1.a1', '2000.a1.a1', '3000.a1.a1'], 'contains': ['18000.a1.a1', '18000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': None, 'generators': [25768, 61200], 'label': '162000.x.6000.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '6000.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6000.b1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
-
id: 62910542
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6000.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.b1.a1', '1200.b1.a1', '2000.a1.a1', '3000.b1.a1'], 'contains': ['18000.a1.a1', '18000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': None, 'generators': [25288, 61200], 'label': '162000.x.6000.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.a1.a1', 'old_label': '6000.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6000.c1.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
-
id: 62910543
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '75.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['150.c1.a1', '150.d1.a1', '150.e1.a1', '225.a1.a1', '375.a1.a1', '675.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [1, 108480, 108000, 2, 7200, 2160, 125640, 119340], 'label': '162000.x.75.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '75.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2160.fi'}
-
id: 62910544
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6480.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.a1.a1', '2160.a1.a1', '2160.j1.a1', '2160.k1.a1', '2160.s1.a1', '2160.t1.a1', '3240.a1.a1', '3240.g1.a1', '3240.j1.a1'], 'contains': ['32400.a1.a1', '32400.b1.a1', '32400.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [97344, 2160], 'label': '162000.x.6480.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '6480.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910545
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6480.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.a1.a1', '2160.b1.a1', '2160.c1.a1', '2160.l1.a1', '2160.m1.a1', '2160.u1.a1', '2160.v1.a1', '2160.w1.a1', '3240.b1.a1', '3240.h1.a1', '3240.k1.a1'], 'contains': ['32400.a1.a1', '32400.c1.a1', '32400.d1.a1', '32400.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [144, 66960], 'label': '162000.x.6480.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '6480.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910546
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6480.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.a1.a1', '2160.d1.a1', '2160.n1.a1', '2160.o1.a1', '2160.x1.a1', '2160.y1.a1', '3240.c1.a1', '3240.f1.a1', '3240.i1.a1', '3240.l1.a1', '3240.m1.a1'], 'contains': ['32400.a1.a1', '32400.b1.a1', '32400.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [97344, 32400], 'label': '162000.x.6480.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6480.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 62910547
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6480.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.a1.a1', '2160.e1.a1', '2160.f1.a1', '2160.g1.a1', '2160.p1.a1', '2160.q1.a1', '2160.z1.a1', '2160.ba1.a1', '2160.bb1.a1', '2160.bc1.a1', '3240.d1.a1'], 'contains': ['32400.b1.a1', '32400.c1.a1', '32400.d1.a1', '32400.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [97344, 66960], 'label': '162000.x.6480.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '6480.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910548
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6480.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.a1.a1', '2160.h1.a1', '2160.i1.a1', '2160.r1.a1', '2160.bd1.a1', '2160.be1.a1', '2160.bf1.a1', '3240.e1.a1'], 'contains': ['32400.d1.a1', '32400.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [32544, 66960], 'label': '162000.x.6480.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '6480.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.1'}
-
id: 62910549
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6750.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6750.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1350.a1.a1', '1350.e1.a1', '2250.a1.a1', '3375.b1.a1'], 'contains': ['13500.a1.a1', '13500.e1.a1', '20250.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3375, 'diagramx': None, 'generators': [75001, 11100, 7200, 10862], 'label': '162000.x.6750.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3375.b1.a1', 'old_label': '6750.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6750.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910550
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6750.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['750.b1.a1', '1350.b1.a1', '1350.f1.a1', '3375.b1.a1'], 'contains': ['13500.a1.a1', '13500.i1.a1', '20250.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3375, 'diagramx': None, 'generators': [1, 10860, 2, 7200], 'label': '162000.x.6750.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3375.b1.a1', 'old_label': '6750.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6750.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910551
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6750.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13500.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1350.c1.a1', '1350.d1.a1', '1350.h1.a1', '2250.a1.a1', '2250.b1.a1'], 'contains': ['13500.c1.a1', '13500.f1.a1', '13500.g1.a1', '20250.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2250, 'diagramx': None, 'generators': [64263, 119340, 10862, 54480], 'label': '162000.x.6750.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2250.a1.a1', 'old_label': '6750.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6750.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910552
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6750.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.d1.a1', '250.a1.a1', '3375.a1.a1'], 'contains': ['13500.l1.a1', '20250.c1.a1', '27000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3375, 'diagramx': None, 'generators': [2, 83128, 10860, 14040], 'label': '162000.x.6750.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3375.a1.a1', 'old_label': '6750.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6750.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 62910553
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '6750.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1350.g1.a1', '1350.i1.a1', '2250.d1.a1', '3375.b1.a1'], 'contains': ['13500.a1.a1', '13500.b1.a1', '13500.j1.a1', '13500.k1.a1', '13500.m1.a1', '20250.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3375, 'diagramx': None, 'generators': [10862, 119340, 125640, 480], 'label': '162000.x.6750.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3375.b1.a1', 'old_label': '6750.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6750.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910554
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.a1.a1'], 'contains': ['240.a1.a1', '240.b1.a1', '240.g1.a1', '2000.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [83128, 66960, 61200, 58080, 108000, 4464], 'label': '162000.x.80.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '80.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2700.o'}
-
id: 62910555
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13500.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.a1.a1', '1620.d1.a1', '2700.a1.a1', '2700.d1.a1', '2700.e1.a1', '2700.h1.a1', '4050.e1.a1'], 'contains': ['16200.a1.a1', '16200.f1.a1', '16200.k1.a1', '40500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [242, 32400, 11100], 'label': '162000.x.8100.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.i1.a1', 'old_label': '8100.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910556
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13500.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.a1.a1', '1620.b1.a1', '2700.b1.a1', '2700.f1.a1', '2700.i1.a1', '4050.b1.a1'], 'contains': ['16200.b1.a1', '16200.g1.a1', '16200.l1.a1', '40500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [242, 97344, 11100], 'label': '162000.x.8100.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.b1.a1', 'old_label': '8100.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.b1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910557
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27000.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.a1.a1', '1620.c1.a1', '2700.c1.a1', '2700.g1.a1', '2700.j1.a1', '2700.k1.a1', '4050.a1.a1'], 'contains': ['16200.d1.a1', '16200.h1.a1', '16200.m1.a1', '40500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [10862, 32544, 11100], 'label': '162000.x.8100.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.a1.a1', 'old_label': '8100.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910558
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13500.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.b1.a1', '1620.c1.a1', '1620.d1.a1', '2700.l1.a1', '2700.m1.a1', '2700.n1.a1', '4050.c1.a1', '4050.d1.a1', '4050.e1.a1'], 'contains': ['16200.a1.a1', '16200.i1.a1', '16200.j1.a1', '40500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [242, 2160, 11100], 'label': '162000.x.8100.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '8100.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910559
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.e1.a1', '1620.e2.a1', '2700.o1.a1', '2700.v1.a1', '2700.z1.a1', '2700.be1.a1', '4050.c1.a1'], 'contains': ['16200.a1.a1', '40500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10503, 2160, 10862], 'label': '162000.x.8100.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.e1.a1', 'old_label': '8100.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.e1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910560
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.e1.a1', '1620.g1.a1', '2700.p1.a1', '2700.q1.a1', '2700.w1.a1', '2700.ba1.a1', '2700.bf1.a1', '2700.bj1.a1'], 'contains': ['16200.c1.a1', '40500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 39024, 10862], 'label': '162000.x.8100.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.x1.a1', 'old_label': '8100.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.f1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910561
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.e1.a1', '1620.f1.a1', '2700.r1.a1', '2700.x1.a1', '2700.bb1.a1', '2700.bh1.a1', '4050.a1.a1'], 'contains': ['16200.d1.a1', '40500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10503, 32544, 10862], 'label': '162000.x.8100.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.a1.a1', 'old_label': '8100.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.g1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910562
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.g2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.e2.a1', '1620.f1.a1', '1620.g1.a1', '1620.h1.a1', '2700.s1.a1', '2700.x2.a1', '2700.bc1.a1', '2700.bg1.a1', '4050.a1.a1'], 'contains': ['16200.d1.a1', '40500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [10503, 129744, 10862], 'label': '162000.x.8100.g2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '8100.g2.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.g2.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910563
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.e1.a1', '1620.h1.a1', '2700.t1.a1', '2700.u1.a1', '2700.y1.a1', '2700.bd1.a1', '2700.bi1.a1'], 'contains': ['16200.e1.a1', '40500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [10503, 41184, 10862], 'label': '162000.x.8100.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.ba1.a1', 'old_label': '8100.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.h1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910564
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8100.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.bl1.a1', '1620.i1.a1', '1620.j1.a1', '2700.bk1.a1', '4050.b1.a1'], 'contains': ['16200.g1.a1', '40500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4050, 'diagramx': None, 'generators': [1, 2, 64944], 'label': '162000.x.8100.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4050.b1.a1', 'old_label': '8100.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910565
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '27.a1.a1', '27.b1.a1'], 'contains': ['162.a1.a1', '162.b1.a1', '162.c1.a1', '405.a1.a1', '2025.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [115201, 2160, 108482, 119340, 125640, 32400, 97344], 'label': '162000.x.81.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '81.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2000.905'}
-
id: 62910566
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8100.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.bm1.a1', '1620.i1.a1', '1620.k1.a1', '2700.bl1.a1', '4050.b1.a1'], 'contains': ['16200.g1.a1', '40500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [1, 97344, 2], 'label': '162000.x.8100.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.b1.a1', 'old_label': '8100.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.j1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910567
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8100.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.l1.a1', '2700.bm1.a1', '2700.bo1.a1', '4050.e1.a1'], 'contains': ['16200.f1.a1', '16200.j1.a1', '40500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2025, 'diagramx': None, 'generators': [17882, 2160, 11100], 'label': '162000.x.8100.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2025.a1.a1', 'old_label': '8100.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910568
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16200.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.bq1.a1', '1620.j1.a1', '1620.k1.a1', '2700.bn1.a1', '4050.d1.a1'], 'contains': ['16200.i1.a1', '40500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [1, 2160, 2], 'label': '162000.x.8100.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.d1.a1', 'old_label': '8100.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.l1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910569
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8100.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.l1.a1', '1620.m1.a1', '2700.bp1.a1', '2700.bq1.a1', '2700.br1.a1', '4050.e1.a1'], 'contains': ['16200.f1.a1', '16200.i1.a1', '16200.k1.a1', '40500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': None, 'generators': [17882, 32400, 11100], 'label': '162000.x.8100.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.e1.a1', 'old_label': '8100.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.m1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910570
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8100.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40500.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1620.n1.a1', '2700.bs1.a1', '2700.bt1.a1', '4050.e1.a1'], 'contains': ['16200.j1.a1', '16200.k1.a1', '40500.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2025, 'diagramx': None, 'generators': [7140, 32400, 125640], 'label': '162000.x.8100.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2025.a1.a1', 'old_label': '8100.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8100.n1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910571
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '9000.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.a1.a1', '1800.b1.a1', '1800.c1.a1', '1800.d1.a1', '1800.e1.a1', '1800.f1.a1', '1800.g1.a1', '1800.h1.a1', '1800.i1.a1', '3000.a1.a1', '3000.b1.a1', '3000.c1.a1', '4500.d1.a1'], 'contains': ['18000.a1.a1', '27000.a1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 500, 'diagramx': None, 'generators': [10862, 115680, 61200], 'label': '162000.x.9000.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '500.a1.a1', 'old_label': '9000.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9000.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910572
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '9000.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.j1.a1', '1800.j1.a1', '3000.a1.a1', '4500.e1.a1'], 'contains': ['18000.b1.a1', '27000.a1.a1', '27000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1500, 'diagramx': None, 'generators': [10862, 25768, 58080], 'label': '162000.x.9000.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1500.b1.a1', 'old_label': '9000.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9000.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910573
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '9000.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.k1.a1', '1800.k1.a1', '3000.b1.a1'], 'contains': ['18000.c1.a1', '27000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3000, 'diagramx': None, 'generators': [10862, 25288, 58080], 'label': '162000.x.9000.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3000.b1.a1', 'old_label': '9000.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9000.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 62910574
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '9000.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.l1.a1', '1800.m1.a1', '1800.n1.a1', '1800.o1.a1', '1800.p1.a1', '1800.q1.a1', '1800.r1.a1', '1800.s1.a1', '1800.t1.a1', '1800.u1.a1', '1800.v1.a1', '1800.w1.a1', '1800.x1.a1', '3000.c1.a1', '4500.a1.a1', '4500.f1.a1', '4500.g1.a1'], 'contains': ['18000.d1.a1', '27000.a1.a1', '27000.b1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 750, 'diagramx': None, 'generators': [10862, 480, 61200], 'label': '162000.x.9000.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '750.a1.a1', 'old_label': '9000.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9000.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910575
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '9000.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.y1.a1', '1800.z1.a1', '1800.ba1.a1', '1800.bb1.a1', '1800.bc1.a1', '1800.bd1.a1', '1800.be1.a1', '1800.bf1.a1', '1800.bg1.a1', '3000.c1.a1', '4500.b1.a1', '4500.c1.a1', '4500.h1.a1'], 'contains': ['18000.e1.a1', '27000.b1.a1', '27000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': None, 'generators': [10862, 480, 7200], 'label': '162000.x.9000.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '9000.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9000.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 62910576
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '90.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.a1.a1'], 'contains': ['180.a1.a1', '180.y1.a1', '180.bd1.a1', '270.a1.a1', '270.c1.a1', '450.a1.a1', '450.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [64263, 97344, 7200, 10862, 119340, 32400, 54480], 'label': '162000.x.90.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '90.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.a1.a1', 'subgroup_fusion': None, 'weyl_group': '600.161'}
-
id: 62910577
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '9000.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.bh1.a1', '1800.bi1.a1', '1800.bj1.a1', '1800.bk1.a1', '1800.bs1.a1', '3000.d1.a1', '4500.a1.a1'], 'contains': ['18000.d1.a1', '27000.e1.a1', '27000.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [54482, 7200, 54480], 'label': '162000.x.9000.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '9000.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9000.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910578
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '9000.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.bl1.a1', '1800.bm1.a1', '1800.bn1.a1', '1800.bo1.a1', '1800.bt1.a1', '3000.d1.a1', '4500.b1.a1', '4500.i1.a1', '4500.k1.a1'], 'contains': ['18000.e1.a1', '27000.e1.a1', '27000.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 7200, 480], 'label': '162000.x.9000.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '9000.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9000.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910579
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '9000.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.bp1.a1', '1800.bq1.a1', '1800.br1.a1', '1800.bu1.a1', '3000.d1.a1', '4500.c1.a1', '4500.j1.a1', '4500.k1.a1'], 'contains': ['18000.e1.a1', '27000.f1.a1', '27000.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [2, 480, 108000], 'label': '162000.x.9000.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '9000.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9000.h1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
-
id: 62910580
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '9000.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.bv1.a1', '1800.by1.a1', '1800.bz1.a1', '1800.ca1.a1', '1800.cb1.a1', '3000.e1.a1', '4500.a1.a1'], 'contains': ['18000.d1.a1', '27000.h1.a1', '27000.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [119340, 7200, 54480], 'label': '162000.x.9000.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.e1.a1', 'old_label': '9000.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9000.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910581
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '9000.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.bw1.a1', '1800.cc1.a1', '1800.cd1.a1', '1800.ce1.a1', '1800.cf1.a1', '3000.e1.a1', '4500.b1.a1', '4500.k1.a1', '4500.l1.a1'], 'contains': ['18000.e1.a1', '27000.h1.a1', '27000.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [11340, 7200, 480], 'label': '162000.x.9000.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.f1.a1', 'old_label': '9000.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9000.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910582
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '9000.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.bx1.a1', '1800.cg1.a1', '1800.ch1.a1', '1800.ci1.a1', '3000.e1.a1', '4500.c1.a1', '4500.i1.a1', '4500.l1.a1'], 'contains': ['18000.e1.a1', '27000.i1.a1', '27000.j1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [119340, 480, 108000], 'label': '162000.x.9000.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '9000.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9000.k1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
-
id: 62910583
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10125.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['405.a1.a1', '1125.a1.a1', '2025.a1.a1', '3375.a1.a1', '3375.b1.a1'], 'contains': ['20250.a1.a1', '20250.b1.a1', '20250.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 10125, 'diagramx': None, 'generators': [115201, 125640], 'label': '162000.x.10125.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10125.a1.a1', 'old_label': '10125.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10125.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910584
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.a1.a1', '2160.b1.a1', '2160.c1.a1', '2160.d1.a1', '3600.a1.a1', '3600.l1.a1', '3600.m1.a1', '5400.a1.a1'], 'contains': ['32400.a1.a1', '54000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [61680, 32400], 'label': '162000.x.10800.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '10800.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910585
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.a1.a1', '2160.d1.a1', '2160.e1.a1', '2160.f1.a1', '2160.g1.a1', '3600.b1.a1', '3600.n1.a1', '3600.o1.a1', '5400.b1.a1'], 'contains': ['32400.b1.a1', '54000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [61680, 97344], 'label': '162000.x.10800.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '10800.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910586
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.b1.a1', '2160.e1.a1', '3600.c1.a1', '3600.j1.a1', '3600.k1.a1', '3600.p1.a1', '5400.c1.a1'], 'contains': ['32400.c1.a1', '54000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [61680, 134064], 'label': '162000.x.10800.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '10800.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910587
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '90.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '30.a1.a1', '45.a1.a1'], 'contains': ['180.c1.a1', '180.bh1.a1', '270.c1.a1', '450.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [64263, 97344, 10862, 54480, 119340, 32400, 108000], 'label': '162000.x.90.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '90.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62910588
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.b1.a1', '2160.c1.a1', '2160.f1.a1', '2160.g1.a1', '3600.d1.a1', '3600.p1.a1', '3600.q1.a1', '5400.d1.a1'], 'contains': ['32400.c1.a1', '54000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [61680, 136224], 'label': '162000.x.10800.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '10800.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910589
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.b1.a1', '2160.d1.a1', '2160.f1.a1', '2160.i1.a1', '3600.f1.a1', '3600.r1.a1', '3600.t1.a1', '5400.e1.a1'], 'contains': ['32400.d1.a1', '54000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [61680, 66960], 'label': '162000.x.10800.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '10800.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910590
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.c1.a1', '2160.d1.a1', '2160.e1.a1', '2160.g1.a1', '2160.h1.a1', '2160.i1.a1', '3600.e1.a1', '3600.s1.a1', '3600.t1.a1', '5400.f1.a1'], 'contains': ['32400.d1.a1', '54000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [61680, 32544], 'label': '162000.x.10800.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '10800.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910591
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.a1.a1', '2160.b1.a1', '2160.f1.a1', '2160.h1.a1', '3600.g1.a1', '3600.u1.a1', '3600.v1.a1', '5400.g1.a1'], 'contains': ['32400.e1.a1', '54000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [61680, 69264], 'label': '162000.x.10800.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '10800.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910592
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.a1.a1', '2160.b1.a1', '2160.g1.a1', '2160.i1.a1', '3600.h1.a1', '3600.u1.a1', '3600.x1.a1', '5400.h1.a1'], 'contains': ['32400.e1.a1', '54000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [61680, 67104], 'label': '162000.x.10800.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '10800.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910593
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.a1.a1', '2160.c1.a1', '2160.e1.a1', '2160.f1.a1', '2160.i1.a1', '3600.i1.a1', '3600.v1.a1', '3600.w1.a1', '3600.x1.a1', '5400.i1.a1'], 'contains': ['32400.e1.a1', '54000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [61680, 41184], 'label': '162000.x.10800.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '10800.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910594
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.j1.a1', '2160.l1.a1', '2160.n1.a1', '3600.l1.a1', '3600.y1.a1', '5400.j1.a1', '5400.bj1.a1', '5400.br1.a1', '5400.bu1.a1', '5400.ca1.a1'], 'contains': ['32400.a1.a1', '54000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [480, 144], 'label': '162000.x.10800.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '10800.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910595
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.k1.a1', '2160.m1.a1', '2160.n1.a1', '2160.o1.a1', '3600.m1.a1', '3600.y1.a1', '3600.z1.a1', '5400.k1.a1', '5400.bg1.a1', '5400.bk1.a1', '5400.bs1.a1', '5400.bv1.a1', '5400.bx1.a1', '5400.cb1.a1'], 'contains': ['32400.a1.a1', '54000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 32400], 'label': '162000.x.10800.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '10800.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910596
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.j1.a1', '2160.o1.a1', '2160.p1.a1', '3600.n1.a1', '3600.ba1.a1', '5400.l1.a1', '5400.bh1.a1', '5400.by1.a1'], 'contains': ['32400.b1.a1', '54000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 34560], 'label': '162000.x.10800.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '10800.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910597
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.k1.a1', '2160.n1.a1', '2160.p1.a1', '2160.q1.a1', '3600.o1.a1', '3600.ba1.a1', '3600.bb1.a1', '5400.m1.a1', '5400.bl1.a1', '5400.cc1.a1'], 'contains': ['32400.b1.a1', '54000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 97344], 'label': '162000.x.10800.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '10800.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910598
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.b1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '40.a1.a1', '200.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [10862, 58080, 99360, 108000, 97344, 32400, 29128, 61200], 'label': '162000.x.8.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '13500.e'}
-
id: 62910599
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '90.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '30.b1.a1', '45.a1.a1'], 'contains': ['180.c1.a1', '180.bk1.a1', '450.d1.a1', '810.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [1, 97344, 2, 108480, 119340, 32400, 108000], 'label': '162000.x.90.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62910600
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.l1.a1', '2160.m1.a1', '2160.p1.a1', '2160.q1.a1', '3600.p1.a1', '3600.q1.a1', '3600.bc1.a1', '5400.n1.a1'], 'contains': ['32400.c1.a1', '54000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 136224], 'label': '162000.x.10800.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '10800.n1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910601
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.l1.a1', '2160.o1.a1', '2160.q1.a1', '2160.r1.a1', '3600.r1.a1', '3600.s1.a1', '3600.bd1.a1', '5400.o1.a1', '5400.bi1.a1', '5400.bz1.a1'], 'contains': ['32400.d1.a1', '54000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 66960], 'label': '162000.x.10800.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '10800.o1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910602
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.m1.a1', '2160.n1.a1', '2160.p1.a1', '2160.r1.a1', '3600.t1.a1', '3600.bd1.a1', '3600.be1.a1', '5400.p1.a1', '5400.bm1.a1', '5400.cd1.a1'], 'contains': ['32400.d1.a1', '54000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 32544], 'label': '162000.x.10800.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '10800.p1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910603
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.k1.a1', '2160.l1.a1', '2160.p1.a1', '2160.r1.a1', '3600.u1.a1', '3600.w1.a1', '3600.bf1.a1', '5400.q1.a1'], 'contains': ['32400.e1.a1', '54000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [480, 73584], 'label': '162000.x.10800.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '10800.q1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910604
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.j1.a1', '2160.k1.a1', '2160.m1.a1', '2160.p1.a1', '2160.q1.a1', '2160.r1.a1', '3600.v1.a1', '3600.x1.a1', '3600.bf1.a1', '3600.bg1.a1', '5400.r1.a1'], 'contains': ['32400.e1.a1', '54000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [480, 41184], 'label': '162000.x.10800.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '10800.r1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910605
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.s1.a1', '2160.u1.a1', '2160.v1.a1', '2160.y1.a1', '3600.a1.a1', '3600.l1.a1', '3600.z1.a1', '5400.s1.a1', '5400.bt1.a1', '5400.bw1.a1'], 'contains': ['32400.a1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [4080, 32400], 'label': '162000.x.10800.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '10800.s1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910606
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.t1.a1', '2160.w1.a1', '2160.x1.a1', '2160.y1.a1', '3600.a1.a1', '3600.m1.a1', '3600.y1.a1', '5400.t1.a1', '5400.bn1.a1', '5400.ce1.a1'], 'contains': ['32400.a1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [4080, 144], 'label': '162000.x.10800.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '10800.t1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910607
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.s1.a1', '2160.x1.a1', '2160.bb1.a1', '2160.bc1.a1', '3600.b1.a1', '3600.n1.a1', '3600.bb1.a1', '5400.u1.a1', '5400.bo1.a1', '5400.cf1.a1'], 'contains': ['32400.b1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [4080, 2304], 'label': '162000.x.10800.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '10800.u1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 62910608
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.t1.a1', '2160.y1.a1', '2160.z1.a1', '2160.ba1.a1', '2160.bb1.a1', '2160.bc1.a1', '3600.b1.a1', '3600.o1.a1', '3600.ba1.a1', '5400.v1.a1'], 'contains': ['32400.b1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [4080, 97344], 'label': '162000.x.10800.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '10800.v1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910609
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.u1.a1', '2160.w1.a1', '2160.ba1.a1', '2160.bb1.a1', '3600.d1.a1', '3600.p1.a1', '3600.bc1.a1', '5400.w1.a1'], 'contains': ['32400.c1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [4080, 136224], 'label': '162000.x.10800.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '10800.w1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910610
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.c1.a1'], 'contains': ['180.e1.a1', '180.w1.a1', '180.bb1.a1', '270.d1.a1', '270.f1.a1', '450.a1.a1', '450.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [64263, 129744, 7200, 10862, 119340, 2160, 54480], 'label': '162000.x.90.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.d1.a1', 'old_label': '90.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.a1', 'subgroup_fusion': None, 'weyl_group': '600.163'}
-
id: 62910611
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.v1.a1', '2160.w1.a1', '2160.z1.a1', '2160.bc1.a1', '3600.c1.a1', '3600.d1.a1', '3600.q1.a1', '3600.bc1.a1', '5400.x1.a1'], 'contains': ['32400.c1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [4080, 36864], 'label': '162000.x.10800.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '10800.x1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910612
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.u1.a1', '2160.x1.a1', '2160.z1.a1', '2160.bd1.a1', '3600.e1.a1', '3600.r1.a1', '3600.be1.a1', '5400.y1.a1', '5400.bp1.a1', '5400.cg1.a1'], 'contains': ['32400.d1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [4080, 6624], 'label': '162000.x.10800.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '10800.y1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910613
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.v1.a1', '2160.x1.a1', '2160.ba1.a1', '2160.be1.a1', '3600.f1.a1', '3600.s1.a1', '3600.be1.a1', '5400.z1.a1', '5400.bq1.a1', '5400.ch1.a1'], 'contains': ['32400.d1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [4080, 4464], 'label': '162000.x.10800.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '10800.z1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
-
id: 62910614
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.w1.a1', '2160.y1.a1', '2160.bb1.a1', '2160.bc1.a1', '2160.bd1.a1', '2160.be1.a1', '3600.e1.a1', '3600.f1.a1', '3600.t1.a1', '3600.bd1.a1', '5400.ba1.a1'], 'contains': ['32400.d1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [4080, 66960], 'label': '162000.x.10800.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '10800.ba1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910615
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.t1.a1', '2160.v1.a1', '2160.bb1.a1', '2160.bd1.a1', '3600.g1.a1', '3600.h1.a1', '3600.w1.a1', '3600.bg1.a1', '5400.bb1.a1'], 'contains': ['32400.e1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [4080, 69264], 'label': '162000.x.10800.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '10800.bb1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910616
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.t1.a1', '2160.u1.a1', '2160.bc1.a1', '2160.be1.a1', '3600.i1.a1', '3600.u1.a1', '3600.bg1.a1', '5400.bc1.a1'], 'contains': ['32400.e1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [4080, 103824], 'label': '162000.x.10800.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '10800.bc1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910617
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.s1.a1', '2160.t1.a1', '2160.w1.a1', '2160.ba1.a1', '2160.bc1.a1', '2160.bd1.a1', '3600.g1.a1', '3600.i1.a1', '3600.x1.a1', '3600.bf1.a1', '5400.bd1.a1'], 'contains': ['32400.e1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [4080, 131904], 'label': '162000.x.10800.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '10800.bd1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910618
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.s1.a1', '2160.t1.a1', '2160.w1.a1', '2160.z1.a1', '2160.bb1.a1', '2160.be1.a1', '3600.h1.a1', '3600.i1.a1', '3600.v1.a1', '3600.bf1.a1', '5400.be1.a1'], 'contains': ['32400.e1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [4080, 41184], 'label': '162000.x.10800.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '10800.be1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.be1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910619
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '10800.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.d1.a1', '3600.j1.a1', '5400.bf1.a1'], 'contains': ['32400.c1.a1', '54000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [83128, 136224], 'label': '162000.x.10800.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.v1.a1', 'old_label': '10800.bf1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910620
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '13500.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6750.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2700.a1.a1', '2700.b1.a1', '2700.c1.a1', '2700.l1.a1', '4500.a1.a1', '4500.b1.a1', '6750.a1.a1', '6750.b1.a1', '6750.e1.a1'], 'contains': ['27000.b1.a1', '27000.e1.a1', '27000.h1.a1', '40500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3375, 'diagramx': None, 'generators': [242, 11100, 7200], 'label': '162000.x.13500.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3375.b1.a1', 'old_label': '13500.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13500.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910621
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '90.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.c1.a1'], 'contains': ['180.f1.a1', '180.x1.a1', '180.bc1.a1', '270.d1.a1', '270.g1.a1', '450.b1.a1', '450.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [64263, 32544, 7200, 10862, 119340, 2160, 54480], 'label': '162000.x.90.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.e1.a1', 'old_label': '90.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.e1.a1', 'subgroup_fusion': None, 'weyl_group': '600.164'}
-
id: 62910622
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '13500.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13500.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2700.d1.a1', '2700.e1.a1', '2700.f1.a1', '2700.g1.a1', '2700.m1.a1', '4500.b1.a1', '4500.c1.a1', '6750.e1.a1'], 'contains': ['27000.b1.a1', '27000.f1.a1', '27000.i1.a1', '40500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2250, 'diagramx': None, 'generators': [2, 11340, 480], 'label': '162000.x.13500.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2250.d1.a1', 'old_label': '13500.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13500.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910623
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '13500.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13500.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2700.h1.a1', '2700.i1.a1', '2700.j1.a1', '2700.k1.a1', '2700.n1.a1', '4500.a1.a1', '4500.c1.a1', '6750.c1.a1'], 'contains': ['27000.c1.a1', '27000.g1.a1', '27000.j1.a1', '40500.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2250, 'diagramx': None, 'generators': [10862, 119340, 54480], 'label': '162000.x.13500.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2250.a1.a1', 'old_label': '13500.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13500.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910624
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '13500.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4500.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2700.o1.a1', '2700.p1.a1', '2700.q1.a1', '2700.r1.a1', '2700.s1.a1', '2700.t1.a1', '2700.u1.a1', '4500.d1.a1', '4500.e1.a1', '4500.f1.a1'], 'contains': ['27000.a1.a1', '40500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4500, 'diagramx': None, 'generators': [10503, 112080, 10862], 'label': '162000.x.13500.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4500.f1.a1', 'old_label': '13500.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13500.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 62910625
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '13500.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2250.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2700.v1.a1', '2700.w1.a1', '2700.x1.a1', '2700.x2.a1', '2700.y1.a1', '4500.f1.a1', '4500.g1.a1', '6750.a1.a1'], 'contains': ['27000.b1.a1', '40500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2250, 'diagramx': None, 'generators': [10503, 7200, 10862], 'label': '162000.x.13500.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2250.a1.a1', 'old_label': '13500.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13500.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 62910626
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '13500.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4500.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2700.z1.a1', '2700.ba1.a1', '2700.bb1.a1', '2700.bc1.a1', '2700.bd1.a1', '4500.f1.a1', '4500.h1.a1', '6750.c1.a1'], 'contains': ['27000.c1.a1', '40500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2250, 'diagramx': None, 'generators': [10503, 108480, 10862], 'label': '162000.x.13500.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2250.a1.a1', 'old_label': '13500.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13500.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910627
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '13500.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4500.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2700.be1.a1', '2700.bf1.a1', '2700.bg1.a1', '2700.bh1.a1', '2700.bi1.a1', '4500.d1.a1', '4500.g1.a1', '4500.h1.a1', '6750.c1.a1'], 'contains': ['27000.c1.a1', '40500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 750, 'diagramx': None, 'generators': [10503, 10862, 54480], 'label': '162000.x.13500.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '750.a1.a1', 'old_label': '13500.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13500.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910630
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '13500.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2700.bm1.a1', '2700.bp1.a1', '2700.bq1.a1', '4500.i1.a1', '4500.k1.a1', '6750.e1.a1'], 'contains': ['27000.e1.a1', '27000.f1.a1', '27000.i1.a1', '40500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1350, 'diagramx': None, 'generators': [17642, 11340, 480], 'label': '162000.x.13500.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1350.i1.a1', 'old_label': '13500.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13500.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910631
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '13500.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8100.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2700.bo1.a1', '2700.br1.a1', '4500.k1.a1', '6750.e1.a1'], 'contains': ['27000.f1.a1', '27000.h1.a1', '40500.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [17882, 11100, 7200], 'label': '162000.x.13500.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '13500.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13500.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910632
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '90.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '30.e1.a1', '45.a1.a1'], 'contains': ['180.c1.a1', '180.k1.a1', '180.bm1.a1', '180.bn1.a1', '180.bt1.a1', '270.h1.a1', '450.f1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [21482, 144, 125640, 4080, 6660, 2160, 7200], 'label': '162000.x.90.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.f1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.cd'}
-
id: 62910633
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '13500.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.l1.a1', '500.b1.a1', '6750.d1.a1'], 'contains': ['40500.e1.a1', '54000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3375, 'diagramx': None, 'generators': [83128, 10860, 14040], 'label': '162000.x.13500.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3375.a1.a1', 'old_label': '13500.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13500.l1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 62910634
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '13500.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2700.bs1.a1', '2700.bt1.a1', '4500.l1.a1', '6750.e1.a1'], 'contains': ['27000.h1.a1', '27000.i1.a1', '40500.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3375, 'diagramx': None, 'generators': [119340, 125640, 480], 'label': '162000.x.13500.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3375.b1.a1', 'old_label': '13500.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13500.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 62910635
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16200.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.a1.a1', '3240.b1.a1', '3240.c1.a1', '5400.a1.a1', '5400.j1.a1', '5400.k1.a1', '5400.s1.a1', '5400.t1.a1', '8100.a1.a1', '8100.d1.a1', '8100.e1.a1'], 'contains': ['32400.a1.a1', '81000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': None, 'generators': [10862, 32400], 'label': '162000.x.16200.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '16200.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16200.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910636
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16200.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.a1.a1', '3240.c1.a1', '3240.d1.a1', '5400.b1.a1', '5400.l1.a1', '5400.m1.a1', '5400.u1.a1', '5400.v1.a1', '8100.b1.a1'], 'contains': ['32400.b1.a1', '81000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 97344], 'label': '162000.x.16200.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.a1', 'old_label': '16200.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16200.b1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910637
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16200.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.b1.a1', '3240.d1.a1', '5400.c1.a1', '5400.d1.a1', '5400.n1.a1', '5400.w1.a1', '5400.x1.a1', '5400.bf1.a1', '8100.f1.a1'], 'contains': ['32400.c1.a1', '81000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': None, 'generators': [10862, 136224], 'label': '162000.x.16200.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '16200.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16200.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910638
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16200.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.b1.a1', '3240.c1.a1', '3240.d1.a1', '3240.e1.a1', '5400.e1.a1', '5400.f1.a1', '5400.o1.a1', '5400.p1.a1', '5400.y1.a1', '5400.z1.a1', '5400.ba1.a1', '8100.c1.a1', '8100.g1.a1', '8100.g2.a1'], 'contains': ['32400.d1.a1', '81000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': None, 'generators': [10862, 66960], 'label': '162000.x.16200.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '16200.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16200.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910639
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16200.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.a1.a1', '3240.b1.a1', '3240.d1.a1', '3240.e1.a1', '5400.g1.a1', '5400.h1.a1', '5400.i1.a1', '5400.q1.a1', '5400.r1.a1', '5400.bb1.a1', '5400.bc1.a1', '5400.bd1.a1', '5400.be1.a1', '8100.h1.a1'], 'contains': ['32400.e1.a1', '81000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [10862, 41184], 'label': '162000.x.16200.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.i1.a1', 'old_label': '16200.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16200.e1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910640
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16200.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.f1.a1', '3240.i1.a1', '5400.bg1.a1', '5400.bj1.a1', '5400.bk1.a1', '5400.bn1.a1', '8100.a1.a1', '8100.k1.a1', '8100.m1.a1'], 'contains': ['32400.a1.a1', '81000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [2, 32400], 'label': '162000.x.16200.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.i1.a1', 'old_label': '16200.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16200.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910641
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16200.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.f1.a1', '3240.g1.a1', '5400.bh1.a1', '5400.bl1.a1', '5400.bo1.a1', '8100.b1.a1', '8100.i1.a1', '8100.j1.a1'], 'contains': ['32400.b1.a1', '81000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [2, 97344], 'label': '162000.x.16200.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.b1.a1', 'old_label': '16200.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16200.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910642
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16200.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.bg1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.f1.a1', '3240.h1.a1', '5400.bi1.a1', '5400.bm1.a1', '5400.bp1.a1', '5400.bq1.a1', '8100.c1.a1'], 'contains': ['32400.d1.a1', '81000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [2, 32544], 'label': '162000.x.16200.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '16200.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16200.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910643
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '90.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '30.c1.a1'], 'contains': ['180.m1.a1', '180.bg1.a1', '180.bg2.a1', '270.f1.a1', '270.g1.a1', '450.c1.a1', '450.g1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': None, 'generators': [64263, 32544, 10862, 54480, 119340, 2160, 108000], 'label': '162000.x.90.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '90.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.632'}
-
id: 62910644
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16200.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.g1.a1', '3240.h1.a1', '3240.i1.a1', '5400.br1.a1', '5400.bs1.a1', '5400.bt1.a1', '8100.d1.a1', '8100.l1.a1', '8100.m1.a1'], 'contains': ['32400.a1.a1', '81000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [2, 2160], 'label': '162000.x.16200.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '16200.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16200.i1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910645
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16200.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.j1.a1', '3240.k1.a1', '3240.l1.a1', '5400.bu1.a1', '5400.bv1.a1', '5400.bw1.a1', '8100.d1.a1', '8100.k1.a1', '8100.n1.a1'], 'contains': ['32400.a1.a1', '81000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [11100, 2160], 'label': '162000.x.16200.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '16200.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16200.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910646
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16200.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.l1.a1', '3240.m1.a1', '5400.bx1.a1', '5400.ca1.a1', '5400.cb1.a1', '5400.ce1.a1', '8100.a1.a1', '8100.m1.a1', '8100.n1.a1'], 'contains': ['32400.a1.a1', '81000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [11100, 32400], 'label': '162000.x.16200.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.h1.a1', 'old_label': '16200.k1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16200.k1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910647
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16200.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.j1.a1', '3240.m1.a1', '5400.by1.a1', '5400.cc1.a1', '5400.cf1.a1', '8100.b1.a1'], 'contains': ['32400.b1.a1', '81000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [11100, 97344], 'label': '162000.x.16200.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.e1.a1', 'old_label': '16200.l1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16200.l1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
-
id: 62910648
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '16200.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3240.k1.a1', '3240.m1.a1', '5400.bz1.a1', '5400.cd1.a1', '5400.cg1.a1', '5400.ch1.a1', '8100.c1.a1'], 'contains': ['32400.d1.a1', '81000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': None, 'generators': [11100, 32544], 'label': '162000.x.16200.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.d1.a1', 'old_label': '16200.m1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16200.m1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
-
id: 62910649
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '18000.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3600.a1.a1', '3600.b1.a1', '3600.c1.a1', '3600.d1.a1', '3600.e1.a1', '3600.f1.a1', '3600.g1.a1', '3600.h1.a1', '3600.i1.a1', '6000.a1.a1', '6000.b1.a1', '6000.c1.a1', '9000.a1.a1'], 'contains': ['54000.a1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [115680, 61200], 'label': '162000.x.18000.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6000.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '18000.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18000.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910650
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '18000.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.j1.a1', '3600.j1.a1', '6000.b1.a1', '9000.b1.a1'], 'contains': ['54000.a1.a1', '54000.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [25768, 58080], 'label': '162000.x.18000.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.e1.a1', 'old_label': '18000.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18000.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910651
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '18000.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.k1.a1', '3600.k1.a1', '6000.c1.a1', '9000.c1.a1'], 'contains': ['54000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': None, 'generators': [25288], 'label': '162000.x.18000.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.b1.a1', 'old_label': '18000.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18000.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 62910652
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '18000.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3600.l1.a1', '3600.m1.a1', '3600.n1.a1', '3600.o1.a1', '3600.p1.a1', '3600.q1.a1', '3600.r1.a1', '3600.s1.a1', '3600.t1.a1', '3600.u1.a1', '3600.v1.a1', '3600.w1.a1', '3600.x1.a1', '6000.a1.a1', '9000.d1.a1', '9000.f1.a1', '9000.i1.a1'], 'contains': ['54000.a1.a1', '54000.b1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [480, 61200], 'label': '162000.x.18000.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6000.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '18000.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18000.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910653
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '18000.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3600.y1.a1', '3600.z1.a1', '3600.ba1.a1', '3600.bb1.a1', '3600.bc1.a1', '3600.bd1.a1', '3600.be1.a1', '3600.bf1.a1', '3600.bg1.a1', '6000.a1.a1', '9000.e1.a1', '9000.g1.a1', '9000.h1.a1', '9000.j1.a1', '9000.k1.a1'], 'contains': ['54000.b1.a1', '54000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [480, 7200], 'label': '162000.x.18000.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6000.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18000.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18000.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 62910654
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '90.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '30.d1.a1'], 'contains': ['180.l1.a1', '180.bo1.a1', '180.bp1.a1', '450.d1.a1', '450.h1.a1', '810.d1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [1, 97344, 2, 108480, 119340, 2160, 108000], 'label': '162000.x.90.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.h1.a1', 'old_label': '90.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.646'}
-
id: 62910655
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '20250.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6750.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4050.a1.a1', '4050.c1.a1', '6750.a1.a1', '6750.c1.a1', '10125.a1.a1'], 'contains': ['40500.a1.a1', '40500.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3375, 'diagramx': None, 'generators': [64263, 11100], 'label': '162000.x.20250.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3375.b1.a1', 'old_label': '20250.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20250.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910656
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '20250.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20250.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2250.c1.a1', '4050.b1.a1', '4050.d1.a1', '6750.b1.a1', '10125.a1.a1'], 'contains': ['40500.a1.a1', '40500.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 10125, 'diagramx': None, 'generators': [1, 10860], 'label': '162000.x.20250.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10125.a1.a1', 'old_label': '20250.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20250.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910657
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '20250.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20250.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4050.e1.a1', '6750.d1.a1', '6750.e1.a1', '10125.a1.a1'], 'contains': ['40500.a1.a1', '40500.d1.a1', '40500.e1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3375, 'diagramx': None, 'generators': [108242, 119100, 125640], 'label': '162000.x.20250.c1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3375.a1.a1', 'old_label': '20250.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20250.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910658
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '27000.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5400.a1.a1', '5400.b1.a1', '5400.c1.a1', '5400.d1.a1', '5400.e1.a1', '5400.f1.a1', '5400.g1.a1', '5400.h1.a1', '5400.i1.a1', '9000.a1.a1', '9000.b1.a1', '9000.c1.a1', '9000.d1.a1', '13500.d1.a1'], 'contains': ['54000.a1.a1', '81000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 500, 'diagramx': None, 'generators': [10862, 61680], 'label': '162000.x.27000.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '500.a1.a1', 'old_label': '27000.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27000.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 62910659
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '27000.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '750.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5400.j1.a1', '5400.k1.a1', '5400.l1.a1', '5400.m1.a1', '5400.n1.a1', '5400.o1.a1', '5400.p1.a1', '5400.q1.a1', '5400.r1.a1', '9000.d1.a1', '9000.e1.a1', '13500.a1.a1', '13500.b1.a1', '13500.e1.a1'], 'contains': ['54000.b1.a1', '81000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': None, 'generators': [10862, 480], 'label': '162000.x.27000.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '27000.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27000.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910660
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '27000.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5400.s1.a1', '5400.t1.a1', '5400.u1.a1', '5400.v1.a1', '5400.w1.a1', '5400.x1.a1', '5400.y1.a1', '5400.z1.a1', '5400.ba1.a1', '5400.bb1.a1', '5400.bc1.a1', '5400.bd1.a1', '5400.be1.a1', '9000.a1.a1', '9000.d1.a1', '9000.e1.a1', '13500.c1.a1', '13500.f1.a1', '13500.g1.a1'], 'contains': ['54000.c1.a1', '81000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 750, 'diagramx': None, 'generators': [10862, 4080], 'label': '162000.x.27000.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '750.a1.a1', 'old_label': '27000.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27000.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910661
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '27000.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.bf1.a1', '5400.bf1.a1', '6750.d1.a1', '9000.b1.a1', '13500.h1.a1'], 'contains': ['54000.d1.a1', '81000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4500, 'diagramx': None, 'generators': [10862, 83128], 'label': '162000.x.27000.d1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4500.e1.a1', 'old_label': '27000.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27000.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910662
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '27000.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '270.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5400.bg1.a1', '5400.bh1.a1', '5400.bi1.a1', '5400.br1.a1', '9000.f1.a1', '9000.g1.a1', '13500.a1.a1', '13500.i1.a1', '13500.j1.a1'], 'contains': ['54000.b1.a1', '81000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 135, 'diagramx': None, 'generators': [2, 7200], 'label': '162000.x.27000.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1.a1', 'old_label': '27000.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27000.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910663
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '27000.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5400.bj1.a1', '5400.bk1.a1', '5400.bl1.a1', '5400.bm1.a1', '5400.bs1.a1', '9000.g1.a1', '9000.h1.a1', '13500.b1.a1', '13500.j1.a1', '13500.k1.a1'], 'contains': ['54000.b1.a1', '81000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [2, 480], 'label': '162000.x.27000.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '27000.f1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27000.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910664
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '27000.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5400.bn1.a1', '5400.bo1.a1', '5400.bp1.a1', '5400.bq1.a1', '5400.bt1.a1', '9000.f1.a1', '9000.h1.a1', '13500.c1.a1'], 'contains': ['54000.c1.a1', '81000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [54482, 54480], 'label': '162000.x.27000.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '27000.g1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27000.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910665
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '90.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '30.e1.a1'], 'contains': ['180.b1.a1', '180.j1.a1', '180.n1.a1', '180.bl1.a1', '180.bq1.a1', '180.br1.a1', '180.bs1.a1', '270.h1.a1', '270.i1.a1', '450.f1.a1', '450.i1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [21482, 144, 125640, 4080, 6660, 32400, 7200], 'label': '162000.x.90.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.i1.a1', 'old_label': '90.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1800.679'}
-
id: 62910666
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '27000.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5400.bu1.a1', '5400.bx1.a1', '5400.by1.a1', '5400.bz1.a1', '9000.i1.a1', '9000.j1.a1', '13500.a1.a1', '13500.k1.a1', '13500.m1.a1'], 'contains': ['54000.b1.a1', '81000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [11100, 7200], 'label': '162000.x.27000.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '27000.h1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27000.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910667
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '27000.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5400.bv1.a1', '5400.ca1.a1', '5400.cb1.a1', '5400.cc1.a1', '5400.cd1.a1', '9000.j1.a1', '9000.k1.a1', '13500.b1.a1', '13500.j1.a1', '13500.m1.a1'], 'contains': ['54000.b1.a1', '81000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [11340, 480], 'label': '162000.x.27000.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.f1.a1', 'old_label': '27000.i1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27000.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910668
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '27000.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5400.bw1.a1', '5400.ce1.a1', '5400.cf1.a1', '5400.cg1.a1', '5400.ch1.a1', '9000.i1.a1', '9000.k1.a1', '13500.c1.a1'], 'contains': ['54000.c1.a1', '81000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': None, 'generators': [119340, 54480], 'label': '162000.x.27000.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.e1.a1', 'old_label': '27000.j1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27000.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910669
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '32400.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6480.a1.a1', '6480.b1.a1', '6480.c1.a1', '10800.a1.a1', '10800.j1.a1', '10800.k1.a1', '10800.s1.a1', '10800.t1.a1', '16200.a1.a1', '16200.f1.a1', '16200.i1.a1', '16200.j1.a1', '16200.k1.a1'], 'contains': ['162000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [32400], 'label': '162000.x.32400.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '32400.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32400.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910670
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '32400.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6480.a1.a1', '6480.c1.a1', '6480.d1.a1', '10800.b1.a1', '10800.l1.a1', '10800.m1.a1', '10800.u1.a1', '10800.v1.a1', '16200.b1.a1', '16200.g1.a1', '16200.l1.a1'], 'contains': ['162000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [97344], 'label': '162000.x.32400.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '32400.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32400.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910671
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '32400.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6480.b1.a1', '6480.d1.a1', '10800.c1.a1', '10800.d1.a1', '10800.n1.a1', '10800.w1.a1', '10800.x1.a1', '10800.bf1.a1', '16200.c1.a1'], 'contains': ['162000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [136224], 'label': '162000.x.32400.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32400.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32400.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910672
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '32400.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6480.b1.a1', '6480.c1.a1', '6480.d1.a1', '6480.e1.a1', '10800.e1.a1', '10800.f1.a1', '10800.o1.a1', '10800.p1.a1', '10800.y1.a1', '10800.z1.a1', '10800.ba1.a1', '16200.d1.a1', '16200.h1.a1', '16200.m1.a1'], 'contains': ['162000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [66960], 'label': '162000.x.32400.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '32400.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32400.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910673
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '32400.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6480.a1.a1', '6480.b1.a1', '6480.d1.a1', '6480.e1.a1', '10800.g1.a1', '10800.h1.a1', '10800.i1.a1', '10800.q1.a1', '10800.r1.a1', '10800.bb1.a1', '10800.bc1.a1', '10800.bd1.a1', '10800.be1.a1', '16200.e1.a1'], 'contains': ['162000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [41184], 'label': '162000.x.32400.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '32400.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32400.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
-
id: 62910674
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '40500.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3375.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8100.a1.a1', '8100.b1.a1', '8100.c1.a1', '8100.d1.a1', '13500.a1.a1', '13500.b1.a1', '13500.c1.a1', '20250.a1.a1', '20250.b1.a1', '20250.c1.a1'], 'contains': ['81000.a1.a1', '81000.b1.a1', '81000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3375, 'diagramx': None, 'generators': [242, 11100], 'label': '162000.x.40500.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3375.b1.a1', 'old_label': '40500.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40500.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 62910675
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '40500.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2250.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8100.e1.a1', '8100.f1.a1', '8100.g1.a1', '8100.g2.a1', '8100.h1.a1', '13500.d1.a1', '13500.e1.a1', '13500.f1.a1', '13500.g1.a1', '13500.h1.a1', '20250.a1.a1'], 'contains': ['81000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2250, 'diagramx': None, 'generators': [10503], 'label': '162000.x.40500.b1.a1', 'mobius_quo': None, 'mobius_sub': 18, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2250.a1.a1', 'old_label': '40500.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40500.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 62910676
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '100.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['200.a1.a1', '300.e1.a1', '300.g1.a1', '500.a1.a1'], 'core': '6000.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': None, 'generators': [75483, 136224, 10862, 25768, 108000, 58080, 61200], 'label': '162000.x.100.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '100.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.a1.a1', 'subgroup_fusion': None, 'weyl_group': '540.37'}
-
id: 62910677
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '40500.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4050.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4500.j1.a1', '8100.i1.a1', '8100.j1.a1', '8100.l1.a1', '13500.i1.a1', '20250.b1.a1'], 'contains': ['81000.b1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4050, 'diagramx': None, 'generators': [1], 'label': '162000.x.40500.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4050.b1.a1', 'old_label': '40500.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40500.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 62910678
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '40500.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4050.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8100.k1.a1', '8100.m1.a1', '13500.j1.a1', '13500.k1.a1', '20250.c1.a1'], 'contains': ['81000.b1.a1', '81000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 2025, 'diagramx': None, 'generators': [17882, 11100], 'label': '162000.x.40500.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2025.a1.a1', 'old_label': '40500.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40500.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910679
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '40500.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20250.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8100.n1.a1', '13500.l1.a1', '13500.m1.a1', '20250.c1.a1'], 'contains': ['81000.c1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3375, 'diagramx': None, 'generators': [119100, 125640], 'label': '162000.x.40500.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3375.a1.a1', 'old_label': '40500.e1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40500.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 62910680
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '54000.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10800.a1.a1', '10800.b1.a1', '10800.c1.a1', '10800.d1.a1', '10800.e1.a1', '10800.f1.a1', '10800.g1.a1', '10800.h1.a1', '10800.i1.a1', '18000.a1.a1', '18000.b1.a1', '18000.c1.a1', '18000.d1.a1', '27000.a1.a1'], 'contains': ['162000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [61680], 'label': '162000.x.54000.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6000.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '54000.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54000.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 62910681
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '54000.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10800.j1.a1', '10800.k1.a1', '10800.l1.a1', '10800.m1.a1', '10800.n1.a1', '10800.o1.a1', '10800.p1.a1', '10800.q1.a1', '10800.r1.a1', '18000.d1.a1', '18000.e1.a1', '27000.b1.a1', '27000.e1.a1', '27000.f1.a1', '27000.h1.a1', '27000.i1.a1'], 'contains': ['162000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [480], 'label': '162000.x.54000.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6000.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '54000.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54000.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910682
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '54000.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10800.s1.a1', '10800.t1.a1', '10800.u1.a1', '10800.v1.a1', '10800.w1.a1', '10800.x1.a1', '10800.y1.a1', '10800.z1.a1', '10800.ba1.a1', '10800.bb1.a1', '10800.bc1.a1', '10800.bd1.a1', '10800.be1.a1', '18000.a1.a1', '18000.d1.a1', '18000.e1.a1', '27000.c1.a1', '27000.g1.a1', '27000.j1.a1'], 'contains': ['162000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [4080], 'label': '162000.x.54000.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6000.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '54000.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54000.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910683
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '54000.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.bf1.a1', '10800.bf1.a1', '13500.l1.a1', '18000.b1.a1', '27000.d1.a1'], 'contains': ['162000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': None, 'generators': [83128], 'label': '162000.x.54000.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.v1.a1', 'old_label': '54000.d1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54000.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 62910684
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '81000.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '125.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16200.a1.a1', '16200.b1.a1', '16200.c1.a1', '16200.d1.a1', '16200.e1.a1', '27000.a1.a1', '27000.b1.a1', '27000.c1.a1', '27000.d1.a1', '40500.a1.a1', '40500.b1.a1'], 'contains': ['162000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': None, 'generators': [10862], 'label': '162000.x.81000.a1.a1', 'mobius_quo': None, 'mobius_sub': -324, 'normal_closure': '648.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '81000.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81000.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 62910685
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '81000.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '135.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16200.f1.a1', '16200.g1.a1', '16200.h1.a1', '16200.i1.a1', '27000.e1.a1', '27000.f1.a1', '27000.g1.a1', '40500.a1.a1', '40500.c1.a1', '40500.d1.a1'], 'contains': ['162000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 135, 'diagramx': None, 'generators': [2], 'label': '162000.x.81000.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '135.a1.a1', 'old_label': '81000.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81000.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 62910686
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '81000.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16200.j1.a1', '16200.k1.a1', '16200.l1.a1', '16200.m1.a1', '27000.h1.a1', '27000.i1.a1', '27000.j1.a1', '40500.a1.a1', '40500.d1.a1', '40500.e1.a1'], 'contains': ['162000.a1.a1'], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': None, 'generators': [11100], 'label': '162000.x.81000.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '81000.c1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81000.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 62910687
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '54.a1.a1', '54.b1.a1', '54.e1.a1'], 'contains': ['216.b1.a1', '216.e1.a1', '216.h1.a1', '324.a1.a1', '540.a1.a1', '540.d1.a1', '540.e1.a1', '540.f1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [242, 32400, 7200, 97344, 11100, 2160], 'label': '162000.x.108.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '108.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2000.905'}
-
id: 62910688
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '162000.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32400.a1.a1', '32400.b1.a1', '32400.c1.a1', '32400.d1.a1', '32400.e1.a1', '54000.a1.a1', '54000.b1.a1', '54000.c1.a1', '54000.d1.a1', '81000.a1.a1', '81000.b1.a1', '81000.c1.a1'], 'contains': [], 'core': '162000.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '162000.x.162000.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '162000.a1.a1', 'normal_contained_in': ['1296.a1.a1', '6000.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '162000.a1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162000.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 62910689
{'ambient': '162000.x', 'aut_centralizer_order': None, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.c1.a1', '54.e1.a1'], 'contains': ['216.b1.a1', '216.f1.a1', '216.i1.a1', '324.a1.a1', '540.b1.a1', '540.g1.a1', '540.h1.a1', '540.i1.a1', '540.j1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2, 32400, 480, 97344, 11340, 2160], 'label': '162000.x.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.b1.a1', 'projective_image': '162000.x', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}